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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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