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Asked by adjacentcalliber10 | 10 May, 2019, 11:32: AM
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Let the medium has variable refractive index along y-direction and trajectory of light ray y = 2x2  as shown in figure.
 
At depth 1 m, its slope dy/dx = 4x = 4/√2 = 2√2  ..................(1)
 
we have for variable refractive index, begin mathsize 12px style fraction numerator d y over denominator d x end fraction equals space fraction numerator square root of mu subscript y superscript 2 space minus space sin squared theta end root over denominator sin begin display style theta end style end fraction space end style .................(2)
for grazing incidence at O, we have sinθ = sin 90 = 1 and using eqn.(1) and (2) we get  begin mathsize 12px style 2 square root of 2 equals space square root of mu subscript y superscript 2 space minus space 1 end root space space o r space mu subscript y space equals space 3 end style
slope dy/dx at y=1 m is 2√2 m . Hence as shown in figure PB/AB = 2√2 or  PA = 3 m . 
 
Hence angle of incidence i = sin-1(1/3)
Answered by Thiyagarajan K | 11 May, 2019, 14:19: PM

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