Question

A double-convex lens of power \( P \), with each face having the same radius of curvature, is cut into two equal parts perpendicular to its principal axis. The power of one part of the lens will be:

Hint:

Cutting a lens perpendicular to its principal axis does not change its focal length or power.

Answer 1

When a lens is cut into two equal parts perpendicular to its principal axis, the curvature of each part remains the same as the original lens. However, the effective thickness of each part is halved. The power of a lens is inversely proportional to its focal length, and the focal length is proportional to the thickness of the lens.
Since the thickness is halved, the focal length of one part will also be halved. This results in the power of one part being twice that of the original lens. Therefore, the power of one part of the lens will be:
\[ \frac{P}{2} \] Thus, the correct answer is: \[ \boxed{\frac{P}{2}}. \]