Comparison of Fringe Widths for Different Light Wavelengths

In Young's double slit experiment, the fringe width $\beta$ is given by the formula: $\beta = \frac{\lambda D}{d}$

where:

• $\lambda$ is the wavelength of the light used,
• $D$ is the distance between the plane of the slits and the screen,
• $d$ is the separation between the two slits.

Since the experimental setup remains unchanged ($D$ and $d$ are constant), the fringe width is directly proportional to the wavelength of the light: $\beta \propto \lambda$

In the visible spectrum, the wavelengths of red, green, and blue light satisfy the inequality: $\lambda_R > \lambda_G > \lambda_B$

Since fringe width is directly proportional to wavelength, the corresponding fringe widths must satisfy the same relation: $\beta_R > \beta_G > \beta_B$

Thus, option (D) is the correct relation.