A ray is incident at an angle of incidence on one surface of a small angle prism (with angle of prism A) and emerges normally from the opposite surface. If the refractive index of the material of the prism is , then the angle of incidence is nearly equal

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Solution

Q.
A ray is incident at an angle of incidence $i$ on one surface of a small angle prism (with angle of prism A) and emerges normally from the opposite surface. If the refractive index of the material of the prism is $μ$ , then the angle of incidence is nearly equal to [2020]

1 $A / 2 μ$

2 $2 A / μ$

3 $μ A$

4 $μ A / 2$

Ans.
(3)

Light ray emerges normally from another surface, so the angle of emergence (e) = 0.

$r_{2} = 0 \Rightarrow r_{1} + r_{2} = A \Rightarrow r_{1} = A$

Using Snell’s law on the first surface, $1 \times \sin i = μ \sin r_{1}$

$\sin i = μ \sin A$

For small angles, $\sin A \approx A$

Hence, $i = μ A$

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