A ray of light travels from air into another medium, making an angle of 1 = 45.0

Question

A ray of light travels from air into another medium, making an angle of 1 = 45.0° with the normal as in the figure below.

http://www.webassign.net/serpse8/35-p-011.gif

(a) Find the angle of refraction 2 if the second medium is fused quartz. (The index of refraction for fused quartz is 1.458.)

(b) Find the angle of refraction 2 if the second medium is ice. (The index of refraction for ice is 1.309.)

(c) Find the angle of refraction 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= 0.485
theta2 = 29 degrees

(b). sin( theta1)/ sin(theta2) = 1.309 => sin(theta2) = sin(theta1) /1.309
sin(theta2) = sin(45) / 1.309= 0.5401
theta2 = 32.6 degrees

(c). sin( theta1)/ sin(theta2) = 1.49 => sin(theta2) = sin(theta1) /1.49
sin(theta2) = sin(45) / 1.49= 0.4745
theta2 = 28.32 degrees

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