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 [latex] \Theta \geq \Theta _{c} [/latex]

The beam is grazed on face BC, e = [latex] 90^{\circ} [/latex]

Refractive index of water, [latex] n_{1} = \frac{4}{3} [/latex]

Refractive index of prism, [latex] n_{2} = 1.5 [/latex]

By using Snell’s law of refraction,

[latex] n_{2}sin\Theta _{c} = n_{1}sin e [/latex]

= [latex] sin\Theta _{c} = \frac{8}{9} [/latex]

For total internal reflection, [latex] sin\Theta \geq sin\Theta_{c} [/latex]

Hence, [latex] sin\Theta \geq \frac{8}{9} [/latex]

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