Question

Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter 0.1 $\mu$m. If the diameter of the pinhole is slightly increased, it will affect the diffraction pattern such that:

• A. its size increases, and intensity increases
• B. its size increases, but intensity decreases
• C. its size decreases, but intensity increases
• D. its size decreases, and intensity decreases

Hint:

A key principle of diffraction is the inverse relationship between the size of the aperture and the size of the diffraction pattern. A wider opening leads to a narrower pattern, and vice versa. This is a consequence of the uncertainty principle.

Answer 1

The Correct Option is C

Let's analyze the two effects of increasing the pinhole diameter.
1. Effect on the size of the diffraction pattern:
The diffraction pattern is characterized by a central bright spot (Airy disk) surrounded by concentric rings. The angular size of the central maximum is inversely proportional to the diameter of the aperture.
For a circular aperture of diameter 'd', the angular position of the first minimum is given by $\sin\theta \approx 1.22 \frac{\lambda}{d}$.
This angle determines the size of the central bright spot. As the diameter 'd' of the pinhole increases, the value of $\sin\theta$ decreases.
This means the diffraction pattern shrinks, so its size decreases.
2. Effect on the intensity of the diffraction pattern:
The intensity of the light in the pattern depends on the total amount of light energy passing through the pinhole per unit time.
The amount of light passing through is proportional to the area of the pinhole, which is $A = \pi(d/2)^2$.
If the diameter 'd' increases, the area of the pinhole increases. More light passes through, and this energy is concentrated into a smaller area (as the pattern shrinks).
Therefore, the intensity of the diffraction pattern increases.
Combining both effects, when the diameter is increased, the size decreases and the intensity increases.