(D) For a prism,the angle of the prism is given by $A = r_1 + r_2$.Since the ray emerges normally from the opposite surface,the angle of emergence $e

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(D) For a prism,the angle of the prism is given by $A = r_1 + r_2$.Since the ray emerges normally from the opposite surface,the angle of emergence $e = 0$,which implies the angle of refraction at the second surface $r_2 = 0$.Substituting $r_2 = 0$ into the prism equation,we get $r_1 = A$.Applying Snell's law at the first surface: $\sin i = \mu \sin r_1$.For small angles,$\sin i \approx i$ and $\sin r_1 \approx r_1$.Therefore,$i = \mu r_1$.Substituting $r_1 = A$,we get $i = \mu A$.

Class 12 Physics Ray Optics and Optical Instruments Refraction Through Prism

Medium

$A$ 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 $\mu$,then the angle of incidence is nearly equal to

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A
$\frac{\mu A}{2}$
B
$\frac{A}{2\mu}$
C
$\frac{2A}{\mu}$
D
$\mu A$

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Ray Optics and Optical Instruments

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Refraction Through Prism

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$A$ 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 $\mu$,then the angle of incidence is nearly equal to

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