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Asked by sarveshvibrantacademy | 02 May, 2019, 11:59: AM
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Left side figure shows the normal incident ray on first surface makes an angle of incidence that eqauls to angle of prism A.
 
Hence if we apply, law of refraction at second surface for grazing emergent ray, 
 
μ = sin(90)/sin(A) = 1/sin(A)  ................(1)
 
where μ is refractive index of material of prism.
 
Right side figure shows when half of right side prism is knocked out, the normal incident ray on first surface makes
angle of incidence A/2 on second surface.
 
Hence angle of emergence r is given by,   sin(r)/sin(A/2) = μ   ........................(2)
 
from eqn.(1) and eqn.(2),   sin(r) = sin(A/2) / sinA  = (1/2) sec(A/2)
 
hence angle of emergence from half-prism,   r = sin-1[ (1/2) sec(A/2) ]
Answered by Thiyagarajan K | 02 May, 2019, 13:38: PM

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