First slide

Prism

Question

Two identical thin isosceles prisms of refracting angle ‘A’ and refractive index $μ$ are placed with their bases touching each other. Two parallel rays of light are incident on this system as shown. The distance of the point where the rays converge from the prism is:

Moderate

A

$\frac{h}{μ A}$
B

$\frac{h}{A}$
C

$\frac{h}{(μ - 1) A}$
D

$\frac{μ h}{(μ - 1) A}$

Solution

Given
Angle of prism = A
Refractive index= $μ$
Minimum deviation $δ_{1} = (μ - 1) A$
$\begin{array}{l} δ_{2} = (μ - 1) A \\ \tan δ_{1} = \frac{h}{b} \\ b = \frac{h}{\tan δ_{1}} \\ = \frac{h}{\tan ((μ - 1) A)} \\ As prism is thin. So \tan ((μ - 1) A) = (μ - 1) A \end{array}$
$∴ b = \frac{h}{(μ - 1) A} (f r o m t h e p r i s m)$

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