Chapter 3: Electromagnetic Theory, Photons, and Light
Source: Eugene Hecht, Optics, fifth Global Edition, Chapter 3. 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 3.1 — vector fields and Maxwell equations: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish.
3. Verification.
The book’s selected-answer check begins Ey = 4 cos [2p × 1014 (t x/c) + π/2] Ey = A cos [2pn(t x/v) + π/2] (a) n = 1014 Hz, v = c, and λ = c/n = 3 × 108 /1014 = 3 × 10-6 m, moves in the positive x-direction, A = 4 V/m, e = π/2 linearly polarized in y-direction. (b) Bx = 0, By = 0, Bz = Ey = 4 c cos [2p × 1014 (t x/c) + π/2].. Substitute the result back into the governing relation to verify its units and sign.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish.
The book’s selected-answer check begins Ey = 4 cos [2p × 1014 (t x/c) + π/2] Ey = A cos [2pn(t x/v) + π/2] (a) n = 1014 Hz, v = c, and λ = c/n = 3 × 108 /1014 = 3 × 10-6 m, moves in the positive x-direction, A = 4 V/m, e = π/2 linearly polarized in y-direction. (b) Bx = 0, By = 0, Bz = Ey = 4 c cos [2p × 1014 (t x/c) + π/2].. Substitute the result back into the governing relation to verify its units and sign.
Problem 3.2 — vector fields and Maxwell equations: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish.
3. Verification.
The book’s selected-answer check begins Ez = 0, Ey = Ex = E0 sin (kz vt) or cosine; Bz = 0, By = -Bx = Ey/c, or if you like, E $ = E0 22 (î + ĵ) sin (kz vt), B $ = E0 c22 (ĵ î) sin (kz vt). Substitute the result back into the governing relation to verify its units and sign.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish.
The book’s selected-answer check begins Ez = 0, Ey = Ex = E0 sin (kz vt) or cosine; Bz = 0, By = -Bx = Ey/c, or if you like, E $ = E0 22 (î + ĵ) sin (kz vt), B $ = E0 c22 (ĵ î) sin (kz vt). Substitute the result back into the governing relation to verify its units and sign.
Problem 3.3* — vector fields and Maxwell equations: derivation
Brief solution
1. Method.
Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular.
2. Decisive step.
Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular. Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish. 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 3.4* — vector fields and Maxwell equations: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish. 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 3.5* — vector fields and Maxwell equations: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish. 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 3.6 — vector fields and Maxwell equations: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish.
3. Verification.
The book’s selected-answer check begins The field is linearly polarized in the y-direction and varies sinusoidally from zero at z = 0 to zero at z = z0. Using the wave equation 02 Ey 0x2 + 02 Ey 0y2 + 02 Ey 0z2 - 1 c2 02 Ey 0t2 = 0 c-k2 p2 z0 2 + v2 c2 d E0 sin pz z0 cos (kx vt) = 0 and since this is true for all x, z, and t, each term must equal zero and so. Substitute the result back into the governing relation to verify its units and sign.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish.
The book’s selected-answer check begins The field is linearly polarized in the y-direction and varies sinusoidally from zero at z = 0 to zero at z = z0. Using the wave equation 02 Ey 0x2 + 02 Ey 0y2 + 02 Ey 0z2 - 1 c2 02 Ey 0t2 = 0 c-k2 p2 z0 2 + v2 c2 d E0 sin pz z0 cos (kx vt) = 0 and since this is true for all x, z, and t, each term must equal zero and so. Substitute the result back into the governing relation to verify its units and sign.
Problem 3.7* — vector fields and Maxwell equations: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish. 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 3.8* — vector fields and Maxwell equations: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish. 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 3.9* — vector fields and Maxwell equations: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish. 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 3.10* — vector fields and Maxwell equations: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish. 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 3.11* — vector fields and Maxwell equations: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish. 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 3.12* — vector fields and Maxwell equations: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish. 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 3.13* — vector fields and Maxwell equations: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish. 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 3.14* — vector fields and Maxwell equations: derivation
Brief solution
1. Method.
Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular.
2. Decisive step.
Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular. Apply the stated divergence/curl or integral Maxwell law and use symmetry to remove components that must vanish. 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 3.15 — electromagnetic-wave energetics: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\).
3. Verification.
Substitution back into the starting relation supplies the final sign and dimensional check.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\). Substitution back into the starting relation supplies the final sign and dimensional check.
Problem 3.16* — electromagnetic-wave energetics: derivation
Brief solution
1. Method.
Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular.
