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.

Solution

Physics sir · 4 steps

Cutting across the axis leaves each half with one curved face, so its power is half the original.

1. What the cut does. The cut runs perpendicular to the principal axis, so each half keeps one curved face and gets one flat face. Each piece is a plano-convex lens. The two halves are identical, so both faces of the original lens have the same radius R.
2. Use lens maker. For the full lens, both curved faces contribute. For each half, the flat face has R = ∞ and contributes nothing.

   1/f = (μ - 1)2/R, 1/f' = (μ - 1)1/R = 1/2f

3. Put in numbers. f' = 2f = 2 × 10 cm = 20 cm = 0.2 m. Power is P = 1/f' = 1/(0.2 m).
4. So. Each half has a power of 5 D, half of the original 10 D.

The common slip: 10. Assuming each half keeps the original focal length of 10 cm gives 10 D. That only happens when the lens is cut along the principal axis.

The idea to keep. Cut perpendicular to the axis and each half loses a curved face, so its power halves. Cut along the axis and both faces stay, so the focal length does not change.

Answer from the NTA final answer key. Solution by PrepWiser.