PHYS 3410/3411/6750/6751: Modern Optics Midterm #2

Transcription

1 Name: PHYS 3410/3411/6750/6751: Modern Optics Midterm #2 Wednesday 17 November 2010 Prof. Bolton Only pen or pencil are allowed. No calculators or additional materials.

2 PHYS 3410/3411/6750/6751 Midterm #2 2 Problem 1 (25 points) Imagine that a sugar substitute called fakeose has a specific rotatory power of +3.6 per centimeter of path traversed through a solution containing 1 g of fakeose per cubic centimeter (cc) of solution, for a wavelength of 500 nm. A 10-liter transparent cylinder with a length of 1 m is to be filled completely with a solution of fakeose. A pair of crossed polarizers is positioned with one at either end of the cylinder. What is the minimum total mass of fakeose that must be dissolved into this solution so that light of wavelength 1000 nm is maximally transmitted out of the second polarizer when shone through the entire system? Please show the steps of your reasoning clearly! The following formula should be of use: β = πd λ 0 (n L n R ) You may assume that n L and n R do not depend upon wavelength, and that any amount of absorption in the solution does not depend upon concentration. Also note that 1 liter = 1000 cc. (figure not to scale) 1000 nm light in 10 liters of solution 1 m 1000 nm light out

3 PHYS 3410/3411/6750/6751 Midterm #2 3 Problem 2 (25 points) A double-slit configuration with slit width b and slit separation a (as diagrammed schematically at left below) is illuminated from one side by coherent monochromatic light of wavelength λ = 500 nm. The irradiance distribution seen on a screen located 1 meter away from the slits is shown at right below (note units of millimeters). Using the result that the far-field irradiance distribution of this configuration is described by ( ) 2 sin β I(θ) =4I 0 cos 2 α β where β = πb πa sin θ and α = sin θ, λ λ determine the values of the slit separation a and slit width b a b b (figure not to scale) θ screen position normalized irradiance m screen position (mm)

4 PHYS 3410/3411/6750/6751 Midterm #2 4 Problem 3 (25 points) In this problem, you will find design parameters for a blazed reflection grating. The desired grating performance is: Resolution R = 6000 Angular dispersion D dθ m /dλ = radians per nanometer (nm). Grating blaze wavelength λ blaze = 600 nm. To deliver this performance, you must determine: (a) The spacing a between adjacent grooves of the grating. (b) The grating blaze angle γ. (c) The total number of grooves N necessary. The grating is to be used in a Littrow autocollimation setup. In this configuration, the angle of incidence equals the grating blaze angle (θ i = γ), and we work in the first diffraction order (m = 1 according to the conventions we have used). The blaze wavelength λ blaze is defined as the wavelength for which θ m = θ i = γ. The two following equations are all you need: a(sin θ m sin θ i )=mλ R = Nm You may use the small-angle approximation sin θ θ for all angles in this problem. θ i a grating normal γ

5 PHYS 3410/3411/6750/6751 Midterm #2 5 Question 1: (5 points) If you are standing upright and viewing glare reflected off the surface of a water puddle at 53, is that light preferentially polarized in a horizontal plane, a vertical plane, or neither? Now suppose you are again standing upright, this time viewing atmospherically scattered sunlight from a direction roughly 90 away from the setting sun. Is that light preferentially polarized in a horizontal plane, a vertical plane, or neither? Question 2: (5 points) Which one of the following can turn a linearly polarized beam into a circularly polarized beam? (a) crossed polaroids (c) half-wave plate (b) half-silvered mirror (d) quarter-wave plate Question 3: (5 points) Use the fact that e iφ =cosφ + i sin φ and e iα e iβ = e i(α+β) and i 1 to derive the expression for cos(α + β) intermsofsinα, sinβ, cosα, andcosβ. Question 4: (5 points) Briefly describe the design and on-axis operating principle of the Fabray-Perot interferometer. Question 5: (5 points) What is the approximate diffraction-limited angular imaging resolution of the Hubble Space Telescope (primary mirror diameter 2.4 meters) at visible wavelengths? (FYI, there are about arc-seconds to one radian.) (a) 0.02 arc-seconds (c) 0.20 arc-seconds (b) 0.05 arc seconds (d) 0.50 arc seconds