Question

The variation of refractive index of a crown glass thin prism with wavelength of the incident light is shown. Which of the following graphs is the correct one, if $D_m$ is the angle of minimum deviation?

• A.

  

• B.

  

• C.

  

• D.

  

Answer 1

The Correct Option is B

To determine the correct graph for the angle of minimum deviation \(D_m\) of a crown glass prism as a function of wavelength, we first need to understand the relationship between the refractive index \(n\) and the angle of minimum deviation \(D_m\). 

The angle of minimum deviation \(D_m\) for a prism is given by the formula:

\(D_m = (n - 1)A\)

where \(A\) is the prism angle and \(n\) is the refractive index of the material.

For dispersive materials like crown glass, the refractive index decreases with an increase in the wavelength of light. This phenomenon is due to dispersion, where different wavelengths of light are refracted by different amounts.

Since \(D_m\) is directly proportional to \((n - 1)\), \(D_m\) will also decrease as the wavelength increases because the refractive index \(n\) decreases with increasing wavelength. This behavior is typical for normal dispersion in materials like crown glass.

Thus, the graph of \(D_m\) versus wavelength should show a decreasing trend, which corresponds with the choice of a graph that shows a decreasing function.

The correct graph, as per the problem, is:

This graph shows that as the wavelength increases, the angle of minimum deviation \(D_m\) decreases, consistent with the relationship between refractive index and wavelength in crown glass.