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A horizontal ray of light is incident on the right angled prism with prism angle $6^\circ$. If the refractive index of the material of the prism is 1.5, then the angle of emergence will be: [add image]
A
$9^\circ$
B
$10^\circ$
C
$4^\circ$
D
$6^\circ$
Detailed Solution
For the given geometry, $A=r_1+r_2=6^\circ$. Since the incident ray is horizontal (normal incidence at the first face for this configuration), $r_1\approx0$, so $r_2\approx6^\circ$. Using $\mu=\dfrac{\sin e}{\sin r_2}$: $1.5=\dfrac{\sin e}{\sin6^\circ}\Rightarrow\sin e=1.5\sin6^\circ\Rightarrow e\approx9^\circ$ (using the small-angle approximation).