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A ray incident at 15⁰ on one refracting surface of a prism of angle 60⁰ suffers a deviation of 55⁰. What is the angle of emergence?
A. 90⁰
B. 45⁰
C. 30⁰
D. None of these

Last updated date: 13th Jun 2024
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Hint: In a prism, the sum of angle of incidence and angle of emergence is equal to the sum of angle of a prism and angle of deviation.

Complete step by step answer:
A prism is a transparent refracting medium bounded by two plane surfaces inclined at some angle. The light passes through these refracting surfaces. A ray is incident at one side of a prism making an angle of incidence i=15⁰. When the ray enters the prism, it bends towards the normal because the ray enters from a rarer (air) to denser medium (glass). Now, this ray strikes the other refracting surface and it travels from denser (glass) to rarer (air) medium. So, it bends away from the normal and emerges out of the prism at an angle of emergence e. The angle of a prism A = 60⁰. In the absence of the prism, the incident ray would have travelled straight but due to the prism, it deviates from its path. The angle between the direction of incident ray (the direction in which it would have travelled in the absence of prism) and emergent ray (when it is produced backwards) is called angle of deviation δ. The required formula is angle of incidence (i) + angle of emergence (e) = angle of prism (A) + angle of deviation (δ).

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$i + e = A + \delta $
${15^ \circ } + e = {60^ \circ } + {55^ \circ }$
${15^ \circ } + e = {115^ \circ }$
$e = {115^ \circ } - {15^ \circ }$
$e = {100^ \circ }$
angle of emergence = ${100^ \circ }$
Therefore, option D is correct.

Note:When a ray travels from rarer to denser medium, the refracted ray bends towards the normal and when it travels from denser to rarer medium, the emergent ray bends away from the normal.