A ray of light travels from air into another medium, making an angle of theta_1

Question

A ray of light travels from air into another medium, making an angle of theta_1 = 45.0 degree with the normal as in the figure below. Find the angle of refraction theta_2 the second medium is fused quartz. (The index of refraction for fused quartz is 1.458.) Find the angle of refraction theta_2 if the second medium is flint glass. (The index fo refraction for flint glass is 1.66.) Find the angle of refraction theta_2 if the second medium is polystyrene. (The index of refraction for polystyrene is 1.49.)

Explanation / Answer

Apply Snell's law, noting that the ray will be refracted to a smaller angle with the normal when the second medium is optically more dense ( theta2 smaller than theta1):

(a). sin( theta1)/ sin(theta2) = 1.458 => sin(theta2) = sin(theta1) /1.458
sin(theta2) = sin(45) / 1.458= 0.484984
theta2 = 29.01 degrees

b) sin(theta2) = sin(45) / 1.66 = 0.42596793975

theta2 = 25.21 degrees

c)

sin(theta2) = sin(45) / 1.49 = 0.47456830872

theta2 = 28.33 degrees

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