Verified Solution • 2025–26 Session moderate

QJEEMP_2025_8: JEE Main 2025 Physics - Class 12 JEEMP_2025_8 Solution: A symmetric thin biconvex lens is cut into four equal parts by…

A symmetric thin biconvex lens is cut into four equal parts by two planes AB and CD as shown in figure. If the power of original lens is 4 D4\text{ D} then the power of a part of the divided lens is

Multiple Choice Options

  • A 2 D2\text{ D}
  • B 8 D8\text{ D}
  • C 4 D4\text{ D}
  • D D

Step-by-Step Verified Solution

To find the power of each part of the divided lens, we analyze the changes using the Lens Maker's Formula:\n
1f=(n−1)(1R1−1R2)\frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)
\n\nFor a symmetric biconvex lens where
R1=RR_1 = R
and
R2=−RR_2 = -R
, the initial power
PP
is:\n
P=1f=(n−1)(2R)=4 DP = \frac{1}{f} = (n - 1) \left( \frac{2}{R} \right) = 4\,\mathrm{D}
\n\nStep 1: Cutting along the horizontal plane (
ABAB
)\nWhen a lens is cut horizontally along its principal axis:\n - The radii of curvature (
R1R_1
and
R2R_2
) of the remaining pieces do not change.\n - The focal length and power remain exactly the same (
4 D4\,\mathrm{D}
).\n - Note: Only the intensity of the image decreases because the light-gathering area (aperture) is halved.\n\nStep 2: Cutting along the vertical plane (
CDCD
)\nWhen the lens is cut vertically through its optical center, each resulting piece becomes a plano-convex lens:\n - One surface remains curved (
R1=RR_1 = R
).\n - The other surface becomes flat (
R2=∞R_2 = \infty
).\n\nApplying the formula for the new power
P′P'
:\n
P′=(n−1)(1R−1∞)=(n−1)(1R)P' = (n - 1) \left( \frac{1}{R} - \frac{1}{\infty} \right) = (n - 1) \left( \frac{1}{R} \right)
\n\nComparing this to the original power:\n
P′=P2=4 D2=2 DP' = \frac{P}{2} = \frac{4\,\mathrm{D}}{2} = 2\,\mathrm{D}
\n\nFinal Conclusion:\nWhen the lens is cut by both planes (
ABAB
and
CDCD
) into four equal parts:\n - The vertical cut reduces the power from
4 D4\,\mathrm{D}
to
2 D2\,\mathrm{D}
.\n - The horizontal cut maintains that power at
2 D2\,\mathrm{D}
.\n - The power of each of the four parts is
2 D2\,\mathrm{D}
.

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