Question

In a Young's Double Slit Experiment, find the fringe width if the distance between slits is doubled and the screen distance is halved.

• A. Fringe width becomes half
• B. Fringe width becomes one-fourth
• C. Fringe width remains unchanged
• D. Fringe width becomes double

Hint:

In YDSE problems, always remember the proportional relation \( \beta \propto \frac{D}{d} \). Increasing slit separation decreases fringe width, while increasing screen distance increases fringe width.

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 slits and screen
• \( d \) = distance between the two slits

Thus, fringe width is: \[ \beta \propto \frac{D}{d} \]
Step 1: {Write the original fringe width.} \[ \beta = \frac{\lambda D}{d} \]
Step 2: {Apply the given changes.} Distance between slits is doubled: \[ d' = 2d \] Screen distance is halved: \[ D' = \frac{D}{2} \]
Step 3: {Substitute into the fringe width formula.} \[ \beta' = \frac{\lambda D'}{d'} \] \[ \beta' = \frac{\lambda \left(\frac{D}{2}\right)}{2d} \] \[ \beta' = \frac{\lambda D}{4d} \]
Step 4: {Compare with original fringe width.} \[ \beta = \frac{\lambda D}{d} \] \[ \beta' = \frac{\beta}{4} \] \[ \therefore \text{New fringe width} = \frac{1}{4} \times \text{original fringe width} \] Thus, the fringe width becomes one-fourth of the original value.