2. Decisive step.
Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\).
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular. Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\). 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 3.17* — electromagnetic-wave energetics: derivation
Brief solution
1. Method.
Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular.
2. Decisive step.
Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\).
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular. Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\). 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 3.18* — electromagnetic-wave energetics: derivation
Brief solution
1. Method.
Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular.
2. Decisive step.
Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\).
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular. Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\). 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 3.19* — electromagnetic-wave energetics: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\).
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\). 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 3.20* — electromagnetic-wave energetics: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\).
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\). 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 3.21* — electromagnetic-wave energetics: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\).
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\). 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 3.22* — electromagnetic-wave energetics: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\).
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\). 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 3.23* — electromagnetic-wave energetics: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\).
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\). 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 3.24* — electromagnetic-wave energetics: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\).
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\). 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 3.25 — electromagnetic-wave energetics: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\).
3. Verification.
Substitution back into the starting relation supplies the final sign and dimensional check.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\). Substitution back into the starting relation supplies the final sign and dimensional check.
Problem 3.26 — electromagnetic-wave energetics: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\).
3. Verification.
Substitution back into the starting relation supplies the final sign and dimensional check.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\). Substitution back into the starting relation supplies the final sign and dimensional check.
Problem 3.27* — electromagnetic-wave energetics: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\).
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\). 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 3.28 — electromagnetic-wave energetics: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\).
3. Verification.
Substitution back into the starting relation supplies the final sign and dimensional check.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Combine \(c=1/\sqrt{\mu_0\epsilon_0}\), \(B_0=E_0/c\), and \(\langle S\rangle=E_0B_0/(2\mu_0)\). Substitution back into the starting relation supplies the final sign and dimensional check.
Problem 3.29* — photons and momentum: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction. 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 3.30 — photons and momentum: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction.
3. Verification.
Substitution back into the starting relation supplies the final sign and dimensional check.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction. Substitution back into the starting relation supplies the final sign and dimensional check.
Problem 3.31* — photons and momentum: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction. 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 3.32 — photons and momentum: construction
Brief solution
1. Method.
Evaluate the boundary and representative interior values, then draw the requested curve or ray construction to scale.
2. Decisive step.
Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction.
3. Verification.
Substitution back into the starting relation supplies the final sign and dimensional check.
Show detailed steps
Evaluate the boundary and representative interior values, then draw the requested curve or ray construction to scale. Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction. Substitution back into the starting relation supplies the final sign and dimensional check.
Problem 3.33* — photons and momentum: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction. 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 3.34 — photons and momentum: derivation
Brief solution
1. Method.
Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular.
2. Decisive step.
Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction.
3. Verification.
Substitution back into the starting relation supplies the final sign and dimensional check.
Show detailed steps
Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular. Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction. Substitution back into the starting relation supplies the final sign and dimensional check.
Problem 3.35* — photons and momentum: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction. 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 3.36 — photons and momentum: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction.
3. Verification.
Substitution back into the starting relation supplies the final sign and dimensional check.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction. Substitution back into the starting relation supplies the final sign and dimensional check.
Problem 3.37* — photons and momentum: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction. 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 3.38* — photons and momentum: derivation
Brief solution
1. Method.
Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular.
2. Decisive step.
Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular. Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction. 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 3.39 — photons and momentum: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction.
3. Verification.
Substitution back into the starting relation supplies the final sign and dimensional check.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction. Substitution back into the starting relation supplies the final sign and dimensional check.
Problem 3.40 — photons and momentum: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction.
3. Verification.
Substitution back into the starting relation supplies the final sign and dimensional check.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Use \(E=h\nu=hc/\lambda\), \(p=h/\lambda\), and conserve energy and momentum for the stated interaction. Substitution back into the starting relation supplies the final sign and dimensional check.
Problem 3.41* — material dispersion: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption. 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 3.42* — material dispersion: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption. 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 3.43 — material dispersion: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption.
3. Verification.
Substitution back into the starting relation supplies the final sign and dimensional check.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption. Substitution back into the starting relation supplies the final sign and dimensional check.
Problem 3.44 — material dispersion: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption.
3. Verification.
Substitution back into the starting relation supplies the final sign and dimensional check.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption. Substitution back into the starting relation supplies the final sign and dimensional check.
Problem 3.45 — material dispersion: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption.
3. Verification.
Substitution back into the starting relation supplies the final sign and dimensional check.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption. Substitution back into the starting relation supplies the final sign and dimensional check.
Problem 3.46 — material dispersion: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption.
