IIT JEE , AIEEE Forum - Physics , Optics

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Using Snell's Law : n(sini) = constant

This constant can be calculated at (0,0) which comes out to 1(sin90⁰) = 1

(ky^3/2+1)^1/2(sini) = 1

If we take slab to be made of small infinte layers and concentrate on any intermediate layer where angle of incidence is i, the incident ray makes an angle of 90⁰-i with x-axis. Let 90⁰-i =

where tan

= dy/dx

Now sini = (ky^3/2+1)^-1/2 = (y^3/2+1)^-1/2 since k = 1

Hence coti = y^3/4

cot(90⁰ -

) = y^3/4

tan

= dy/dx = y^3/4

y^-3/4dy = dx

Integrating both sides we get

x = 4y^1/4 + c

Since it passes through (0,0) hence c = 0

hence equation of trajectory : x = 4y^1/4

Ray intersects the upper surface of the slab at y = 1.0 m

which gives x = 4.0 m

Hence it intersects the upper surface of the slab at (4,1)

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