A symmetrical double convex lens is cut into two equal parts by a plane containing the principal axis: The power of the divided lens is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → equal to that of the original lens
The focal length of a thin lens depends only on its refractive index and the radii of its two surfaces (lens maker's formula).
\( \displaystyle \frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \)
A cut by a plane containing the principal axis leaves each half with the same two curved surfaces and the same material. So \( f \) does not change, and the power \( P = 1/f \) is the same. Only the aperture is halved, so the image is dimmer but formed at the same place.
Why the other options are incorrect
Option (1) Half of the original lens — Incorrect. Power halves when the lens is cut by a plane perpendicular to the principal axis, because each half is then plano-convex with focal length \( 2f \). That is not the cut described here.
Option (3) double of the original lens — Incorrect. Cutting changes neither \( \mu \) nor the radii, so the power cannot double.
Option (4) four times of the original lens — Incorrect. For the same reason the power cannot become four times.