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# A ray of light undergoes deviation of 30∘ when incident on an equilateral prism of refractive index √2. The angle made by the ray inside the prism with the base of the prism is:

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Solution

## Given: A ray of light undergoes deviation of 30∘ when incident on an equilateral prism of refractive index √2.To find the angle made by the ray inside the prism with the base of the prism.Solution:As per the given criteria,angle of deviation, δ=30∘refractive index of the prism, μ=√2As the prism is equilateral, the refractive angle, A=60∘And we know,μ=sin(A+δm2)sinA2Substituting the values, we get√2=sin(60+δm2)sin602⟹√2=sin(60+δm2)sin30⟹√2×12=sin(60+δm2)⟹60+δm2=sin−1(1√2)⟹60+δm2=45⟹δm=90−60=30∘Hence the minimum deviation angle is equal to the deviation angle, hence at minimum deviation condition the ray travels parallel to the base inside the prism.The angle between the ray and base inside the prism is zero.

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