Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter `0.1mum`. If the diameter of the pinhole is slightly increased, it will affect the diffraction pattern such thtat :

Options

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

Answer

To solve the problem regarding the effect of increasing the diameter of a pinhole on the diffraction pattern, we can follow these steps:

### Step 1: Understand the relationship between pinhole diameter and diffraction pattern
The diffraction pattern produced by a pinhole can be described using the angular width of the central maximum, which is given by the formula:
\[ \theta = \frac{1.22 \lambda}{d} \]
where:
- \(\theta\) is the angular width of the central maximum,
- \(\lambda\) is the wavelength of the light,
- \(d\) is the diameter of the pinhole.

### Step 2: Analyze the effect of increasing the pinhole diameter
If the diameter \(d\) of the pinhole is slightly increased, the value of \(\theta\) will decrease because \(\theta\) is inversely proportional to \(d\). This means that:
\[ \text{If } d \text{ increases, then } \theta \text{ decreases.} \]

### Step 3: Determine the implications for the size of the diffraction pattern
The size of the diffraction pattern on a screen is related to the angular width \(\theta\). A smaller \(\theta\) implies that the central maximum will be narrower, leading to a decrease in the size of the diffraction pattern. Therefore:
\[ \text{Size of the diffraction pattern decreases.} \]

### Step 4: Analyze the effect on intensity
The intensity of the diffraction pattern is related to the area of the pinhole. As the area of the pinhole increases (since the diameter is increased), the intensity of the light passing through the pinhole also increases. This is because intensity is proportional to the area of the aperture:
\[ \text{If area increases, intensity increases.} \]

### Step 5: Conclusion
In conclusion, when the diameter of the pinhole is slightly increased:
- The size of the diffraction pattern decreases.
- The intensity of the diffraction pattern increases.

### Final Answer
Thus, the correct statement regarding the effect of slightly increasing the diameter of the pinhole is that the size of the diffraction pattern decreases and the intensity increases.

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