Question #226999
If a convex lens is cut along diameter into two equal parts,what will be the focal length of each part..
1
Expert's answer
2021-08-19T14:24:55-0400

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

1f=1f1+1f2\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 f1f_1 and f2f_2

Since the two halves are identical, then f1=f2f_1 = f_2 . So the equation becomes:

1f=1f1+1f2=2f1 \large\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} = \frac{2}{f_1} \space or  f=f12or \space \space f = \large\frac{f_1}{2}

Solving for one of the lens half:  f1=2f.f_1 = 2f.


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