Question

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 figure). Choose the incorrect option for the reported pieces.
\includegraphics[width=0.5\linewidth]{27.png}

• A. Power of \( L_1 = \frac{P}{2} \)
• B. Power of \( L_2 = \frac{P}{2} \)
• C. Power of \( L_3 = \frac{P}{2} \)
• D. Power of \( L_1 = P \)

Hint:

For cutting lenses:
- Cutting along the principal axis does not change the power.
- Cutting perpendicular to the principal axis reduces power by half.

Answer 1

The Correct Option is A

When a convex lens of power \( P \) is cut into two equal halves along its principal axis, the focal length of each half remains the same as the original lens, but the aperture reduces. Since power is given by: \[ P = \frac{1}{f} \] where \( f \) is the focal length, cutting along the principal axis does not change the focal length, meaning each half still has the same power as the original lens, i.e., \( P \). Now, when one of these halves is further cut into two equal parts perpendicular to the principal axis, each new piece retains the same curvature and focal length. Since power is an intrinsic property dependent on focal length and not on aperture reduction along the perpendicular direction, all pieces should retain the same power. Thus, we analyze the given options: - \( L_1 \) is one of the halves obtained from the first cut (along the principal axis). Since power remains unchanged in this case, the power of \( L_1 \) should be \( P \), making option (A) incorrect.
- \( L_2 \) and \( L_3 \) are the pieces obtained after the second cut (perpendicular to the principal axis), and they should each retain the same power, i.e., \( \frac{P}{2} \). - The correct power of \( L_1 \) should be \( P \), not \( \frac{P}{2} \). Final Answer: (A) Power of \( L_1 = \frac{P}{2} \) is incorrect.