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Q.

A ray incident on a droplet of water at an angle of incidence i  undergoes two reflections (not total) and emerges. If the deviation suffered by the ray within the drop is minimum and the refractive index of the droplet be  μ,  then  cosi=μ21x. x is

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answer is 8.

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Detailed Solution

 δTotal=δRefraction+2δReflection+δRefraction
or   δ=(ir)+2(180°2r)+(ir)
 =360°+2i6r
 =360°+2i6sin1(siniμ)
For deviation to be minimum,  dδdi=0
By putting first derivative of  δ  (w.r.t. i) equal to zero, we get the desired result.

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