Visible light passing through a circular hole forms a diffraction disc of radius 0.1 mm on a screen. If X-ray is passed through the same set-up, the radius of the diffraction disc will be

Options

A. zero
B. `lt0.1 mm`
C. `0.1 mm`
D. `gt0.1 mm`

Answer

To solve the problem, we need to understand the relationship between the wavelength of light and the radius of the diffraction disc formed when light passes through a circular hole.

### Step-by-step Solution:

1. **Understanding Diffraction**: When light passes through a circular aperture (hole), it diffracts and forms a pattern on a screen. The central maximum is surrounded by a series of rings, and the radius of the central maximum is known as the diffraction disc radius.

2. **Relationship Between Wavelength and Radius**: The radius of the diffraction disc (R) is directly proportional to the wavelength (λ) of the light used. This can be expressed as:
\[ R \propto \lambda \]
This means that if the wavelength increases, the radius of the diffraction disc also increases, and vice versa.

3. **Wavelength of Visible Light vs. X-rays**: We know that the wavelength of visible light is significantly larger than that of X-rays. For example, the wavelength of visible light is in the range of approximately 400 to 700 nm, while the wavelength of X-rays is typically in the range of 0.01 to 10 nm.

4. **Comparing the Two**: Since the wavelength of X-rays is much smaller than that of visible light, we can conclude that:
\[ \text{If } \lambda_{X-ray} < \lambda_{visible \, light}, \text{ then } R_{X-ray} < R_{visible \, light} \]

5. **Applying the Information**: Given that the radius of the diffraction disc for visible light is 0.1 mm, we can deduce:
\[ R_{X-ray} < 0.1 \, \text{mm} \]

6. **Conclusion**: Therefore, when X-rays are passed through the same setup, the radius of the diffraction disc will be less than 0.1 mm.

### Final Answer:
The radius of the diffraction disc when X-rays are passed through the same setup will be **less than 0.1 mm**.

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