Question

In a Young's Double Slit Experiment, if the distance between the slits is halved and the distance to the screen is doubled, what happens to the fringe width?

• A. Doubled
• B. Halved
• C. Quadrupled
• D. Unchanged

Hint:

In Young's Double Slit Experiment, fringe width follows \[ \beta \propto \frac{D}{d} \] Increasing screen distance increases fringe width, while increasing slit separation decreases it.

Answer 1

The Correct Option is C

Concept: The fringe width in Young's Double Slit Experiment is given by \[ \beta = \frac{\lambda D}{d} \] where
• \( \lambda \) = wavelength of light
• \( D \) = distance between slit and screen
• \( d \) = distance between the slits

Step 1: Write the original fringe width. \[ \beta = \frac{\lambda D}{d} \]

Step 2: Apply the new conditions. Distance to screen is doubled: \[ D' = 2D \] Distance between slits is halved: \[ d' = \frac{d}{2} \]

Step 3: Substitute into the fringe width formula. \[ \beta' = \frac{\lambda D'}{d'} \] \[ \beta' = \frac{\lambda (2D)}{d/2} \] \[ \beta' = \frac{2\lambda D}{d/2} \] \[ \beta' = 4 \frac{\lambda D}{d} \] \[ \beta' = 4\beta \] Thus, the fringe width becomes four times the original value. \[ \boxed{\beta' = 4\beta} \]