Question

Consider the diffraction pattern for a small pinhole. As the diameter of the hole is increased

• A. The diameter of central bright spot decreases
• B. The diameter of central bright spot increases
• C. The intensity of the central bright spot increases
• D. The intensity of the central bright spot decreases

Answer 1

Answer: (A), (C)

The intensity of the central bright spot increases

The diameter of the central bright spot for a diffraction pattern of a pinhole is given by

$R=\frac{1.22\lambda D}{b}$

Where,
$b$ is the diameter of the pinhole.
$\lambda$ is the wavelength of light used
$D$ is the distance between the pinhole and the screen.

Radius of the central bright spot, when the size of the pinhole is doubled,

$R^{\prime }=\frac{1.22\lambda D}{2b}==\frac{0.61\lambda D}{b}$

As, the diameter of the pinhole increases, the diameter of the central bright spot decreases.

Now, as the diameter of the central bright spot decreases but the same amount of light emerging is now distributed over a smaller area, so the intensity increases.

Hence, options $\left(A\right)$ and $\left(C\right)$ are correct.