Question #248995

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]

1
Expert's answer
2021-10-10T15:55:51-0400

1)

sinθ=1n=11.6,    θ=38.7°,\sin\theta=\frac 1n=\frac 1{1.6},\implies \theta=38.7°,

r1=60°38.7°=21.3°,r_1=60°-38.7°=21.3°,

sinisinr1=n,    i=35.5°.\frac{\sin i}{\sin r_1}=n,\implies i=35.5°.

2)

α=30°, n=1.66,\alpha=30°,~n=1.66,

a)

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

b)

γ=α=30°.\gamma=\alpha=30°.


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