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=μ2-1x. Find the value of x.

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answer is 0008.00.

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Detailed Solution

δTotal =δRefraction +2δReflection +δRefraction ​⇒δ=i−r+2180°−2r+i−r​⇒δ=360°+2i−6r​⇒δ=360°+2i−6sin−1siniμ​ For deviation to be minimum, dδdi=0​⇒2−61−siniμ2cosiμ=0​⇒cosi=μ2−18​∴x=8
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