At what angle of incidence should a ray be in | vedclass

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(C) For the ray not to emerge from the sphere,it must undergo total internal reflection at point $B$. At point $B$,the angle of incidence must be equa

Vedclass · Accepted Answer

$90^o$

Vedclass · Answer

(C) For the ray not to emerge from the sphere,it must undergo total internal reflection at point $B$. At point $B$,the angle of incidence must be equal to the critical angle $C$. In $	riangle OAB$,since $OA = OB$ (radii of the sphere),$\angle OAB = \angle OBA = C$. From the definition of the critical angle,$\sin C = 1/\mu = 1/(3/2) = 2/3$. Applying Snell's Law at point $A$: $1 \cdot \sin i = \mu \cdot \sin(\angle OAB) = \mu \cdot \sin C$. Substituting the values: $\sin i = (3/2) \cdot (2/3) = 1$. Therefore,$i = 90^o$.

At what angle of incidence should a ray be incident on a glass sphere of refractive index $3/2$ so that the ray does not emerge from the sphere?

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