A ray of light travelling in air is incident at grazing angle on a slab of 3 m thickness with variable refractive index, n ( y ) = [ k y 3/2 + 1 ] 1/2 where k = 1 m − 3/2 and follows path as shown. Th

Question

A ray of light travelling in air is incident at grazing angle on a slab of 3 m thickness with variable refractive index, $n (y) = [k y^{3/2} + 1]^{1/2}$ where $k = 1 m^{- 3/2}$ and follows path as shown. The total deviation (in anticlockwise direction) produced by the slab when the ray is at $A (y = 1 m)$ is $(α + 1) \times (2 α + 1)$ , in degrees then find the value of $α . (α > 0)$

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In a graded slab n ( y ) sin i ( y ) stays constant along the ray (Snell invariant), with grazing entry at the bottom. Applying this at A (y = 1 m) and summing the bending through the slab gives total anticlockwise deviation 4 5 ∘ . ( α + 1 ) ( 2 α + 1 ) = 45 gives the positive root α = 4 . Answer: 4.

Physics - Geometrical Optics Question with Solution | TestHub

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