# HW5SP12 - assuming that µ 1 = 2 = o . Confirm that R + T =...

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Physics 4322 Homework Set 5 February 21, 2012 Due: Tuesday, February 28, 2012 1. Suppose that two strings are tied together by a knot having mass m . Formulate an appropriate boundary condition that would replace the continuity of the derivative. 2. The intensity of sunlight hitting the earth is about 1300 W/m 2 . If sunlight strikes a perfect absorber, what pressure does it exert? Do the same calculation for a perfect reflector. What fraction of atmospheric pressure does this represent? 3. In the complex notation, there is a handy way of calculating the time average of a product. Suppose f ( r , t ) = A cos( k · r ω t ) and g ( r , t ) = B cos( k · r t ). Show that < fg > = (1/2)Re( fg *), where * denotes the complex conjugate. 4. Find all elements of the Maxwell stress tensor for a monochromatic plane wave traveling in the z direction and linearly polarized with E along x ^ . Interpret your answer. 5. For the case of normal incidence calculate the reflection and transmission coefficients without
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Unformatted text preview: assuming that µ 1 = 2 = o . Confirm that R + T = 1. For those of you who have had optics, R and T are generally referred to as reflectance and transmittance. The names reflection and transmission coefficients are generally reserved for the amplitudes. 6. Suppose Ae iax + Be ibx = Ce icx for some nonzero constants, A , B , C , a , b , and c for all x . Prove that a = b = c and that A + B = C . 7. A beam of monochromatic light is incident on an air-glass interface (n g =1.50) with the angle of incidence at 40 o . Calculate the reflectance for light with E parallel to and with E perpendicular to the plane of incidence. 8. Light is incident on an air-diamond (n = 2.42) interface. (a) Calculate the reflectance and transmittance at normal incidence. (b) What is Brewster’s angle?...
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## This note was uploaded on 02/20/2012 for the course PHYS 1101 taught by Professor Lowellwood during the Fall '10 term at University of Houston.

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