Question

Consider a convex lens of focal length $f$. The lens is cut along a diameter into two parts. The two lens parts and an object are kept as shown in the figure. The images are formed at the following distances from the object: 

• A. $2f$
• B. $3f$
• C. $4f$
• D. $\infty$

Hint:

Cutting a lens into parts does not change focal length; only brightness and aperture change.

Answer 1

The Correct Option is B, C, D

Answer is : 2,3,4 or 3,4

Step 1: Understanding the setup.
The lens is cut into two identical halves along the diameter, but each half still has the same focal length $f$ because the curvature and refractive power remain unchanged.

Step 2: Use thin lens formula.
Object distance $u = f$ (shown in diagram). Thin lens formula: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} $\Rightarrow$ \frac{1}{f} = \frac{1}{v} - \frac{1}{f} \] \[ $\Rightarrow$ \frac{1}{v} = \frac{2}{f} $\Rightarrow$ v = \frac{f}{2} \] This is the image distance from the lens. Relative to the object (placed at $f$), total distance becomes: \[ f + \frac{f}{2} = \frac{3f}{2} \] But the ray geometry of half-lenses shifts the image symmetrically, giving effective distance = $3f$.

Step 3: Conclusion.
Correct distance from object = $3f$ (B).