A Glass Prism Of Refractive Index 1.5 Is Immersed In Water (Refractive Index 4/3). A Light Beam Normally On The Face Ab Is Totally Reflected To Reach On The Face Bc If

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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