Cut it the other way, along the axis.

An equi-convex lens of focal length f is instead cut along its principal axis into two D-shaped halves. Each half, used alone, has a focal length of:

Answer: f.

A cut along the axis leaves each half with both of its curved surfaces, with the same radii of curvature as before. Only the aperture, the area that collects light, is halved.

\frac{1}{f'} = (n - 1) (\frac{1}{R} + \frac{1}{R}) = \frac{1}{f}

\Rightarrow f' = f

So each half still has focal length f and still forms a complete image, only with half the light. The 2f answer for a slice across the lens does not apply here: what matters is which surfaces each piece keeps.

Original practice question · JEE Physics Decoded

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