What is the required condition, if the light incident on one face of a prism, does not emerge from the other face?

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TestHub · Accepted Answer

Consider the situation shown in figure.

Light rays $P Q$ is incident on the face $A B$ . It goes along $Q R$ and then along $R S$ .

Here,

$i =$ angle of incidence at the face $A B$

$r_{1} =$ angle of refraction through $A B$

$r_{2} =$ angle of incidence at $A C$

$n =$ refractive index of the material of the prims.

For the prism, we have

$r_{1} + r_{2} = A$ .....(i)

Now for light not to emerge from the face $A C,$

$r_{2} > C$

Similarly for no emergence from the face $A B,$

$r_{1} > C$

$\Rightarrow r_{1} + r_{2} > 2 C$

Here, $C$ is critical angle.

$\Rightarrow A > 2 C$ $[∵ r_{1} + r_{2} = A]$

$\Rightarrow \frac{A}{2} > C$

$\Rightarrow \sin \frac{A}{2} > \sin C$

$\Rightarrow \sin \frac{A}{2} > \frac{1}{n}$

$\Rightarrow n > \frac{1}{\sin \frac{A}{2}}$

$\Rightarrow n > cosec (\frac{A}{2})$

Physics - Geometrical Optics Question with Solution | TestHub

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