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A ray of light is incident at an angle of incidence, i on one face of a prism of angle A (assumed to be small) and emerges normally from the opposite face. If the refractive index of the prism is $\mu$, the angle of incidence i, is nearly equal to
A
$\frac{A}{2\mu}$
B
$\mu A$
C
$\frac{\mu A}{2}$
D
$\frac{A}{\mu}$
Detailed Solution
The ray emerges normally, so the angle of incidence at the second face $r_2 = 0$.
$r_1 + r_2 = A \Rightarrow r_1 = A$
Snell's law at the first face: $\sin i = \mu\sin r_1 = \mu\sin A$
For small angles $\sin i \approx i$ and $\sin A \approx A$, so $i \approx \mu A$
$r_1 + r_2 = A \Rightarrow r_1 = A$
Snell's law at the first face: $\sin i = \mu\sin r_1 = \mu\sin A$
For small angles $\sin i \approx i$ and $\sin A \approx A$, so $i \approx \mu A$