Question

Angular width of the first minimum on either side of the central maximum due to a single slit of width \(a\), illuminated by a light of wavelength \(\lambda\) is

• A. \(\dfrac{\lambda}{a}\)
• B. \(\dfrac{\lambda}{2a}\)
• C. \(\dfrac{2\lambda}{a}\)
• D. \(\dfrac{\lambda}{4a}\)
• E. \(\dfrac{4\lambda}{a}\)

Hint:

Single-slit central maximum extends from first minimum on one side to first minimum on the other side, so its angular width is doubled.

Answer 1

The Correct Option is C

For the first minimum in single slit diffraction: \[ a\sin\theta=\lambda \] For small angles: \[ \theta\approx \frac{\lambda}{a} \] The first minimum occurs on both sides of the central maximum, so angular width is: \[ 2\theta = 2\frac{\lambda}{a} \] Hence, \[ \boxed{(C)\ \frac{2\lambda}{a}} \]