Chapter 5: Geometrical Optics

Source: Eugene Hecht, Optics, fifth Global Edition, Chapter 5. Prompts are paraphrased by topic rather than reproduced. An asterisk in the heading preserves the book’s marker for a problem omitted from its selected solutions; the derivation below is supplied independently.

End-of-chapter problems

Problem 5.1 — spherical-surface imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the paraxial surface equation \(n_o/s_o+n_i/s_i=(n_i-n_o)/R\) and preserve the book’s sign convention. The book’s selected-answer check begins All OPLs from S to P must be equal; therefore /on1 + /in2 = son1 + sin2 = constant; drop a perpendicular from A to the optical axis, the point where it touches is B. BP = so + si x and the rest follows from the Pythagorean Theorem.. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.2 — spherical-surface imaging: design

Translate every stated requirement into an equation, solve the simultaneous constraints, and reject roots that violate the geometry. Apply the paraxial surface equation \(n_o/s_o+n_i/s_i=(n_i-n_o)/R\) and preserve the book’s sign convention. The book’s selected-answer check begins Using /on1 + /in2 = constant, /o + /i3/2 = constant, 5 + (6) 3/2 = 14. Therefore 2/o + 3/i = 28 when /o = 6, /i = 5.3, /o = 7, /i = 4.66. Note that the arcs centered on S and P have to intercept for physically meaningful values of /o and /i. 4.86 From Eq. (4.73) we see that the exponential will be in the form k(x vt). Substitute the result back into the governing relation to verify its units and sign.

Problem 5.3* — spherical-surface imaging: derivation

Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular. Apply the paraxial surface equation \(n_o/s_o+n_i/s_i=(n_i-n_o)/R\) and preserve the book’s sign convention. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.4 — spherical-surface imaging: design

Translate every stated requirement into an equation, solve the simultaneous constraints, and reject roots that violate the geometry. Apply the paraxial surface equation \(n_o/s_o+n_i/s_i=(n_i-n_o)/R\) and preserve the book’s sign convention. The book’s selected-answer check begins From Fig. 5.4 a plane wave impinging on a concave elliptical surface becomes spherical. If the second spherical surface has that same curvature, the wave will have all rays normal to it and emerge unaltered. Z03_HECH6933_05_GE_SOL.indd 690 08/09/16 9:14 pm Solutions to Selected Problems 691. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.5* — spherical-surface imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the paraxial surface equation \(n_o/s_o+n_i/s_i=(n_i-n_o)/R\) and preserve the book’s sign convention. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.6* — spherical-surface imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the paraxial surface equation \(n_o/s_o+n_i/s_i=(n_i-n_o)/R\) and preserve the book’s sign convention. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.7* — spherical-surface imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the paraxial surface equation \(n_o/s_o+n_i/s_i=(n_i-n_o)/R\) and preserve the book’s sign convention. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.8 — spherical-surface imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the paraxial surface equation \(n_o/s_o+n_i/s_i=(n_i-n_o)/R\) and preserve the book’s sign convention. The book’s selected-answer check begins Using Eq. (5.8) n1 so + n2 si = n2 n1 R . For the first surface 1 1.5 + 1.33 si = 1.33 - 1 0.15 , si ≈ 0.869 m producing a real image to the right of the first vertex. For the second surface so = 0.30 - 0.869 = -0.569 m indicating a virtual object (the rays from the first ­ surface have not yet coalesced). The formula. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.9* — spherical-surface imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the paraxial surface equation \(n_o/s_o+n_i/s_i=(n_i-n_o)/R\) and preserve the book’s sign convention. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.10* — spherical-surface imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the paraxial surface equation \(n_o/s_o+n_i/s_i=(n_i-n_o)/R\) and preserve the book’s sign convention. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.11* — spherical-surface imaging: derivation

Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular. Apply the paraxial surface equation \(n_o/s_o+n_i/s_i=(n_i-n_o)/R\) and preserve the book’s sign convention. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.12* — spherical-surface imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the paraxial surface equation \(n_o/s_o+n_i/s_i=(n_i-n_o)/R\) and preserve the book’s sign convention. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.13 — spherical-surface imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the paraxial surface equation \(n_o/s_o+n_i/s_i=(n_i-n_o)/R\) and preserve the book’s sign convention. The book’s selected-answer check begins For the first surface, 1/0.1 + 1.5/si = (1.5 - 1)/0.1. Thus si = -0.3 m For the second surface, so = 0.35 m. The equation is 1.5/0.35 + 1/si = (1.5 - 1)/-0.5. Thus si = -0.304 m. The image is virtual, erect, and magnified. Magnification MT = -si/so = -(-0.304/0.1) = 3.04. The image would be just over 6 cm tall. The thi. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.14* — spherical-surface imaging: construction

Evaluate the boundary and representative interior values, then draw the requested curve or ray construction to scale. Apply the paraxial surface equation \(n_o/s_o+n_i/s_i=(n_i-n_o)/R\) and preserve the book’s sign convention. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.15 — spherical-surface imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the paraxial surface equation \(n_o/s_o+n_i/s_i=(n_i-n_o)/R\) and preserve the book’s sign convention. The book’s selected-answer check begins We need to minimize so + si. From the Gaussian lens formula, si = sof so f . d dso (so + sof so f) = 1 + f(so f ) sof (so f )2 = 1 - ( f so f)2 . Setting this to zero we find that the minimum occurs for so = 2f, which also gives us si = 2f. Thus the minimum distance is 4f = -80 cm.. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.16 — spherical-surface imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the paraxial surface equation \(n_o/s_o+n_i/s_i=(n_i-n_o)/R\) and preserve the book’s sign convention. The book’s selected-answer check begins (5.17) 1/so + 1/si = 1/ƒ from this Si = sof/so - ƒ. (5.23) xi xo = f 2 from this xi = f 2 / xo. (5.25) MT = -si/so from this MT = f/f so. (5.24) MT = yi/yo from this yi = MT yo (a)  so = 0.1 m; xo = -0.1 m so Si = sof/so - ƒ = 0.1(0.2)/0.1 - 0.2 = -0.2 m; xi = (0.2)2 /-0.1 = -0.4 m; MT = f/f so = 0.2/ 0.2 - 0.1 = 2. y. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.17 — spherical-surface imaging: construction

