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

Step 1: Understanding the Question:
Fringe width (\( \beta \)) is the distance between two consecutive bright or dark fringes. We need to determine how \( \beta \) changes when the experimental geometry is altered.
Step 2: Key Formula or Approach:
The fringe width formula is:
\[ \beta = \frac{\lambda D}{d} \]
where \( D \) is the screen distance and \( d \) is the slit separation.
Step 3: Detailed Explanation:
Let the initial fringe width be \( \beta_1 = \frac{\lambda D}{d} \).
According to the problem:
New screen distance \( D' = \frac{D}{2} \).
New slit separation \( d' = 2d \).
New fringe width \( \beta_2 = \frac{\lambda D'}{d'} \).
\[ \beta_2 = \frac{\lambda (D/2)}{2d} = \frac{\lambda D}{4d} \]
Comparing \( \beta_2 \) with \( \beta_1 \):
\[ \beta_2 = \frac{1}{4} \beta_1 \]
Step 4: Final Answer:
The fringe width becomes one-fourth of the original value.