Question

If fringe width obtained in a YDSE is 1.3mm. If the whole system is dipped in a liquid of refractive index 1.3, then the new fringe width will be:

• A. 1.3mm
• B. 1mm
• C. 1.6mm
• D. 0.8mm

Hint:

When the YDSE setup is dipped in a medium with a refractive index \( n \), the fringe width decreases by a factor of \( n \). The fringe width is directly proportional to the wavelength and inversely proportional to the refractive index of the medium.

Answer 1

The Correct Option is A

In Young's Double Slit Experiment (YDSE), the fringe width is given by the formula: \[ \beta = \frac{\lambda D}{d} \] Where: - \( \lambda \) is the wavelength of light, - \( D \) is the distance between the slits and the screen, - \( d \) is the distance between the slits. When the entire setup is dipped into a liquid with refractive index \( n \), the wavelength of light changes to \( \lambda' = \frac{\lambda}{n} \). The new fringe width is given by: \[ \beta' = \frac{\lambda' D}{d} = \frac{\lambda}{n} \times \frac{D}{d} = \frac{\beta}{n} \] Given that \( n = 1.3 \) and the initial fringe width \( \beta = 1.3 \, \text{mm} \), the new fringe width will be: \[ \beta' = \frac{1.3}{1.3} = 1.3 \, \text{mm} \] Thus, the new fringe width is 1.3mm.