DIRECTIONS: Work the problem. You must show all work to receive credit, and you

Question

DIRECTIONS: Work the problem. You must show all work to receive credit, and you return this sheet. The problem is worth 20 points. If you have to construct a graph, use the graph paper provided in the laboratory. A student studying the index of refraction n was not able to find a semicircle like she used in the laboratory, so she did measurements on a rectangular block as shown. The block is in air. The angle ß was 65.0 degrees, a 2.50 cm, and n -2.10. From these data, determine (a) the value for d, b) the angle , and (c) the critical angle for tal internal reflection if light is incident from the block into air 90-m 90R

Explanation / Answer

a)theta = 90 - beta

theta = 90 - 65 = 25 deg

using trigonometry

tan(theta) = d/a

d = a tan(theta) = 2.5 x tan25 = 1.17 cm

Hence, d = 1.17 cm

b)Applying Snell's law:

n1 sin(theta1) = n2 sin(theta2)

n(air) sin(90 - alpha) = n(block) sin(90 - beta)

sin(90 - alpha) = 2.1 x sin25 = 0.8875

90 - alpha = sin^1(0.8875) = 62.56

alpha = 90 - 62.56 = 27.44

Hence, alpha = 27.44 deg

c)we know that the condition for total internal reflection for given setup is:

n(block) sin(theta-c) = n(air) sin90

sin(theta-c) = 1/2.1 = 0.4762

theta-c = sin^-1(0.4762) = 28.44 deg

Hence, theta-c = 28.44 deg

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