Answer to Question #248995 in Optics for Angel

Question

A prism has a refracting angle of 60° and a refractive index of 1.60. Calculate the angle of incidence on the first face for a ray that is just totally reflected at the second face of the prism. 

A ray is incident at 30° to the normal of a flat piece of uniformly thick glass, as shown in the figure below. If the refractive index of glass is 1.66,

 

 

(a)   What is the angle of refraction in the glass?                     [2]

(b)   What is the angle at which the ray emerges from the glass?            [3]

Answer 1

1)

$\sin\theta=\frac 1n=\frac 1{1.6},\implies \theta=38.7°,$

$r_1=60°-38.7°=21.3°,$

$\frac{\sin i}{\sin r_1}=n,\implies i=35.5°.$

2)

$\alpha=30°,~n=1.66,$

a)

$\frac{\sin\alpha}{\sin \beta}=n,\implies \beta=17.5°,$

b)

$\gamma=\alpha=30°.$