Question

A slit of width `a' is illuminated with a monochromatic light of wavelength \(\lambda\) from a distant source and the diffraction pattern is observed on a screen placed at a distance `D' from the slit. To increase the width of the central maximum one should

• A. decrease \(D\)
• B. decrease \(a\)
• C. decrease \(\lambda\)
• D. the width cannot be changed

Hint:

Central maximum width in single slit diffraction increases when slit width decreases.

Answer 1

The Correct Option is B

Step 1: Recall the formula for central maximum width.
For single slit diffraction, angular width of central maximum is:
\[ \theta = \frac{2\lambda}{a} \]
Step 2: Convert into linear width on the screen.
Linear width on screen:
\[ W = 2D\theta = 2D \left(\frac{\lambda}{a}\right) = \frac{2D\lambda}{a} \]
Step 3: Identify what increases width.
From the formula, \(W\) is inversely proportional to \(a\).
So if we decrease \(a\), width \(W\) increases.
Step 4: Match with options.
Hence the correct option is (B).
Final Answer:
\[ \boxed{\text{(B) decrease \(a\)}} \]