Question

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

• A. Halved
• B. Unchanged
• C. Doubled
• D. Quadrupled

Hint:

Fringe width is directly proportional to \(D\) and inversely proportional to \(d\). Any fractional changes can be directly multiplied: \((2) \times (1 / 0.5) = 4\).

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We are asked to find the new fringe width in a Young's double-slit experiment (YDSE) after changing the slit separation and the distance to the screen.

Step 2: Key Formula or Approach:
The fringe width (\(\beta\)) in YDSE is defined by the formula:
\[ \beta = \frac{\lambda D}{d} \] where \(\lambda\) is the wavelength of light, \(D\) is the distance between the slits and the screen, and \(d\) is the distance between the two slits.

Step 3: Detailed Explanation:
Let the initial fringe width be \(\beta\).
According to the given conditions, the new distance between the slits and the screen is doubled:
\[ D' = 2D \] The separation between the slits is halved:
\[ d' = \frac{d}{2} \] Substitute these new values into the fringe width formula to find the new fringe width \(\beta'\):
\[ \beta' = \frac{\lambda D'}{d'} \] \[ \beta' = \frac{\lambda (2D)}{(d/2)} \] \[ \beta' = 4 \left( \frac{\lambda D}{d} \right) \] Since \(\frac{\lambda D}{d}\) is the initial fringe width \(\beta\), we have:
\[ \beta' = 4\beta \] Thus, the fringe width becomes four times its original value, which means it is quadrupled.

Step 4: Final Answer:
The correct choice is (D).