Question

There are four convex lenses \( L_1 \), \( L_2 \), \( L_3 \), and \( L_4 \) of focal length 2, 4, 6, and 8 cm respectively. Two of these lenses form a telescope of length 10 cm and magnifying power 4. The objective and eye lenses are respectively

• A. \( L_1, L_2 \)
• B. \( L_1, L_4 \)
• C. \( L_2, L_3 \)
• D. \( L_4, L_1 \)

Hint:

For telescopes, the magnifying power is determined by the ratio of the focal lengths of the objective and eye lenses, and the total length is the difference of these focal lengths.

Answer 1

The Correct Option is D

Step 1: Understanding the telescope setup.
For a telescope, the focal length of the objective lens and eye lens are related to the length of the telescope and magnifying power. The length of the telescope is the difference between the focal lengths of the objective and eye lenses: \[ L = f_{\text{objective}} - f_{\text{eye lens}} \] The magnifying power \( M \) of the telescope is given by: \[ M = \frac{f_{\text{objective}}}{f_{\text{eye lens}}} \]
Step 2: Given values.
We are given that \( L = 10 \, \text{cm} \) and \( M = 4 \). Using the magnifying power formula: \[ 4 = \frac{f_{\text{objective}}}{f_{\text{eye lens}}} \] This gives the relationship between the focal lengths of the objective and eye lenses.
Step 3: Solve for the correct combination.
By trial and error, the correct combination of objective and eye lenses that satisfies the equation is \( L_4 = 8 \, \text{cm} \) (objective) and \( L_1 = 2 \, \text{cm} \) (eye lens). Thus, the correct answer is (D).