A glass prism of angle A = 6 0 ∘ gives a minimum angle of deviation θ = 3 0 ∘ with the maximum error of 1 ∘ when a beam of parallel light passed through the prism during an experiment. The permissible error in the measurement of refractive index μ of the material of the prism is :

Step-by-step solution

μ = sin δ + A 2 sin A 2 , where δ is the minimum deviation d μ dδ = cos δ + A 2 2sin A 2 ⇒    d μ μ = cos  δ + A 2 2sin  δ + A 2 d δ ⇒    d μ μ = 1 2 cot δ + A 2 dδ δ + A 2 = 45 ° ⇒    d μ μ × 100 = 1 2 cot 45 ° π 180 ×100 Percentage error = 5 π 1 8 %