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Question 14

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

In single-slit (or pinhole) diffraction, the angular width of the central maximum is inversely proportional to the diameter of the aperture. Specifically, for a circular pinhole of diameter $$d$$, the angular radius of the first dark ring (Airy disk) is given by $$\sin\theta \approx 1.22\frac{\lambda}{d}$$.

When the diameter of the pinhole is slightly increased, the ratio $$\frac{\lambda}{d}$$ decreases, which means the angular spread of the diffraction pattern decreases. Therefore, the size of the diffraction pattern (the central bright spot and the surrounding rings) decreases.

At the same time, increasing the diameter of the pinhole allows more light to pass through it. The amount of light collected by the pinhole is proportional to its area, which is proportional to $$d^2$$. Therefore, the intensity of the diffraction pattern increases when the pinhole diameter is increased.

Hence, when the pinhole diameter is slightly increased, the size of the diffraction pattern decreases but the intensity increases.

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