Answer to Question #226999 in Optics for Amir Star

Question

If a convex lens is cut along diameter into two equal parts,what will be the focal length of each part..

Answer 1

The focal length for each turns out to be double the original focal length. You can solve this from combination lens equation:

$\large\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2}$

Where the original focal length is f, and the focal length of each half is $f_1$ and $f_2$

Since the two halves are identical, then $f_1 = f_2$ . So the equation becomes:

$\large\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} = \frac{2}{f_1} \space$ $or \space \space f = \large\frac{f_1}{2}$

Solving for one of the lens half:  $f_1 = 2f.$