JEE Main · 2022 · 27 Jun 2022 · Shift 2 · Geometrical Optics

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A convex lens has power P. It is cut into two halves along its principal axis. Further one piece (out of the two halves) is cut into two halves perpendicular to the principal axis (as shown in figure). Choose the incorrect option for the reported pieces.

(A)Power of $L_{1} = \frac{P}{2}$ ✓ Correct
(B)Power of $L_{2} = \frac{P}{2}$
(C)Power of $L_{3} = \frac{P}{2}$
(D)Power of $L_{1} = P$

Answer: (A)

Solution

When a lens is cut:

Cut along the principal axis (horizontally through the optical center): Each half retains the same focal length, hence the same power P. So $L_{1}$ has power P.

Cut perpendicular to the principal axis (vertically): The focal length doubles (because the lens maker's formula shows that reducing the aperture while keeping the radii of curvature constant effectively doubles the focal length for the usable portion). Since power $P = \frac{1}{f}$ , when $f$ doubles, power becomes $\frac{P}{2}$ . So $L_{2}$ and $L_{3}$ each have power $\frac{P}{2}$ .

Option (A) states "Power of

L_{1} = \frac{P}{2}

", which is incorrect. The correct power of

L_{1}

is P.

Therefore, option (A) is the incorrect statement.

JEE Main · 2022 · 27 Jun 2022 · Shift 2 · Single correct option

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JEE Main · 2022 · 27 Jun 2022 · Shift 2 · Geometrical Optics

Solution

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