Question

Angle of minimum deviation is equal to the angle of prism A of an equilateral glass prism. The angle of incidence at which minimum deviation will be obtained will be obtained as
A. ${{60}^{{}^\circ }}$
B. ${{30}^{{}^\circ }}$
C. ${{45}^{{}^\circ }}$
D. ${{\sin }^{-1}}(\dfrac{2}{3})$

Answer 1

Hint: Find the angle of the prism and angle of minimum deviation from the information given in the question. Calculate the answer by using the formula for angle of incidence in case of minimum deviation. Understand the concept of the prism and what happens to light when it is incident on the prism.

Complete answer:
We have an equilateral glass prism, therefore, angle of prism = A = ${{60}^{{}^\circ }}$
Given that angle of minimum deviation is equal to the angle of the prism, therefore,
${{\delta }_{m}}=A={{60}^{{}^\circ }}$
At the minimum deviation position, the angle of incidence is given as
$i=(\dfrac{A+{{\delta }_{m}}}{2})$
Therefore,
$\begin{align}
  & i=(\dfrac{{{60}^{{}^\circ }}+{{60}^{{}^\circ }}}{2}) \\
 & i={{60}^{{}^\circ }} \\
\end{align}$
Option A is correct , ${{60}^{{}^\circ }}$

Additional Information:
A prism is a three dimensional object that has two triangular faces and three rectangular faces joined together. In the prism, the base rest of the sides are perfectly transparent. While traveling through the prism, the light gets deviated from its original path and splits into its constituent wavelengths (colour). This phenomenon is called the dispersion of light. The speed of light is changed when it travels through the prism.
Types of prisms:
There are four main types of prisms:
1. Dispersion prisms
2. Deviation or reflection prisms
3. Rotation prisms
4. Displacement prisms.

Note: Different types of prisms are available in the market. An equilateral prism has an angle of prism equal to ${{60}^{{}^\circ }}$. Prisms are used in many applications such as spectroscopy, telescope, surveying equipment, wavelength separation, telecommunication, etc. The angle at which the deviation of the incident ray is minimum is called the angle of minimum deviation.