Chapter 8: Polarization
=======================

Source: Eugene Hecht, *Optics*, fifth Global Edition, Chapter 8.
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 8.1* — polarization states and polarizers: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Resolve the orthogonal field components, compare their phase, and use Malus's law :math:`I=I_0\cos^2\theta` where applicable.
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 8.2* — polarization states and polarizers: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Resolve the orthogonal field components, compare their phase, and use Malus's law :math:`I=I_0\cos^2\theta` where applicable.
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 8.3* — polarization states and polarizers: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Resolve the orthogonal field components, compare their phase, and use Malus's law :math:`I=I_0\cos^2\theta` where applicable.
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 8.4 — polarization states and polarizers: physical interpretation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

State the controlling conservation or symmetry principle first, then use it to determine signs, directions, and limiting behavior.
Resolve the orthogonal field components, compare their phase, and use Malus's law :math:`I=I_0\cos^2\theta` where applicable.
The book's selected-answer check begins ``(a)  E $ = îE0 cos(kz vt) + ĵE0 cos(kz vt + π). Equal amplitudes, Ey lags Ex by π. Therefore 𝒫-state at 135° or -45°. (b)  E $ = îE0 cos(kz vt π/2) + ĵE0 cos(kz vt + π/2). Equal amplitudes, Ey lags Ex by π. Therefore same as (a). (c)  Ex leads Ey by π/4. They have equal amplitudes. Therefore it is an ellipse til``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.5 — polarization states and polarizers: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Resolve the orthogonal field components, compare their phase, and use Malus's law :math:`I=I_0\cos^2\theta` where applicable.
The book's selected-answer check begins ``E $x = î cosvt, E $y = ĵ sinvt Left-handed circular standing wave. y z x``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.6 — polarization states and polarizers: derivation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular.
Resolve the orthogonal field components, compare their phase, and use Malus's law :math:`I=I_0\cos^2\theta` where applicable.
The book's selected-answer check begins ``E $ℛ = îE0 cos(kz vt) + ĵE0 sin(kz vt) E $ℒ = îE′ 0 cos(kz vt) ĵE′ 0 sin(kz vt) E $ = E $ℛ + E $ℒ = î (E0 + E′ 0) cos(kz vt) + ĵ(E0 - E′ 0) sin(kz vt). Eo1 Eo1 cosu Eo1 cosu Eo1 cosu cos(90 – u) 90 – u u``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.7 — polarization states and polarizers: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Resolve the orthogonal field components, compare their phase, and use Malus's law :math:`I=I_0\cos^2\theta` where applicable.
Substitution back into the starting relation supplies the final sign and dimensional check.

Problem 8.8* — polarization states and polarizers: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Resolve the orthogonal field components, compare their phase, and use Malus's law :math:`I=I_0\cos^2\theta` where applicable.
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 8.9 — polarization states and polarizers: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Resolve the orthogonal field components, compare their phase, and use Malus's law :math:`I=I_0\cos^2\theta` where applicable.
Substitution back into the starting relation supplies the final sign and dimensional check.

Problem 8.10* — polarization states and polarizers: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Resolve the orthogonal field components, compare their phase, and use Malus's law :math:`I=I_0\cos^2\theta` where applicable.
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 8.11* — polarization states and polarizers: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Resolve the orthogonal field components, compare their phase, and use Malus's law :math:`I=I_0\cos^2\theta` where applicable.
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 8.12* — polarization states and polarizers: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Resolve the orthogonal field components, compare their phase, and use Malus's law :math:`I=I_0\cos^2\theta` where applicable.
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 8.13* — polarization states and polarizers: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Resolve the orthogonal field components, compare their phase, and use Malus's law :math:`I=I_0\cos^2\theta` where applicable.
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 8.14* — polarization states and polarizers: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Resolve the orthogonal field components, compare their phase, and use Malus's law :math:`I=I_0\cos^2\theta` where applicable.
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 8.15 — polarization states and polarizers: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Resolve the orthogonal field components, compare their phase, and use Malus's law :math:`I=I_0\cos^2\theta` where applicable.
Substitution back into the starting relation supplies the final sign and dimensional check.

Problem 8.16* — polarization states and polarizers: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Resolve the orthogonal field components, compare their phase, and use Malus's law :math:`I=I_0\cos^2\theta` where applicable.
