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Question

Physics Question on spherical lenses

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 . Choose the incorrect option for the reported pieces.

A

Power of L1=P2L_1 = \frac{P}{2}

B

Power of L2=P2L_2 = \frac{P}{2}

C

Power of L3=P2L_3 = \frac{P}{2}

D

Power of L1=PL_1 = P

Answer

Power of L1=P2L_1 = \frac{P}{2}

Explanation

Solution

As We know that,

P=1f=(µ−1)(1R1−1R2)P=\frac{1}{f}=(µ-1)\bigg(\frac{1}{R_1}-\frac{1}{R_2}\bigg)

L1:1f=(µ−1)(1R1−1R2)=P1=(µ−1)(2R)=PL_1:\frac{1}{f}=(µ-1)\bigg(\frac{1}{R_1}-\frac{1}{R_2}\bigg)=P_1=(µ-1)\bigg(\frac{2}{R}\bigg)=P

L2:1f=(µ−1)(1R1)=P2=(µ−1)RL_2:\frac{1}{f}=(µ-1)\bigg(\frac{1}{R_1}\bigg)=P_2=\frac{(µ-1)}{R}

L3:1f=(µ−1)(−1R2)=P3=(µ−1)RL_3:\frac{1}{f}=(µ-1)\bigg(-\frac{1}{R_2}\bigg)=P_3=\frac{(µ-1)}{R}

Hence, Correct option is (A) : Power of L1=P2L_1 = \frac{P}{2}