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How to calculate refractive index of prism
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Asked by Prashant DIGHE | 08 Jul, 2019, 17:29: PM
answered-by-expert 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,
 
begin mathsize 12px style 1 over mu square root of 1 space minus space fraction numerator 1 over denominator 4 mu squared end fraction end root space plus space fraction numerator 1 over denominator 2 mu end fraction square root of 1 space minus space 1 over mu squared end root space equals space fraction numerator square root of 3 over denominator 2 end fraction square root of 4 mu squared minus 1 end root space plus square root of mu squared minus 1 end root space equals space square root of 3 space mu squared space.................. left parenthesis 5 right parenthesis end style
 
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, 20:59: PM

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