NEET Class neet Answered
How to calculate refractive index of prism
Asked by Prashant DIGHE | 08 Jul, 2019, 05:29: PM
Expert Answer
If we assume light ray makes incident angle at side PR nearly equal to critical angle c,
then we have, sin c = 1/μ ...............(1)
at side QR, if r is angle of incidence, then we have,
( sinα / sin r ) = μ , since α=30° . we have, sin r = 1(2μ) .............. (2)
As per geometry shown in figure, we have (90-c) + (90-r) = 120° or c + r = 60°
sin(c+r) = sin 60 = √3/2 ...........................(3)
eqn.(3) can be written as, ( sin c )( cos r ) + ( cos c )( sin r ) = √3/2 ................(4)
using eqns.(1) and (2), eqn.(4) is re written as,
It can be verified that the substitution, μ2 = 7/3 satisfies the eqn.(5).
Hence refractive index μ of material of prism is given by, μ = (7/3)1/2
Answered by Thiyagarajan K | 08 Jul, 2019, 08:59: PM
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