Question

It has been mentioned that two beams of red and violet colours are produced to pass separately through a prism (angle of the prism will be $60{}^\circ $). What will be the angle of refraction in the position of minimum deviation?
A. $30{}^\circ $ for both the colours.
B. greater for the violet colour.
C. greater for the red colour.
D. equivalent but not $30{}^\circ $for both the colours.

Answer 1

Hint: The angle of minimum deviation can be defined as the smallest angle through which the light will be bent by an optical instrument or a system. In the case of a prism, the angle of deviation will be a minimum when the incident and emerging rays form identical angles with the faces of the prism. This will help you in answering this question.

Complete step by step answer:
The angle of minimum deviation can be defined as the smallest angle through which the light will be bent by an optical instrument or a system. In the case of a prism, the angle of deviation will be a minimum when the incident and emerging rays form identical angles with the faces of prism. During the minimum deviation, we can write that,
${{r}_{1}}={{r}_{2}}=\dfrac{A}{2}$
It has been already given in the question that, the angle of the prism will be,
$A=60{}^\circ $
Substituting this values in the equation can be shown as,
\[{{r}_{1}}={{r}_{2}}=\dfrac{60}{2}=30{}^\circ \]
Therefore the angle of refraction will be independent of the colour and $30{}^\circ $for both the colours.

So, the correct answer is “Option A”.

Note: The angle of incidence will be identical to the angle of refraction only when the angle the deviation is zero. This will be practically impossible because if the light enters a medium from another medium it must undergo the process of refraction. Therefore the angle of minimum deviation will never be zero even though it can be a very small value.