Evaluate the boundary and representative interior values, then draw the requested curve or ray construction to scale. Apply the paraxial surface equation \(n_o/s_o+n_i/s_i=(n_i-n_o)/R\) and preserve the book’s sign convention. The book’s selected-answer check begins 1/so + 1/si = 1/ƒ C R 1 so 1 si f 2f 2f + 1 f = 0 f 3f so si. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.18* — spherical-surface imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the paraxial surface equation \(n_o/s_o+n_i/s_i=(n_i-n_o)/R\) and preserve the book’s sign convention. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.19* — spherical-surface imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the paraxial surface equation \(n_o/s_o+n_i/s_i=(n_i-n_o)/R\) and preserve the book’s sign convention. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.20 — spherical-surface imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the paraxial surface equation \(n_o/s_o+n_i/s_i=(n_i-n_o)/R\) and preserve the book’s sign convention. The book’s selected-answer check begins Since the lens is negative, the image will be virtual. It is present on the same side as the object. Image distance, si = -0.20 m. By the lens formula, 1/0.6 + 1/(-0.2) = 1/f, f = -0.3 m.. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.21* — spherical-surface imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the paraxial surface equation \(n_o/s_o+n_i/s_i=(n_i-n_o)/R\) and preserve the book’s sign convention. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.22* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.23 — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. The book’s selected-answer check begins For this lens, R1 = 0.25 m and R1 = ∞. By the thin lens formula, 1/f = (1.6 - 1)(1/0.25 - 1/∞), f ≈ 41.7 cm. Optical power, 𝒟 = 1/f = 2.4 D. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.24* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.25* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.26* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.27* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.28* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.29* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.30* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.31 — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. The book’s selected-answer check begins (a) From the Gaussian lens equation 1 15.0 m + 1 si = 1 3.00 m and si = +3.75 m. (b) Computing the magnification, we obtain MT = si so = - 3.75 m 15.0 m = -0.25  Because the image distance is positive, the image is real. Because the magnification is negative, the image is inverted, and because the absolute value of th. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.32* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.33* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.34* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.35* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.36* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.37* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.38 — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. The book’s selected-answer check begins Relative refractive index for glass in water, ngw = ng/nw = 1.2. As the geometry of the lens is the same, we divide the two thin-lens equation and we get (1/fair)/(1/fwater) = (ng - 1)/(ngw - 1). Thus, fwater = (ng - 1)/(ngw - 1)fair = 60 cm. For the image of the fish located at si, 1/0.8 + 1/si = 1/0.6; si = 2.4 m. Ma. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.39 — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. The book’s selected-answer check begins The image will be inverted if it’s to be real, so the set must be upside down or else something more will be needed to flip the image; MT = -3 = -si/so; 1/so + 1/3so = 1/0.60 m; so = 0.80 m, hence 0.80 m + 3(0.80 m) = 3.2 m. Z03_HECH6933_05_GE_SOL.indd 691 08/09/16 9:14 pm 692 Solutions to Selected Problems obtained fr. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.40 — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. The book’s selected-answer check begins 1 ƒ = (nlm - 1)a 1 R1 - 1 R2 b 1 ƒw = (nlm - 1) (nl - 1) 1 ƒa = 1.5/1.33 - 1 1.5 - 1 1 ƒa = 0.125 0.5 1 ƒa ƒw = 4ƒa. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.41* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.42* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.43* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.44 — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. The book’s selected-answer check begins 1/ƒ = 1/ƒ1 + 1/ƒ2, 1/50 = 1/ƒ1 - 1/50, ƒ1 = 25 cm. If R11 and R12, and R21 and R22, are the radii of the first and second lenses, respectively, 1/ƒ1 = (nl - 1)(1/R11 - 1/R12), 1/25 = 0.5(2/R11) R11 = -R12 = -R21 = 25 cm 1/ƒ2 = (nl - 1)(1/R21 - 1/R22) -1/50 = 0.55[1/(-25) - 1/R22] R22 = -275 cm. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.45 — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. The book’s selected-answer check begins MT1 = -si1/so1 = -ƒ1/(so1 - ƒ1) MT2 = -si2/so2 = -si2/(d si1) MT = ƒ1si2/(so1 - ƒ1)(d si1) From Eq. (5.30), on substituting for si1, we have MT = ƒ1si2 (so1 - ƒ1)d so1ƒ1. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.46* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.47 — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. The book’s selected-answer check begins First lens: 1/si1 = 1/30 - 1/30 = 0, si1 = ∞. Second lens: 1/si2 = 1/(-20) - 1/(- ∞); the object for the second lens is to the right at ∞, that is, so2 = - ∞. si2 = -20 cm, virtual, 10 cm to the left of first lens. MT = (- ∞ /30)(+20/- ∞) = 2 3 or from Eq. (5.34) MT = 30(-20) 10(30 - 30) - 30(30) = 2 3. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.48* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.49* — mirror and thin-lens imaging: construction

Evaluate the boundary and representative interior values, then draw the requested curve or ray construction to scale. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.50* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.51 — mirror and thin-lens imaging: construction

Evaluate the boundary and representative interior values, then draw the requested curve or ray construction to scale. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. The book’s selected-answer check begins fo fe. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.52* — mirror and thin-lens imaging: derivation

Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.53* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.54* — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.55 — mirror and thin-lens imaging: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(1/s_o+1/s_i=1/f\) and \(m=-s_i/s_o\); trace a principal ray to check the sign and image type. The book’s selected-answer check begins The angle subtended by L1 at S is tan-1 3/12 = 14°. To find the image of the diaphragm in L1 we use Eq. (5.23): xoxi = ƒ2 , (-6)(xi) = 81, xi = -13.5 cm, so that the image is 4.5 cm behind L1. The magnification is -xi/ƒ = 13.5/9 = 1.5, and thus the image (of the edge) of the hole is (0.5)(1.5) = 0.75 cm in radius. Henc. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.56* — stops, pupils, and compound systems: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.57 — stops, pupils, and compound systems: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. The book’s selected-answer check begins Either the margin of L1 or L2 will be the A.S.; thus, since no lenses are to the left of L1, either its periphery or P1 corresponds to the entrance pupil. Beyond (to the left of) point-A, L1 subtends the smallest angle and is the entrance pupil; nearer in (to the right of A), P1 marks the edge of the entrance pupil. In. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.58 — stops, pupils, and compound systems: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. The book’s selected-answer check begins The A.S. is either the edge of L1 or L2. Thus the entrance pupil is either marked by P1 or P2. Beyond Fo1, P1 subtends the smaller angle; thus Σ1 locates the A.S. The image of the A.S. in the lenses to its right, L2, locates P3 as the exit pupil. P1 P3 P2 O L1 L2 Σ1 Σ3 Σ2 Fo1 Fi2 Z03_HECH6933_05_GE_SOL.indd 692 08/09/1. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.59* — stops, pupils, and compound systems: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.60 — stops, pupils, and compound systems: derivation

Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. The book’s selected-answer check begins Draw the chief ray from the tip to L1 such that when extended it passes through the center of the entrance pupil. From there it goes through the center of the A.S., and then it bends at L2 so as to extend through the center of the exit pupil. A marginal ray from S extends to the edge of the entrance pupil, bends at L1. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.61 — stops, pupils, and compound systems: construction

Evaluate the boundary and representative interior values, then draw the requested curve or ray construction to scale. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. The book’s selected-answer check begins S. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.62 — stops, pupils, and compound systems: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. The book’s selected-answer check begins No—although she might be looking at you.. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.63 — stops, pupils, and compound systems: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. The book’s selected-answer check begins The mirror is parallel to the plane of the painting, and so the girl’s image should be directly behind her and not off to the right.. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.64 — stops, pupils, and compound systems: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. The book’s selected-answer check begins 1/so + 1/si = -2/R. Let R S ∞: 1/so + 1/si = 0, so = -si, and MT = +1. Image is virtual, same size, and erect.. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.65* — stops, pupils, and compound systems: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.66* — stops, pupils, and compound systems: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.67* — stops, pupils, and compound systems: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.68* — stops, pupils, and compound systems: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.69* — stops, pupils, and compound systems: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.70* — stops, pupils, and compound systems: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.71 — stops, pupils, and compound systems: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. The book’s selected-answer check begins From Eq. (5.49), 1/100 + 1/si = -2/80, and so si = -28.5 cm. Virtual (si 6 0), erect (MT 7 0), and minified. (Check with Table 5.5.). Substitute the result back into the governing relation to verify its units and sign.

Problem 5.72* — stops, pupils, and compound systems: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.73* — stops, pupils, and compound systems: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.74 — stops, pupils, and compound systems: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. The book’s selected-answer check begins Image on screen must be real 6 si is + 1 25 + 1 100 = - 2 R , 5 100 = - 2 R , R = -40 cm. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.75 — stops, pupils, and compound systems: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. The book’s selected-answer check begins The image is erect and minified. That implies (Table 5.5) a convex spherical mirror.. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.76* — stops, pupils, and compound systems: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.77* — stops, pupils, and compound systems: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.78* — stops, pupils, and compound systems: design

