A ray of light travelling in air is incident at grazing angle on a long rectangular slab
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Explanation: Trajectory of the curve is shown by dotted curve the slope of the target at point B
Tan Ф= dy /dx
The angle of incidence at B is Ф = 90- Ф
Tan Ф = tan (90- Ф) = cot Ф= dy /dx
From snell law at A and B
1 sin 90 = n(y) sin Ф
sin Ф= 1/n (y) = {1/ ky ³/² +1 }1/2
cos Ф= √1-sin ²Ф= √1-{ 1/ky³/² + 1 }1/2
cot Ф= k 1/2 y ³/4
Applying boundary condition
x= 0, y=0, c=0
4y 1/4 =√kx
y 1/4 = (√kx
y = k²(x/4 )⁴
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