Question

In a classic Young’s Double Slit Experiment, how does the fringe width change if the entire apparatus is immersed in water?

• A. Fringe width increases
• B. Fringe width decreases
• C. Fringe width remains unchanged
• D. Fringe width becomes infinite

Hint:

In YDSE, if the experiment is performed in a medium with refractive index \(n\), the new fringe width becomes \[ \beta' = \frac{\beta}{n} \] Hence fringe width decreases.

Answer 1

The Correct Option is B

Concept: In Young’s Double Slit Experiment (YDSE), the fringe width \(\beta\) is given by \[ \beta = \frac{\lambda D}{d} \] where

• \(\lambda\) = wavelength of light
• \(D\) = distance between the screen and slits
• \(d\) = separation between the slits

Step 1: Effect of medium on wavelength.} When light enters a medium like water with refractive index \(n\), its wavelength changes according to \[ \lambda' = \frac{\lambda}{n} \]
Step 2: Substitute new wavelength in fringe width formula.} \[ \beta' = \frac{\lambda' D}{d} \] \[ \beta' = \frac{\lambda D}{nd} \]
Step 3: Compare fringe widths.} \[ \beta' = \frac{\beta}{n} \] Since \(n>1\) for water, the fringe width becomes smaller. Thus, the fringe width decreases.