An astronomical telescope in normal adjustment receives light from a distant source `S`. The tube length is now decreased slightly

Options

A. no image will be formed
B. a virtual image of S will be formed at finite distance
C. a large, real image of S will be formed behined the eye place,for it
D. a small, real image of S will be formed behind the eye-piece closed to it

Explanation

To solve the problem, we need to analyze the effect of decreasing the tube length of an astronomical telescope that is initially in normal adjustment.

### Step-by-Step Solution:

1. **Understanding Normal Adjustment**:
- In normal adjustment, the focal lengths of the objective (f₀) and eyepiece (fₑ) are related to the tube length (L) by the equation:
\[ L = f₀ + fₑ \]
- This setup allows the telescope to produce a clear image of a distant object at infinity.

2. **Effect of Decreasing Tube Length**:
- When the tube length (L) is decreased slightly, the new tube length becomes:
\[ L' < f₀ + fₑ \]
- This means the telescope is no longer in normal adjustment.

3. **Image Formation**:
- With the tube length decreased, the light rays from the distant source (S) will converge at a point that is closer to the eyepiece than the focal point of the eyepiece.
- The image will be formed between the focus of the eyepiece and the optical center of the eyepiece.

4. **Nature of the Image**:
- When the image is formed between the focus and the optical center of the eyepiece, it results in a virtual image.
- A virtual image cannot be projected onto a screen; it appears to be located behind the eyepiece.

5. **Conclusion**:
- Therefore, the correct answer is that a virtual image of S will be formed at a finite distance.

### Final Answer:
**A virtual image of S will be formed at a finite distance. (Option B)**

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