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 8.17* — polarization states and polarizers: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Resolve the orthogonal field components, compare their phase, and use Malus's law :math:`I=I_0\cos^2\theta` where applicable.
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 8.18* — polarization states and polarizers: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Resolve the orthogonal field components, compare their phase, and use Malus's law :math:`I=I_0\cos^2\theta` where applicable.
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 8.19* — polarization states and polarizers: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Resolve the orthogonal field components, compare their phase, and use Malus's law :math:`I=I_0\cos^2\theta` where applicable.
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 8.20* — polarization states and polarizers: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Resolve the orthogonal field components, compare their phase, and use Malus's law :math:`I=I_0\cos^2\theta` where applicable.
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 8.21* — Jones and phasor analysis: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
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 8.22* — Jones and phasor analysis: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
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 8.23* — Jones and phasor analysis: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
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 8.24* — Jones and phasor analysis: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
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 8.25* — Jones and phasor analysis: design
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Translate every stated requirement into an equation, solve the simultaneous constraints, and reject roots that violate the geometry.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
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 8.26* — Jones and phasor analysis: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
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 8.27* — Jones and phasor analysis: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
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 8.28* — Jones and phasor analysis: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
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 8.29* — Jones and phasor analysis: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
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 8.30 — Jones and phasor analysis: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
Substitution back into the starting relation supplies the final sign and dimensional check.

Problem 8.31 — Jones and phasor analysis: derivation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
The book's selected-answer check begins ``No. The crystal performs as if it were two oppositely oriented specimens in series. Two similarly oriented crystals in series would behave like one thick specimen and thus separate the oand e-rays even more.``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.32* — Jones and phasor analysis: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
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 8.33 — Jones and phasor analysis: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
The book's selected-answer check begins ``Light scattered from the paper passes through the polaroids and becomes linearly polarized. Light from the upper left filter has its E $field parallel to the principal section (which is diagonal across the second and fourth quadrants) and is therefore an e-ray. Notice how the letters P and T are shifted downward in an``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.34 — Jones and phasor analysis: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
The book's selected-answer check begins ``(a) and (c) are two aspects of the previous problem. (b) shows double refraction because the polaroid’s axis is at roughly 45° to the principal section of the crystal. Thus both an oand an e-ray will exist. Z03_HECH6933_05_GE_SOL.indd 697 08/09/16 9:14 pm 698 Solutions to Selected Problems (c)  Undesired energy in the``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.35 — Jones and phasor analysis: physical interpretation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

State the controlling conservation or symmetry principle first, then use it to determine signs, directions, and limiting behavior.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
The book's selected-answer check begins ``When E $ is perpendicular to the CO3 plane, the polarization will be less than when it is parallel. In the former case, the field of each polarized oxygen atom tends to reduce the polarization of its neighbors. In other words, the induced field, as shown in the figure, is down while E $ is up. When E $ is in the carbon``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.36 — Jones and phasor analysis: derivation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
The book's selected-answer check begins ``Calcite no 7 ne. Two spectra will be visible when (b) or (c) is used in a spectrometer. The indices are computed in the usual way, using n = sin1 2 (a + dm) sin1 2 a where dm is the angle of minimum deviation of either beam.``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.37 — Jones and phasor analysis: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
The book's selected-answer check begins ``sinuc = nbalsam n0 = 1.55 1.658 = 0.935; uc ≈ 69°``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.38* — Jones and phasor analysis: construction
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Evaluate the boundary and representative interior values, then draw the requested curve or ray construction to scale.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
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 8.39* — Jones and phasor analysis: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
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 8.40 — Jones and phasor analysis: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
The book's selected-answer check begins ``e o (a) Calcite e o (b) Quartz E + − Oxygen + − Oxygen + − Oxygen Carbon o, e (a) − − − Carbon a o e (b) o e (c) Z03_HECH6933_05_GE_SOL.indd 698 08/09/16 9:14 pm Solutions to Selected Problems 699 ≥ 1 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 -1 ¥ ≥ 1 0 0 -1 ¥ = ≥ 1 0 0 1 ¥ ≥ 1 0 0 0 0 1 0 0 0 0 0 1 0 0 -1 0 ¥ ≥ 1 0 0 0 0 1 0 0 0 0``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.41* — Jones and phasor analysis: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
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 8.42* — Jones and phasor analysis: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
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 8.43* — Jones and phasor analysis: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
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 8.44* — Jones and phasor analysis: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
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 8.45* — Jones and phasor analysis: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Write the input Jones vector, multiply device matrices in propagation order, and remove any physically irrelevant common phase.