3. Verification.
Substitution back into the starting relation supplies the final sign and dimensional check.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption. Substitution back into the starting relation supplies the final sign and dimensional check.
Problem 3.47* — material dispersion: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption. 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 3.48* — material dispersion: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption. 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 3.49* — material dispersion: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption. 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 3.50* — material dispersion: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption. 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 3.51 — material dispersion: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption.
3. Verification.
Substitution back into the starting relation supplies the final sign and dimensional check.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption. Substitution back into the starting relation supplies the final sign and dimensional check.
Problem 3.52* — material dispersion: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption. 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 3.53* — material dispersion: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption. 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 3.54* — material dispersion: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption. 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 3.55* — material dispersion: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption. 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 3.56 — material dispersion: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption.
3. Verification.
Substitution back into the starting relation supplies the final sign and dimensional check.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption. Substitution back into the starting relation supplies the final sign and dimensional check.
Problem 3.57 — material dispersion: derivation
Brief solution
1. Method.
Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular.
2. Decisive step.
Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption.
3. Verification.
Substitution back into the starting relation supplies the final sign and dimensional check.
Show detailed steps
Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular. Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption. Substitution back into the starting relation supplies the final sign and dimensional check.
Problem 3.58* — material dispersion: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption. 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 3.59 — material dispersion: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption.
3. Verification.
Substitution back into the starting relation supplies the final sign and dimensional check.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Start from the driven-oscillator susceptibility and retain the real or imaginary part required for refraction or absorption. Substitution back into the starting relation supplies the final sign and dimensional check.
Problem 3.60* — relativistic and quantum-light check: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Write the invariant or photon-counting relation first, then evaluate its limiting classical behavior.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Write the invariant or photon-counting relation first, then evaluate its limiting classical behavior. 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 3.61 — relativistic and quantum-light check: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Write the invariant or photon-counting relation first, then evaluate its limiting classical behavior.
3. Verification.
The book’s selected-answer check begins With v in the visible, (v0 2 v2 ) is smaller for lead glass and larger for fused silica. Hence n(v) is larger for the former and smaller for the latter.. Substitute the result back into the governing relation to verify its units and sign.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the invariant or photon-counting relation first, then evaluate its limiting classical behavior.
The book’s selected-answer check begins With v in the visible, (v0 2 v2 ) is smaller for lead glass and larger for fused silica. Hence n(v) is larger for the former and smaller for the latter.. Substitute the result back into the governing relation to verify its units and sign.
Problem 3.62* — relativistic and quantum-light check: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Write the invariant or photon-counting relation first, then evaluate its limiting classical behavior.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Write the invariant or photon-counting relation first, then evaluate its limiting classical behavior. 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 3.63 — relativistic and quantum-light check: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Write the invariant or photon-counting relation first, then evaluate its limiting classical behavior.
3. Verification.
The book’s selected-answer check begins C1 is the value that n approaches as λ gets larger.. Substitute the result back into the governing relation to verify its units and sign.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the invariant or photon-counting relation first, then evaluate its limiting classical behavior.
The book’s selected-answer check begins C1 is the value that n approaches as λ gets larger.. Substitute the result back into the governing relation to verify its units and sign.
Problem 3.64 — relativistic and quantum-light check: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Write the invariant or photon-counting relation first, then evaluate its limiting classical behavior.
3. Verification.
The book’s selected-answer check begins The horizontal values of n(v) approached in each region between absorption bands increase as v decreases.. Substitute the result back into the governing relation to verify its units and sign.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the invariant or photon-counting relation first, then evaluate its limiting classical behavior.
The book’s selected-answer check begins The horizontal values of n(v) approached in each region between absorption bands increase as v decreases.. Substitute the result back into the governing relation to verify its units and sign.
Problem 3.65* — relativistic and quantum-light check: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Write the invariant or photon-counting relation first, then evaluate its limiting classical behavior.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Write the invariant or photon-counting relation first, then evaluate its limiting classical behavior. 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 3.66* — relativistic and quantum-light check: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Write the invariant or photon-counting relation first, then evaluate its limiting classical behavior.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Write the invariant or photon-counting relation first, then evaluate its limiting classical behavior. 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 3.67* — relativistic and quantum-light check: calculation
Brief solution
1. Method.
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
2. Decisive step.
Write the invariant or photon-counting relation first, then evaluate its limiting classical behavior.
3. Verification.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.
Show detailed steps
List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result. Write the invariant or photon-counting relation first, then evaluate its limiting classical behavior. Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.