A biconvex lens has power $P$. It is cut into two symmetrical halves by a plane containing the principal axis.

Question

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

Accepted Answer

1. **Lens Maker's Formula:** The power $P$ of a lens is given by $P = \frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$.
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 ($R_1$ and $R_2$) remains unchanged.
   - The refractive index ($\mu$) of the material remains unchanged.
4. **Conclusion:** Since none of the factors determining the focal length change, the focal length $f$ and the power $P$ 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 $P/2$. However, here the cut is along the axis.

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