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 8.46* — birefringence: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Separate ordinary and extraordinary waves, apply the appropriate index surface, and enforce tangential wavevector matching.
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 8.47* — birefringence: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Separate ordinary and extraordinary waves, apply the appropriate index surface, and enforce tangential wavevector matching.
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 8.48* — birefringence: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Separate ordinary and extraordinary waves, apply the appropriate index surface, and enforce tangential wavevector matching.
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 8.49* — birefringence: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Separate ordinary and extraordinary waves, apply the appropriate index surface, and enforce tangential wavevector matching.
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 8.50* — birefringence: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Separate ordinary and extraordinary waves, apply the appropriate index surface, and enforce tangential wavevector matching.
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 8.51* — birefringence: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Separate ordinary and extraordinary waves, apply the appropriate index surface, and enforce tangential wavevector matching.
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 8.52 — birefringence: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Separate ordinary and extraordinary waves, apply the appropriate index surface, and enforce tangential wavevector matching.
The book's selected-answer check begins ``no = 1.6584, ne = 1.4864. Snell’s Law: sinui = no sinuto = 0.766 sinui = ne sinute = 0.766 sinuto ≈ 0.463, uto ≈ 27°35′ sinute ≈ 0.516, ute ≈ 31°4′ ∆u ≈ 3°29′``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.53* — birefringence: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Separate ordinary and extraordinary waves, apply the appropriate index surface, and enforce tangential wavevector matching.
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 8.54 — birefringence: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Separate ordinary and extraordinary waves, apply the appropriate index surface, and enforce tangential wavevector matching.
The book's selected-answer check begins ``Ex leads Ey by π/2. They were initially in-phase and Ex 7 Ey. Therefore the wave is left-handed, elliptical, and horizontal.``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.55* — birefringence: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Separate ordinary and extraordinary waves, apply the appropriate index surface, and enforce tangential wavevector matching.
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 8.56* — birefringence: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Separate ordinary and extraordinary waves, apply the appropriate index surface, and enforce tangential wavevector matching.
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 8.57* — birefringence: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Separate ordinary and extraordinary waves, apply the appropriate index surface, and enforce tangential wavevector matching.
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 8.58* — birefringence: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Separate ordinary and extraordinary waves, apply the appropriate index surface, and enforce tangential wavevector matching.
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 8.59* — birefringence: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Separate ordinary and extraordinary waves, apply the appropriate index surface, and enforce tangential wavevector matching.
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 8.60* — birefringence: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Separate ordinary and extraordinary waves, apply the appropriate index surface, and enforce tangential wavevector matching.
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 8.61* — birefringence: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Separate ordinary and extraordinary waves, apply the appropriate index surface, and enforce tangential wavevector matching.
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 8.62* — birefringence: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Separate ordinary and extraordinary waves, apply the appropriate index surface, and enforce tangential wavevector matching.
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 8.63* — birefringence: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Separate ordinary and extraordinary waves, apply the appropriate index surface, and enforce tangential wavevector matching.
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 8.64* — birefringence: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Separate ordinary and extraordinary waves, apply the appropriate index surface, and enforce tangential wavevector matching.
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 8.65* — birefringence: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Separate ordinary and extraordinary waves, apply the appropriate index surface, and enforce tangential wavevector matching.
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 8.66* — retarders and electro-optics: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Use :math:`\delta=(2\pi/\lambda)\Delta n\,d`, then rotate into and out of the plate axes before interpreting the output state.
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 8.67* — retarders and electro-optics: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Use :math:`\delta=(2\pi/\lambda)\Delta n\,d`, then rotate into and out of the plate axes before interpreting the output state.
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 8.68 — retarders and electro-optics: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Use :math:`\delta=(2\pi/\lambda)\Delta n\,d`, then rotate into and out of the plate axes before interpreting the output state.
The book's selected-answer check begins ``The ℛ-state (looking toward the source) incident on the glass screen drives the electrons in circular orbits, and they reradiate reflected circular light whose E $-field rotates in the same direction as that of the incoming beam. But the propagation direction has been reversed on reflection, so that although the incide``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.69 — retarders and electro-optics: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Use :math:`\delta=(2\pi/\lambda)\Delta n\,d`, then rotate into and out of the plate axes before interpreting the output state.
