devarshi-dt-logo

Question:

A ray PQ incident on the refracting face BA is refracted in the prism BAC as shown 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.

Solution:

As AQ=AR it means ray QR is parallel to the base BC, hence the prism is in the position of minimum deviation ,now μ=sin(A+θ)/2sinA/2 given μ=√3, A=60° therefore √3=sin(60+θ)/2sin60/2 or sin(60+θ)/2=√3×sin30 or sin(60+θ)/2=√3/2=sin60 or (60+θ)=120 or θ=60°