A convex lens has power $$P$$. It is cut into two halves along its principal axis. Further one piece (out of the two halves) is cut into two halves perpendicular to the principal axis (as shown in figures). Choose the incorrect option for the reported pieces.

Concept:
Power of a lens depends on curvature, not on aperture (size).

Step 1: Lens cut along principal axis

• Focal length remains same ⇒ power unchanged

$$P_1 = P$$

Step 2: One half cut perpendicular to principal axis

• Radius of curvature effectively doubles ⇒ focal length doubles

$$P = \frac{1}{f} \Rightarrow P_{\text{new}} = \frac{1}{2f} = \frac{P}{2}$$​

So,

$$P_2 = \frac{P}{2}, \quad P_3 = \frac{P}{2}$$

Final Result:

$${P_1 = P,\quad P_2 = \frac{P}{2},\quad P_3 = \frac{P}{2}}$$