An observer is using an astronomical refracting telescope to observe planets in normal adjustment. The focal l

Question

An observer is using an astronomical refracting telescope to observe planets in normal adjustment. The focal lengths of the objective and eyepiece used in the telescope construction are $20 	ext{ m}$ and $2 	ext{ cm}$ respectively. Consider the following statements about the telescope:
(A) The distance between the objective and the eyepiece is $20.02 	ext{ m}$.
(B) The magnification of the telescope is $-1000$.
(C) The image of the planet is erect and diminished.
(D) The aperture of the eyepiece is smaller than that of the objective.

The correct statements are:

Accepted Answer

1. **Analyze Given Data:**
   - Focal length of objective ($f_o$) = $20 	ext{ m}$.
   - Focal length of eyepiece ($f_e$) = $2 	ext{ cm} = 0.02 	ext{ m}$.
   - Normal adjustment implies the final image is formed at infinity.

2. **Evaluate Statement A (Length):**
   - In normal adjustment, the distance between the lenses (length of the telescope, $L$) is the sum of their focal lengths.
   - $L = f_o + f_e = 20 	ext{ m} + 0.02 	ext{ m} = 20.02 	ext{ m}$.
   - **Statement A is Correct.**

3. **Evaluate Statement B (Magnification):**
   - The magnifying power ($m$) in normal adjustment is given by $m = -f_o / f_e$.
   - $m = -20 / 0.02 = -1000$.
   - The negative sign indicates the image is inverted.
   - **Statement B is Correct.**

4. **Evaluate Statement C (Image Nature):**
   - An astronomical refracting telescope produces an **inverted** image. It is not erect.
   - **Statement C is Incorrect.**

5. **Evaluate Statement D (Aperture):**
   - The objective lens must have a large aperture to gather sufficient light from distant objects and to provide high resolution ($RP \propto a$). The eyepiece has a smaller aperture.
   - **Statement D is Correct.**

6. **Conclusion:** Statements A, B, and D are correct.

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