The book's selected-answer check begins ``∆w = 2p l0 d∆n but ∆w = (1/4)(2p) because of the fringe shift. Therefore ∆w = π/2 and π 2 = 2p d(0.005) 589.3 × 10-9 d = 589.3 × 10-9 2(10-2 ) = 2.94 × 10-5 m``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.70 — retarders and electro-optics: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Use :math:`\delta=(2\pi/\lambda)\Delta n\,d`, then rotate into and out of the plate axes before interpreting the output state.
The book's selected-answer check begins ``Yes. If the amplitudes of the 𝒫-states differ. The transmitted beam, in a pile-of-plates polarizer, especially for a small pile.``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.71* — retarders and electro-optics: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Use :math:`\delta=(2\pi/\lambda)\Delta n\,d`, then rotate into and out of the plate axes before interpreting the output state.
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 8.72 — retarders and electro-optics: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Use :math:`\delta=(2\pi/\lambda)\Delta n\,d`, then rotate into and out of the plate axes before interpreting the output state.
The book's selected-answer check begins ``Place the photoelastic material between circular polarizers with both retarders facing it (as in Fig. 8.59). Under circular illumination no orientation of the stress axes is preferred over any other, and they will thus all be indistinguishable. Only the birefringence will have an effect, and so the isochromatics will b``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.73* — retarders and electro-optics: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Use :math:`\delta=(2\pi/\lambda)\Delta n\,d`, then rotate into and out of the plate axes before interpreting the output state.
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 8.74 — retarders and electro-optics: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Use :math:`\delta=(2\pi/\lambda)\Delta n\,d`, then rotate into and out of the plate axes before interpreting the output state.
The book's selected-answer check begins ``Vl/2 = l0/2n3 0r63[8.51] = 500 × 10-9 /2(1.58)3 × 5.5 × 10-12 = 11.5 kV.``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.75* — retarders and electro-optics: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Use :math:`\delta=(2\pi/\lambda)\Delta n\,d`, then rotate into and out of the plate axes before interpreting the output state.
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 8.76 — retarders and electro-optics: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Use :math:`\delta=(2\pi/\lambda)\Delta n\,d`, then rotate into and out of the plate axes before interpreting the output state.
The book's selected-answer check begins ``E $1 · E $× 2 = 0, E $2 = c e21 e22 d E $1 · E $× 2 = (1)(e21)× + (-2i)(e22)× = 0 E $2 = c 2 i d E $1 is E $2 is``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.77* — retarders and electro-optics: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Use :math:`\delta=(2\pi/\lambda)\Delta n\,d`, then rotate into and out of the plate axes before interpreting the output state.
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 8.78* — retarders and electro-optics: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Use :math:`\delta=(2\pi/\lambda)\Delta n\,d`, then rotate into and out of the plate axes before interpreting the output state.
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 8.79* — retarders and electro-optics: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Use :math:`\delta=(2\pi/\lambda)\Delta n\,d`, then rotate into and out of the plate axes before interpreting the output state.
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 8.80* — retarders and electro-optics: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Use :math:`\delta=(2\pi/\lambda)\Delta n\,d`, then rotate into and out of the plate axes before interpreting the output state.
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 8.81* — optical activity and polarization devices: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Compose the required rotator, analyzer, or stress-induced retardance and verify the result with intensity bounds.
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 8.82* — optical activity and polarization devices: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Compose the required rotator, analyzer, or stress-induced retardance and verify the result with intensity bounds.
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 8.83* — optical activity and polarization devices: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Compose the required rotator, analyzer, or stress-induced retardance and verify the result with intensity bounds.
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 8.84 — optical activity and polarization devices: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Compose the required rotator, analyzer, or stress-induced retardance and verify the result with intensity bounds.
The book's selected-answer check begins ``≥ 1 0 0 0 0 0 0 1 0 0 1 0 0 -1 0 0 ¥ ≥ 1 0 0 0 0 0 0 -1 0 0 1 0 0 1 0 0 ¥ = ≥ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ¥``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.85* — optical activity and polarization devices: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Compose the required rotator, analyzer, or stress-induced retardance and verify the result with intensity bounds.
