Question

An equilateral prism is lying on a prism table of a spectrometer in a minimum deviation position. If the angle of incidence is \[60^\circ \] , then the angle of deviation will be:
A. \[90^\circ \]
B. \[60^\circ \]
C. \[45^\circ \]
D. \[30^\circ \]

Answer 1

Hint:
First of all, we will find the expression of deviation which relates incident angle, emergent angle and angle of the prism. In case of minimum deviation, the angle of incidence and the angle of emergence is equal. We will manipulate the expression accordingly and obtain the result.

Complete step by step solution:

In the given question, we are supplied with the following data:
The prism is equilateral in shape and hence its all the angles are equal to \[60^\circ \] .
The angle of incidence is \[60^\circ \] .
We are asked to find the angle of deviation.

We have a formula which gives angle of deviation:
\[\delta = {i_1} + {i_2} - A\] …… (1)
Where,
\[\delta \] indicates the angle of deviation.
\[{i_1}\] indicates the angle of incidence.
\[{i_2}\] indicates the angle of emergence.
\[A\] indicates the angle of the prism.

We know, for the case of minimum deviation:
The angle of incidence is equal to the angle of emergence. So, we can write the equation (1) as:
 $ \delta = {i_1} + {i_2} - A \\
  \delta = {i_1} + {i_1} - A \\ $
\[\delta = 2{i_1} - A\] …… (2)

Now, we substitute the required values in the equation (2), we get:
  $ \delta = 2{i_1} - A \\
  \delta = 2 \times 60^\circ - 60^\circ \\
  \delta = 120^\circ - 60^\circ \\
  \delta = 60^\circ $

Hence, the angle of deviation is \[60^\circ \] .
The correct option is B.

Additional information:
A transparent optical element with flat, polished surfaces that refract light is an optical prism. Elements with two parallel surfaces are not prisms; at least one surface must be angled. To split white light into its constituent spectral colours (the colours of the rainbow), a dispersive prism can be used. In addition, it is possible to use prisms to reflect light or divide light into components with different polarizations.

Note:
While solving this problem, it is important to note that in case of minimum deviation the incident angle is equal to the angle of emergence. In a prism, deviation is formed. When a beam of light passes a mirror, it deviates, as the refractive index increases.