Question

An astronomical telescope consists of an objective of focal length 50 cm and eyepiece of focal length 2 cm is focused on the moon so that the final image is formed at the least distance of distinct vision (25 cm). Assuming angular diameter of the moon as \( \frac{1}{2^\circ} \) at the objective, the angular size of image is:

• A. 1.27°
• B. 13.5°
• C. 1°
• D. 11.2°

Hint:

In an astronomical telescope, the angular size of the image is determined by the focal lengths of the objective and eyepiece.

Answer 1

The Correct Option is A

The angular size of the image formed by the telescope is given by: \[ \theta_{\text{image}} = \frac{\theta_{\text{object}} \times f_{\text{eyepiece}}}{f_{\text{objective}}} \] Where: - \(\theta_{\text{object}} = \frac{1}{2^\circ} \), - \(f_{\text{objective}} = 50 \, \text{cm}\), - \(f_{\text{eyepiece}} = 2 \, \text{cm}\). Substituting the values, we get: \[ \theta_{\text{image}} = \frac{\frac{1}{2^\circ} \times 2}{50} = 1.27^\circ \]