A bi convex lens of focal length $$10$$ cm is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is _____ D.

A biconvex lens of focal length 10 cm is cut perpendicular to the principal axis into two identical halves. Each half becomes a plano-convex lens.

For the original biconvex lens (assuming symmetric with equal radii of curvature $$R$$):

$$\frac{1}{f} = (n-1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) = (n-1)\left(\frac{2}{R}\right)$$

When cut perpendicular to the principal axis, each half is a plano-convex lens with one curved surface (radius $$R$$) and one flat surface (radius $$\infty$$):

$$\frac{1}{f'} = (n-1)\left(\frac{1}{R}\right) = \frac{1}{2} \times \frac{1}{f} = \frac{1}{2 \times 10} = \frac{1}{20}$$

$$f' = 20$$ cm $$= 0.2$$ m

Power: $$P = \frac{1}{f'} = \frac{1}{0.2} = 5$$ D

The power of each lens is $$\mathbf{5}$$ D.