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

Topic - Wave Optics (Interference):
This question focuses on Young's Double Slit Experiment (YDSE) and how the geometric parameters of the setup influence the interference pattern.
Step 1: Understanding the Question:
We need to find the ratio of the new fringe width to the old fringe width based on changes in slit separation (\(d\)) and screen distance (\(D\)).
Step 2: Key Formula or Approach:
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.
Step 3: Detailed Solution:
1. Let the initial parameters be \(D\) and \(d\). Initial fringe width \(\beta = \frac{\lambda D}{d}\).
2. New screen distance \(D' = 2D\).
3. New slit separation \(d' = \frac{d}{2}\).
4. Substitute these into the formula for new fringe width \(\beta'\):
\[ \beta' = \frac{\lambda D'}{d'} = \frac{\lambda (2D)}{(d/2)} \] \[ \beta' = \frac{2 \lambda D}{d/2} = 4 \left( \frac{\lambda D}{d} \right) \] \[ \beta' = 4\beta \] Step 4: Final Answer:
The fringe width becomes quadrupled (4 times).