Question

In a Young's double slit experiment, a student observes 8 fringes in a certain segment of screen when a monochromatic light of 600 nm wavelength is used. If the wavelength of light is changed to 400 nm, then the number of fringes he would observe in the same region of the screen is

• A. 6
• B. 8
• C. 9
• D. 12

Answer 1

The Correct Option is D

In a Young's double slit experiment, the number of fringes observed in a segment of the screen is directly related to the wavelength of the light used. The relationship between the number of fringes \( n \), wavelength \( \lambda \), and constant region width \( w \) can be expressed as follows:

\[ n \propto \frac{1}{\lambda} \]

Given that the initial wavelength \( \lambda_1 = 600 \) nm results in 8 fringes, when the wavelength is changed to \( \lambda_2 = 400 \) nm, we can use the ratio of wavelengths to find the new number of fringes \( n_2 \):

\[\frac{n_1}{n_2} = \frac{\lambda_2}{\lambda_1}\]

Substitute the known values:

\[\frac{8}{n_2} = \frac{400}{600}\]

Simplifying gives:

\[\frac{8}{n_2} = \frac{2}{3}\]

Therefore, solving for \( n_2 \):

\[n_2 = 8 \times \frac{3}{2} = 12\]

Hence, the student would observe 12 fringes when the wavelength is changed to 400 nm.