Question

When a lens is cut into two halves along \(XOX'\), then focal length of each half lens:

• A. increases
• B. decreases
• C. remains same
• D. None of the above

Hint:

Cutting lens along principal axis changes brightness, not focal length.

Answer 1

The Correct Option is C

Concept: Lens maker formula: \[ \frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \]

Step 1:Focal length depends only on:
•Refractive index \((\mu)\)
•Radii of curvature \((R_1, R_2)\)

Step 2:When lens is cut along \(XOX'\) (i.e., along principal axis):
•Curvature of surfaces remains unchanged
•Only aperture (size) reduces

Step 3:Since curvature is unchanged: \[ f \text{ remains same} \] Final: \[ \Rightarrow \text{Focal length does not change} \]