Question

Two identical symmetric double convex lenses of focal length \( f \) are cut into two equal parts \( L_1, L_2 \) by the AB plane and \( L_3, L_4 \) by the XY plane as shown in the figure respectively. The ratio of focal lengths of lenses \( L_1 \) and \( L_3 \) is:

• A. 1 : 4
• B. 1 : 1
• C. 2 : 1
• D. 1 : 2

Hint:

When symmetric lenses are cut into two equal parts, the focal length of the new lenses is halved compared to the original lens.

Answer 1

The Correct Option is D

When a lens is cut into two equal parts, the focal length of the resulting parts is affected. The general relation for the focal length of a lens cut into two parts is given by: \[ f_{\text{new}} = \frac{f}{2} \] For lenses \( L_1 \) and \( L_2 \), the focal length remains \( f \), but for the lenses cut by the XY plane (\( L_3 \) and \( L_4 \)), the focal length becomes half of the original focal length. Hence, the ratio of the focal lengths of \( L_1 \) and \( L_3 \) is: \[ \frac{f_1}{f_3} = \frac{f}{2f} = \frac{1}{2} \] Therefore, the correct answer is \( \boxed{1 : 2} \).