Question

In Young's double slit --- if slit separation is halved and screen distance doubled, fringe width becomes:

• A. Halved
• B. Doubled
• C. 4 times
• D. Unchanged

Hint:

Fringe width is directly proportional to screen distance and inversely proportional to slit separation.

Answer 1

The Correct Option is C

Step 1: Concept
The fringe width ($\beta$) in Young's Double Slit Experiment is given by the formula $\beta = \frac{\lambda D}{d}$, where $\lambda$ is the wavelength, $D$ is the distance to the screen, and $d$ is the slit separation.

Step 2: Meaning
Halving the slit separation means the new separation $d' = \frac{d}{2}$. Doubling the screen distance means the new distance $D' = 2D$.

Step 3: Analysis
Substituting the new values into the fringe width formula: $\beta' = \frac{\lambda (2D)}{(d/2)} = 4 \times \frac{\lambda D}{d}$.

Step 4: Conclusion
The calculation shows that the new fringe width $\beta'$ is exactly 4 times the original fringe width $\beta$. Final Answer: (C)