Question

In an astronomical telescope in normal adjustment a straight black line of length $L$ is drawn on inside part of objective lens. The eye-piece forms a real image of this line. The length of this image is $I$ . The magnification of the telescope is

• A. $ \frac{L+I}{ L-I}$
• B. $\frac {L}{I}$
• C. $\frac{L}{I}+ I$
• D. $\frac{L}{I}- I$

Answer 1

The Correct Option is B

To find the magnification of the telescope, we begin by understanding how an astronomical telescope works, especially in terms of forming images.

1. In a typical astronomical telescope in normal adjustment, the objective lens captures light from a distant object and forms an intermediate real image, which is then magnified by the eyepiece.
2. In this problem, a straight black line of length \( L \) is drawn on the inside part of the objective lens. This line forms a real image of length \( I \) through the eyepiece.
3. The magnification of a telescope in normal adjustment is given by the ratio of the focal length of the objective lens \( f_o \) to the focal length of the eyepiece \( f_e \), but we can relate magnification in terms of size changes, as here:
4. Magnification \( M \) is defined as the ratio of the length of the image formed to the actual length of the object viewed:

M = \frac{ \text{Image Length (} I \text{)}}{ \text{Object Length (} L \text{)}}

5. From this formula, we can see that the magnification when a real image is formed by the eyepiece is:

M = \frac{L}{I}

6. Thus, the given answer aligns with this derived formula. Therefore, the correct answer is \frac{L}{I}.

This logical and formulaic approach clarifies why this option is correct. The other options don't fit this definition of magnification correctly:

• \frac{L+I}{ L-I} does not represent a standard formula regarding the changes in image size relative to object size in telescopes.
• \frac{L}{I} + I would incorrectly describe magnification, combining magnification with an actual length measure which is dimensionally inconsistent.
• \frac{L}{I} - I similarly combines dimensions incorrectly.

Hence, the understanding of the fundamental process in telescopic magnification leads us to the conclusion that the magnification is \frac{L}{I}.