Q.Consider the diffraction patern for a small pinhole. As the size of the hole is increased

For a circular aperture (pinhole), the diffraction pattern is the Airy pattern, whose central bright spot has angular radius $\theta \approx 1.22\dfrac{\lambda}{D}$, where $D$ is the hole diameter.

1. As $D$ increases, $\theta \propto 1/D$ decreases, so the pattern shrinks — option (a) is true.
2. The total power passing through grows as $D^2$ while it is concentrated into a smaller angular area, so the central intensity increases — option (b) is true. …

The diffraction pattern from a circular aperture (a pinhole) is described by the Airy pattern — a central bright disc surrounded by alternating dark and bright rings. The angular radius of the first dark ring (the boundary of the central maximum) is given by:

where $D$ is the diameter of the pinhole and $\lambda$ is the wavelength of light. This is the fundamental relation.

Now, what happens when $D$ increases? Let's think physically.

1. The ratio $\lambda/D$ decreases. Since $\theta \propto 1/D$, a larger hole means a smaller angular spread of the diffraction pattern. The central bright spot becomes narrower, and the rings crowd closer together. → Option (a) is true: the size decreases (the pattern shrinks).

2. The overall pattern shrinks. If you project the pattern onto a screen at a fixed distance, the radius of the first dark ring is $r = L \theta \approx 1.22 \lambda L / D$. As $D$ grows, $r$ shrinks. The pattern becomes more compact.

3. The intensity in the central maximum increases. The total power passing through the hole grows as $D^2$ (area), but the central maximum covers a smaller area. The result is a much brighter, tighter spot — approaching the geometric-optics limit where the hole simply casts a sharp image of itself. → Option (b) is true: the intensity increases.

4. The number of visible rings changes. For a very small pinhole, the pattern is so broad that only the central maximum may be visible; the rings are too faint and spread out. As $D$ increases, more rings become discernible within a given angular range, but they are all smaller in angular size. …

Method: Relating Aperture Diameter to Diffraction-Pattern Size Using the Airy Relation

Applies to circular-aperture (pinhole) diffraction questions asking how the pattern changes as the hole size is varied.

Steps

Step 1: Recall the governing relation for a circular aperture

where $\theta$ is the angular radius of the central bright disc (and, correspondingly, of each dark ring) and $D$ is the aperture diameter.

Step 2: Read off the inverse relationship

Since $\theta \propto 1/D$, increasing $D$ decreases $\theta$ — the whole angular pattern contracts. Converting to a linear size on a screen at distance $L$, $r \approx L\theta \propto 1/D$, so the physical pattern also shrinks.

Step 3: Track the brightness/intensity separately …