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 :

Question

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 :, 1 0 0 π 1 8 0 %, 5 π 1 8 0 %, 5 0 π 1 8 0 %, 5 π 1 8 %

MARKS App · Accepted Answer

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 %

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