Question

A double-convex lens of power \( P \), with each face having the same radius of curvature, is cut along its principal axis. The two parts are arranged as shown in the figure. The power of the combination will be: \includegraphics[width=0.3\linewidth]{14image.png}

Hint:

- When a convex lens is cut along its principal axis, each half acts as a plano-convex lens.
- The focal length of each part is halved, and since power is inversely proportional to focal length, the power of each part doubles.
- The total power of the combination is the sum of individual powers, making it \(2P\).
- This concept is useful in understanding how lens cutting affects optical power in practical applications.

Answer 1

When a double-convex lens is cut along its principal axis, the resulting two parts will each behave as a plano-convex lens. The focal length of each part will be halved, and the power is inversely proportional to the focal length. Since the focal length of each part is halved, the power of each part will be doubled.
When these two parts are combined, their powers will add up. Therefore, the total power of the combination will be:
\[ P_{\text{total}} = P + P = 2P \] Thus, the power of the combination is \(2P\). Thus, the correct answer is: \[ \boxed{2P}. \]