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Q.

A medium is separated from other medium of refractive index μ0 by x-z plane. Refractive index of the medium varies as  μ=μ0μ1y+μ2y2, choose the CORRECT statement(s). A ray is incident from the other medium to this medium ( μ0,μ1&μ2 are positive):-

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a

Ray will definitely return in the medium of refractive index  μ0.

b

Ray will never return in the medium of refractive index μ0 for any value of  θ,μ1&μ2

c

If ray crosses a particular y, then it will never return to medium having refractive index  μ0.

d

For ray to not return in medium of refractive index  μ0,θ<sin1[1μ124μ0μ2]

answer is C, D.

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Detailed Solution

If  μmin is such that ray suffers TIR at that point it will return to medium having refractive index  μ0
 μmin=4μ0μ2μ124μ2=μ0μ124μ2
 For no TIR,
μ0sinθ(μ0μ124μ2) θsin1[1μ124μ0μ2]
μmin will be at  y=μ12μ2

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