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A biconvex lens has power PP. It is cut into two symmetrical halves by a plane containing the principal axis. The power of one part will be:

A

0

B

P2\frac{P}{2}

C

P4\frac{P}{4}

D

PP

Step-by-Step Solution

  1. Lens Maker's Formula: The power PP of a lens is given by P=1f=(μ−1)(1R1−1R2)P = \frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right).
  2. Analysis of the Cut: The lens is cut into two symmetrical halves by a plane containing the principal axis (a horizontal or longitudinal cut).
  3. Effect on Parameters:
  • The radius of curvature of the curved surfaces (R1R_1 and R2R_2) remains unchanged.
  • The refractive index (μ\mu) of the material remains unchanged.
  1. Conclusion: Since none of the factors determining the focal length change, the focal length ff and the power PP of each half remain the same as the original lens.
  • Note: If the lens were cut perpendicular to the principal axis, it would become two plano-convex lenses, and the power would become P/2P/2. However, here the cut is along the axis.
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