### A thin ?lm of oil (n = 1.25) is located on smooth, wet pavement. When viewed perpendicular to the pavement

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**A+ Work!! 100% CORRECT PHYSICS TUTORIAL

INCLUDES ANSWERS TO THE FOLLOWING QUESTIONS

Problem 1.

A thin ?lm of oil (n = 1.25) is located on smooth, wet pavement. When viewed perpendicular to the pavement, the ?lm re?ects most strongly red light at ?red = 640 nm and re?ects no green light at ?green = 512 nm.

How thick is the oil ?lm? [2 points]

Problem 2.

Interference e?ects are produced at point P on a screen as a result of direct rays from a 500-nm sourse and re?ected rays from the mirror as shown below. Assume the source is 100 m to the left of the screen and 1.00 cm above the mirror. Find the distance y to the ?rst dark band above the mirror. [2 points]

Problem 3.

Determine polarization state of the electromagnetic plane wave E propagating along the x axis which is obtained from a superposition of two linearly polarized waves E1 = E10 y cos(?t ? kx) and E2 = E20 z cos(?t ? kx + ?). Here y () denotes unit vector along y(z) axis, correspondingly. The amplitudes are related as E10 = 2E20 , and the phase z shift is ? = ?/2. [3 points]

Problem 4.

(a) Calculate Fraunhofer di?raction from rectangular aperture of width b and height a (see Figure). This can be done (rather simply) by two-dimensional integration or by representing the aperture as a collection of a large number of small emitters, in close similarity to the calculation of the di?raction pattern from a single slit in the lecture notes,

and then taking the limit of the number of those emitters approaching in?nity. [2 points] (b) Sketch the resulting two-dimensional intensity plot. [1 point]

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