Question

A ray PQ incident on the refracting face BA is refracted in the prism in the figure and emerges from the other refracting face AC as RS such that AQ=AR. If the angle of prism A= 60° and refractive index of material of prism is √3, calculate angle θ.

Answer 1

The angle θ = 60°

Explanation:

PQ = incident ray

RS = Emergent ray

∟A=60 degrees

μ = ​√3

AQ= QR

∟AQR=∟ARQ

Therefore the opposite angles are also equal.

i1 = i2

r1 = r2

• Using the formula:

μ= Sin(A+Dm)/2/SinA/2

​√3=Sin(60+Dm)/2 / Sin60/2

​√3×Sin(30)= Sin(60+Dm)/2

​√3/2 = Sin ( 60 +Dm)/2

sin^-1(​√3/2)=(60+Dm)/2

i = 60°

θ = i + e - A

θ = 60 + 60 - 60

θ = 60°

Thus the angle θ = 60°

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