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.
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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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