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 8.86 — optical activity and polarization devices: construction
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Evaluate the boundary and representative interior values, then draw the requested curve or ray construction to scale.
Compose the required rotator, analyzer, or stress-induced retardance and verify the result with intensity bounds.
The book's selected-answer check begins ``≥ 1 0 0 0 0 1 0 0 0 0 0 -1 0 0 1 0 ¥ ≥ 1 0 0 0 0 1 0 0 0 0 0 -1 0 0 1 0 ¥ = ≥ 1 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 -1 ¥ ≥ 1 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 -1 ¥ ≥ 1 0 0 1 ¥ = ≥ 1 0 0 -1 ¥ Z03_HECH6933_05_GE_SOL.indd 699 08/09/16 9:14 pm 700 Solutions to Selected Problems (c)  Since the fringes vary as cosine-squared and the an``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.87 — optical activity and polarization devices: design
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Translate every stated requirement into an equation, solve the simultaneous constraints, and reject roots that violate the geometry.
Compose the required rotator, analyzer, or stress-induced retardance and verify the result with intensity bounds.
The book's selected-answer check begins ``≥ 1 0 0 0 0 1 0 0 0 0 0 -1 0 0 1 0 ¥ 1 2 ≥ 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 ¥ = 1 2 ≥ 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 ¥ 1 2 ≥ 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 ¥ ≥ 1 0 0 0 ¥ = 1 2 ≥ 1 0 0 1 ¥ 1 2 ≥ 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 ¥ ≥ 1 0 0 1 ¥ = 1 2 ≥ 1 0 0 1 ¥ 1 2 ≥ 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 ¥ ≥ 1 0 0 1 ¥ = 1 2 ≥ 1``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.88* — optical activity and polarization devices: derivation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Start from the governing relation rather than the desired result; rearrange until the requested form follows, so the argument is not circular.
Compose the required rotator, analyzer, or stress-induced retardance and verify the result with intensity bounds.
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 8.89 — optical activity and polarization devices: design
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Translate every stated requirement into an equation, solve the simultaneous constraints, and reject roots that violate the geometry.
Compose the required rotator, analyzer, or stress-induced retardance and verify the result with intensity bounds.
The book's selected-answer check begins ``c teiw 0 0 teiwd where a phase increment of w is introduced into both components as a result of traversing the plate. c 1 0 0 1 d c 0 0 0 0 d``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.90 — optical activity and polarization devices: design
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Translate every stated requirement into an equation, solve the simultaneous constraints, and reject roots that violate the geometry.
Compose the required rotator, analyzer, or stress-induced retardance and verify the result with intensity bounds.
The book's selected-answer check begins ``≥ t2 0 0 0 0 t2 0 0 0 0 t2 0 0 0 0 t2 ¥ ≥ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ¥``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.91 — optical activity and polarization devices: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Compose the required rotator, analyzer, or stress-induced retardance and verify the result with intensity bounds.
The book's selected-answer check begins ``V = Ip Ip + Iu = ( 2 1 + 2 2 + 2 3)1/2 0 Ip = ( 2 1 + 2 2 + 2 3)1/2 ; I - Ip = Iu``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.92* — optical activity and polarization devices: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Compose the required rotator, analyzer, or stress-induced retardance and verify the result with intensity bounds.
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 8.93 — optical activity and polarization devices: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Compose the required rotator, analyzer, or stress-induced retardance and verify the result with intensity bounds.
The book's selected-answer check begins ``(a) c cos2 a cosa sina cosa sina sin2 a d c cosu sinu d = c cos2 a cosu + cosa sina sinu cosa sina cosu + sin2 a sinu d = cos(u a) c cosa sina d (b) Emerging beam is polarized at angle a to the horizontal and its amplitude is reduced by a factor cos(u a). This is exactly what an ideal linear polarizer would do if its t``.  Substitute the result back into the governing relation to verify its units and sign.

Problem 8.94* — optical activity and polarization devices: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Compose the required rotator, analyzer, or stress-induced retardance and verify the result with intensity bounds.
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 8.95* — optical activity and polarization devices: calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities with units, substitute only after the symbolic relation is isolated, and retain guard digits until the final result.
Compose the required rotator, analyzer, or stress-induced retardance and verify the result with intensity bounds.
Finish by checking the governing equation, the dimensions, and the zero/large-parameter limit; these checks replace reliance on an unavailable answer-key entry.