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  • A glass prism of refractive index 1.56 is immersed in water <img alt="\mathrm{(R . I .=4 / 3)}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%28R%20.%20I%20.%3D4%20/%203%29%7D"

A glass prism of refractive index 1.56 is immersed in water \mathrm{(R . I .=4 / 3)}.The beam of light incident normally on the face \mathrm{A B}  is totally reflected to reach the face \mathrm{BC}, if

Option: 1

\sin \theta \geq 8 / 9


Option: 2

\operatorname{Sin} \theta<2 / 3


Option: 3

2 / 3<\sin \theta<8 / 9


Option: 4

None of these


Answers (1)

best_answer

The light ray is just reflected internally at the point \mathrm{P} (say). Therefore the critical angle \mathrm{\cong \theta}.Applying Snell's Law of refraction at the critical angle of incidence \mathrm{(\theta)} we obtain


\frac{\sin \theta}{\operatorname{Sin} 90}=\frac{\mathrm{n}_{\mathrm{w}}}{\mathrm{n}_{\mathrm{g}}} \quad \Rightarrow \quad \sin \theta=\frac{4 / 3}{3 / 2}=\frac{8}{9}
\Rightarrow \quad \theta \leq \sin ^{-1} \frac{8}{9}

\therefore \mathrm{D}

Posted by

himanshu.meshram

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