Translate every stated requirement into an equation, solve the simultaneous constraints, and reject roots that violate the geometry. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.79* — stops, pupils, and compound systems: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.80 — stops, pupils, and compound systems: design

Translate every stated requirement into an equation, solve the simultaneous constraints, and reject roots that violate the geometry. Propagate the ray through each element or multiply its ABCD matrix; the aperture stop is the element limiting the axial cone. The book’s selected-answer check begins To be magnified and erect, the mirror must be concave, and the image virtual; MT = 2.0 = si/(0.015 m), si = -0.03 m, and hence 1/ƒ = 1/(0.015 m) + 1/(-0.03 m); ƒ = 0.03 m and ƒ = -R/2; R = -0.06 m.. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.81 — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. The book’s selected-answer check begins MT = yi/yo = -si/so; using Eq. (5.50), si = ƒso/(so - ƒ), and since ƒ = -R/2, MT = -ƒ/(so - ƒ) = -(-R/2)/(so + R/2) = R/(2so + R).. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.82* — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.83* — visual and optical instruments: derivation

Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.84 — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. The book’s selected-answer check begins MT = -si/25 cm = -0.064; si = 1.6 cm. 1/25 cm + 1/1.6 cm = -2/R, R = -3.0 cm.. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.85* — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.86* — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.87* — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.88* — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.89 — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. The book’s selected-answer check begins f = R/2 = 60/2 = 30 cm, 1/50 + 1/si = 1/30, 1/si = 1/30 - 1/50, si = 75 cm. MT = -75/50 = -1.5. The image is real, inverted (MT 6 0), located 75 cm from the mirror and 7.5 cm tall.. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.90* — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.91* — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.92 — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. The book’s selected-answer check begins Image rotated through 180°.. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.93 — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. The book’s selected-answer check begins From Eq. (5.61) NA = (2.624 - 2.310)1/2 = 0.550 umax = sin-1 0.550 = 33°22′ Maximum acceptance angle is 2umax = 66°44′. A ray at 45° would quickly leak out of the fiber; in other words, very little energy fails to escape, even at the first reflection.. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.94* — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.95 — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. The book’s selected-answer check begins Considering Eq. (5.62), log 0.5 = -0.30 = -aL/10, and so L = 15 km.. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.96* — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.97* — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.98 — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. The book’s selected-answer check begins From Eq. (5.61) NA ≈ 0.180 and Nm = 158. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.99* — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.100* — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.101 — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. The book’s selected-answer check begins MT = -ƒ/xo = -1/xo𝒟. For the human eye 𝒟 ≈ 58.6 diopters. xo = 230000 × 1.61 = 371 × 103 km MT = -1/3.71 × 106 (58.6) = 4.6 × 10-11 yi = 2160 × 1.61 × 103 × 4.6 × 10-11 = 0.16 mm. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.102* — visual and optical instruments: derivation

Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.103 — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. The book’s selected-answer check begins 1/20 + 1/sio = 1/4, sio = 5 m 1/0.3 + 1/sie = 1/0.6, sie = -0.6 m MTo = -5/10 = -0.5 MTe = -(-0.6)/0.5 = +1.2 MToMTe = -0.6. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.104* — visual and optical instruments: derivation

Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.105* — visual and optical instruments: derivation

Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.106* — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.107 — visual and optical instruments: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Form the intermediate image first and then compute angular magnification, keeping relaxed-eye and near-point cases distinct. The book’s selected-answer check begins Ray-1 in the figure next page misses the eye-lens, and there is, therefore, a decrease in the energy arriving at the corresponding image point. This is vignetting. Eye relief CR CR Exit pupil Eye lens Field lens Objective Z03_HECH6933_05_GE_SOL.indd 693 08/09/16 9:14 pm 694 Solutions to Selected Problems 6.3 From Eq. (. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.108 — fiber and graded-index rays: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use total internal reflection and \(\mathrm{NA}=\sqrt{n_1^2-n_2^2}\) or integrate the paraxial GRIN ray equation. The book’s selected-answer check begins Rays that would have missed the eye-lens in the previous problem are made to pass through it by the field-lens. Note how the field-lens bends the chief rays a bit so that they cross the optical axis slightly closer to the eye-lens, thereby moving the exit pupil and shortening the eye relief. (For more on the subject, s. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.109* — fiber and graded-index rays: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use total internal reflection and \(\mathrm{NA}=\sqrt{n_1^2-n_2^2}\) or integrate the paraxial GRIN ray equation. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.110* — fiber and graded-index rays: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use total internal reflection and \(\mathrm{NA}=\sqrt{n_1^2-n_2^2}\) or integrate the paraxial GRIN ray equation. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.111* — fiber and graded-index rays: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use total internal reflection and \(\mathrm{NA}=\sqrt{n_1^2-n_2^2}\) or integrate the paraxial GRIN ray equation. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.112* — fiber and graded-index rays: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use total internal reflection and \(\mathrm{NA}=\sqrt{n_1^2-n_2^2}\) or integrate the paraxial GRIN ray equation. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.113* — fiber and graded-index rays: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use total internal reflection and \(\mathrm{NA}=\sqrt{n_1^2-n_2^2}\) or integrate the paraxial GRIN ray equation. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.114* — fiber and graded-index rays: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use total internal reflection and \(\mathrm{NA}=\sqrt{n_1^2-n_2^2}\) or integrate the paraxial GRIN ray equation. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.115* — fiber and graded-index rays: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use total internal reflection and \(\mathrm{NA}=\sqrt{n_1^2-n_2^2}\) or integrate the paraxial GRIN ray equation. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.116* — fiber and graded-index rays: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use total internal reflection and \(\mathrm{NA}=\sqrt{n_1^2-n_2^2}\) or integrate the paraxial GRIN ray equation. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.117 — fiber and graded-index rays: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use total internal reflection and \(\mathrm{NA}=\sqrt{n_1^2-n_2^2}\) or integrate the paraxial GRIN ray equation. The book’s selected-answer check begins 𝒟l - 𝒟c 1 + 𝒟c d = 3.2D 1 + (3.2D)(0.017 m) = +3.03D or to two figures +3.0D. ƒ1 = 0.330 m, and so the far point is 0.330 m - 0.017 m = 0.313 m behind the eye lens. For the contact lens ƒc = 1/3.2 = 0.313 m. Hence the far point at 0.31 m is the same for both, as it indeed must be.. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.118* — fiber and graded-index rays: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use total internal reflection and \(\mathrm{NA}=\sqrt{n_1^2-n_2^2}\) or integrate the paraxial GRIN ray equation. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.119 — fiber and graded-index rays: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use total internal reflection and \(\mathrm{NA}=\sqrt{n_1^2-n_2^2}\) or integrate the paraxial GRIN ray equation. The book’s selected-answer check begins (a)  The intermediate image-distance is obtained from the lens formula applied to the objective: 1 27 mm + 1 si = 1 25 mm and si = 3.38 × 102 mm. This is the distance from the objective to the intermediate image, to which must be added the focal length of the eyepiece to get the lens separation: 3.38 × 102 mm + 25 mm. Substitute the result back into the governing relation to verify its units and sign.

Problem 5.120* — fiber and graded-index rays: derivation

Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular. Use total internal reflection and \(\mathrm{NA}=\sqrt{n_1^2-n_2^2}\) or integrate the paraxial GRIN ray equation. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.121* — fiber and graded-index rays: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use total internal reflection and \(\mathrm{NA}=\sqrt{n_1^2-n_2^2}\) or integrate the paraxial GRIN ray equation. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.

Problem 5.122* — fiber and graded-index rays: calculation

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use total internal reflection and \(\mathrm{NA}=\sqrt{n_1^2-n_2^2}\) or integrate the paraxial GRIN ray equation. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.