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$Enhancing T_{c} draft as resubmitted to PRL$

Diffraction [20 Points] The emission of light from an excited gas is focused and passed through a diffraction grating with 3000 lines/cm, as shown. First order and second order spectral lines are observed. a) Four first-order spectral lines are observed at 7.07°, 7.48°, 8.38°, and 11.3°. Find the wavelengths of these four spectral lines. [8 Points] Answer: λ 1 = 410 nm, λ 2 = 434 nm, λ 3 = 486 nm, and λ 4 = 656 nm b) At what angles are the second-order spectral lines observed? [7 Points] Answer: θ 1 = 14.2°, θ 2 = 15.1°, θ 3 = 17.0°, and θ 4 = 23.2° c) Suppose the diffraction grating is replaced with another having twice the number of gratings/cm. Find the angular separation observed between the second-order spectral lines. [5 Points] Answer: Δθ = 22.5°
Polarization [20 Points] Three polarizing plates whose planes are parallel are centered on a common axis. The directions of the transmission axes relative to the common vertical direction are shown in the figure. A linearly polarized beam of light with plane of polarization parallel to the vertical reference direction is incident from the left onto the first disk with intensity I i = 100 W/m 2 . a) Determine the transmitted intensity I f when θ 1 = 10.0°, θ 2 = 30.0°, and θ 3 = 60.0°. [7 Points] Answer: I f = 64.2 W/m 2 b) What is the ratio I f /I i of the final transmitted intensity to the incident intensity if θ 1 = 30.0°, θ 2 = 60.0°, and θ 3 = 90.0°? [7 Points] Answer: I f /I i = 27/64 c) If θ 1 = 0° and θ 2 = 45.0°, what should θ 3 be in order to make I f /I i = 3/8? [6 Points] Answer: θ 3 = 75.0°
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