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The refractive index of material of prism is given by μ=sinA+Dm2sinA2,A&Dm have their usual meanings. A glass prism of A=600 gives minimum angle of deviation at 300 with maximum error of 10, when a beam of parallel light passed through prism during experiment. Then percentage error in the measurement of μ of material of prism is

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a

0.87%

b

2.22%

c

3.11%

d

1.65%

answer is A.

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Detailed Solution

⇒μ=SinA+δ2SinA2=Sin60+302Sin602=1212=2After differentiating we get,dμ=1sinA2cosA+Dm2.dδ2 =cosecA2cosA+Dm2.dδ2 =cosec602cos60+302.1°2 =cosec30cos45.1°2×π180=π1802dμμ×100=π18022×100=π360×100=0.872%

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