# HW2 - EE 119 Homework 2 Professor Jeff Bokor TA Xi Luo Due...

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EE 119 Homework 2 Professor: Jeff Bokor TA: Xi Luo Due Tuesday , Feb 9 th 2010 (Please submit your answers in EE119 homework box located in 240 Cory Hall) 1. (a) In class, the angle of deviation ( δ ) has been formulated for a prism with an apex angle ( α ). Plot the angle of deviation ( δ ) versus incident angle for n = 1.5 and apex angle of 60°. (b) The angle of deviation should have a minimum. Derive a general expression for the incidence angle at which the deviation δ is minimized. Your answer should be given as a function of the apex angle α and refractive index of the prism. Show that the ray for which the deviation is a minimum traverses the prism symmetrically. This means that the incident angle and the exit angle are the same. (Hint: Show cos( θ 1 )/cos( θ 2 ) = cos( θ 1 )/cos( θ 2 ), then make use of Snell’s law once again. There are other ways to do this problem, so you don’t need to follow the hint. ) (c) In the case when the angle of deviation is a minimum, find an expression for a refractive index of the prism. Express the refraction index in terms of the minimum angle of deviation δ m and the apex angle α . This equation forms the basis of one of the most accurate techniques for determining the refractive index of a transparent substance. (d) Now a prism (n = 1.5 at λ o ) with an apex angle of 4° is immersed in a liquid (n = 1.3 at λ o ). If a laser beam at wavelength of λ o passes through this prism and is then reflected by a mirror (Fig. 1), how much do you need to rotate the mirror so that the reflected beam is parallel to the incoming laser beam? Note that here you have to modify the expression of δ given in the lecture note, since that expression is derived for the case when the prism is in the air (n = 1). 4 o

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2. In birefringent crystals such as quartz, there exists a direction called the optical axis . For light propagating in the crystal along a direction other than the optical axis, its polarization can be decomposed into the ordinary component that is perpendicular to the optical axis, and the
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HW2 - EE 119 Homework 2 Professor Jeff Bokor TA Xi Luo Due...

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