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# A right angled prism ABC is dipped in water . such that the surface AB is in air as shown. A ray of light is normally. What must be the possible value of $\theta$ so that the say gets totally reflected at AC to reach surface BC.

$(a)\;\sin \theta \geq \frac{8}{9} \\ (b)\;\frac{2}{3} < \sin \theta < \frac{8}{9} \\ (c)\;\sin \theta \leq \frac{2}{3} \\ (d)\;\sin \theta \geq \frac{4}{3}$

At D if total internal reflection just takes place, when the refracted ray just grazes the surface.
$\large\frac{3}{2}$$\sin \theta =\large\frac{4}{3}$$ \sin 90$
$\sin \theta =\large\frac{4}{3} \times \frac{2}{3}$
$\qquad= \large\frac{8}{9}$
So the value of $\theta$ for total internal reflection $\sin \theta \geq \large\frac{8}{9}$
Hence a is the correct answer.