a ) 2 tan μ
b ) 2 tan-1 μ
c ) 2 cot-1 μ
Solution :
Given :
δ m = π – 2 A
The refractive index of prism can be given as
μ = { sin [ ( δ m + A ) / 2 ] } / { sin ( A / 2 ) }
putting the value of δ m in above equation we get,
μ = { sin [ ( π – 2 A ) + A ) / 2 ] } / { sin ( A / 2 ) }
μ = { sin [ ( π + A ) / 2 ] } / { sin ( A / 2 ) }
μ = { sin [ ( π / 2 ) + ( A / 2 ) ] } / { sin ( A / 2 ) }
but, We know that
sin [ ( π / 2 ) + θ ] = cos θ
Therefore above equation becomes,
μ = { cos ( A / 2 ) } / { sin ( A / 2 ) }
μ = { cot ( A / 2 ) }
( A / 2 ) = cot - 1 μ
A = 2 cot – 1 μ
The angle of prism = A = 2 cot – 1 μ.
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