Answer to Question #201484 in Physics for Lex

Question

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A light beam makes an angle of 60 degrees to the normal as it strikes a transparent substance. Part of the beam is reflected from the surface into the air (n = 1) and part is refracted through the substance. The reflected and the refracted beams make an angle of 90 degrees with each other.

  a. Calculate the index of refraction of the substance.

 

 

  b. Calculate the critical angle for light leaving the substance and going into a material with an index of refraction of 1.30

Answer 1

a. The incident ray is 60° to the normal, so is the reflected ray. Thus, the refracted ray is

$$\theta_r=180°-60°-90°=30°.$$

According to Snell's law:

$$\frac{n_1}{n_2}=\frac{\sin\theta_i}{\sin\theta_r},\\\space\\ n_1=1.73.$$

b. The critical angle for the total internal reflection is

$$\theta_c=\arcsin(n_2/n_1)=\arcsin(1.3/1.73)=48.7°.$$