$(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} $

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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.

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