Question

Two identical symmetric double convex lenses of focal length \(f\) are cut into two equal parts \(L_1, L_2\) by \(AB\) plane and \(L_3, L_4\) by \(XY\) plane as shown in figure respectively. The ratio of focal lengths of lenses \(L_1\) and \(L_3\) is graphics[width=0.5\linewidth]{Q10.png}

• A. \(1:4\)
• B. \(1:1\)
• C. \(2:1\)
• D. \(1:2\)

Hint:

Cutting a lens changes: \[ \mathrm{Aperture} \] but focal length remains unchanged if radii of curvature remain same.

Answer 1

The Correct Option is B

Step 1: Understand cutting by plane \(AB\).
Plane \(AB\) cuts the lens horizontally through principal axis. Each part still retains:
• Same radii of curvature
• Same refractive index Only aperture changes. Hence focal length remains unchanged. Thus: \[ f_{L_1}=f \]

Step 2: Understand cutting by plane \(XY\).
Plane \(XY\) cuts the lens vertically along principal axis. Again:
• Curvatures remain same
• Lens maker formula remains unchanged Therefore focal length also remains unchanged. Thus: \[ f_{L_3}=f \]

Step 3: Find the ratio.
\[ \frac{f_{L_1}}{f_{L_3}} = \frac{f}{f} \] \[ \frac{f_{L_1}}{f_{L_3}}=1 \] Hence: \[ f_{L_1}:f_{L_3}=1:1 \]

Step 4: Identify the correct option.
Therefore, the correct answer is: \[ \boxed{1:1} \] Hence: \[ \boxed{\mathrm{(B)}} \]