A light beam incident generally on the face AB is reflected to reach on the face BC if
\(\begin{array}{l} \Theta \geq \Theta _{c} \end{array} \)
The beam is grazed on face BC, e =
\(\begin{array}{l} 90^{\circ} \end{array} \)
Refractive index of water,
\(\begin{array}{l} n_{1} = \frac{4}{3} \end{array} \)
Refractive index of prism,
\(\begin{array}{l} n_{2} = 1.5 \end{array} \)
By using Snell’s law of refraction,
\(\begin{array}{l} n_{2}sin\Theta _{c} = n_{1}sin e \end{array} \)
=
\(\begin{array}{l} sin\Theta _{c} = \frac{8}{9} \end{array} \)
For total internal reflection,
\(\begin{array}{l} sin\Theta \geq sin\Theta_{c} \end{array} \)
Hence,
\(\begin{array}{l} sin\Theta \geq \frac{8}{9} \end{array} \)
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