Question

In Young's double slit experiment, if the distance between the slits is halved and the distance between the slits and the screen is doubled, the fringe width will become

• A. half
• B. double
• C. four times
• D. eight times
• E. remain same

Hint:

Fringe width is "pro-screen" (it likes being far away) and "anti-slit" (it likes the slits being close together). By doing both—moving the screen away AND bringing the slits closer—you are boosting the width from both directions!

Answer 1

The Correct Option is C

Concept:
Physics - Wave Optics (Interference).
Step 1: State the formula for fringe width.
The fringe width ($\beta$) in Young's Double Slit Experiment (YDSE) is given by: $$ \beta = \frac{\lambda D}{d} $$ Where:

• $\lambda$ = Wavelength of light used.
• $D$ = Distance between the slits and the screen.
• $d$ = Distance between the two slits.

Step 2: Apply the given changes.

• New distance to screen ($D'$) = $2D$
• New slit separation ($d'$) = $d/2$

Step 3: Calculate the new fringe width ($\beta'$).
$$ \beta' = \frac{\lambda (2D)}{(d/2)} $$ $$ \beta' = 4 \left( \frac{\lambda D}{d} \right) $$ $$ \beta' = 4\beta $$
Step 4: Conclusion.
The fringe width will become four times its original value.