Fringe Width in Interference Pattern in Different Medium

To find the new fringe width when Young's double-slit experiment is conducted in a different medium, we analyze how the wavelength of light changes in that medium.

1. Fringe Width in Air (or Vacuum): The fringe width $\beta$ in Young's double-slit experiment is given by the formula: $\beta = \frac{\lambda D}{d}$ where:

• $\lambda$ is the wavelength of light in air,
• $D$ is the distance between the slits and the screen,
• $d$ is the distance between the two slits.

Given that the initial fringe width in air is $\beta = 2.4\text{ }\mu\text{m}$.

1. Fringe Width in a Medium: When the entire setup is immersed in a medium with refractive index $\mu = 1.2$, the wavelength of light in the medium changes to: $\lambda' = \frac{\lambda}{\mu}$

Since the geometrical parameters $D$ and $d$ remain unchanged, the new fringe width $\beta'$ in the medium is: $\beta' = \frac{\lambda' D}{d} = \frac{\left(\frac{\lambda}{\mu}\right) D}{d} = \frac{\beta}{\mu}$

1. Calculation: Substituting the given values into the formula: $\beta' = \frac{2.4\text{ }\mu\text{m}}{1.2} = 2\text{ }\mu\text{m}$

Thus, the fringe width will be $2\text{ }\mu\text{m}$, which corresponds to Option B.