Ray Optics

JEE Main level, numerical answer, medium

166 of 295

Question 166 of 295

A bi convex lens of focal length 10cm10cm is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is _____ DD.

Show answer and solution

Answer: 5

The focal length of the bi-convex lens (f)\left(f\right) can be calculated as follows:
1f=(μ−1)(1R−1−R)=2(μ−1)R...(1)\begin{matrix}\dfrac{1}{f} & = & (\mu -1)\left(\dfrac{1}{R}-\dfrac{1}{-R}\right) \\ & = & \dfrac{2\left(\mu -1\right)}{R}...\left(1\right)\end{matrix}
When the lens is cut into two halves, the focal length (f′)\left(f'\right) of each part can be calculated as follows:
1f′=(μ−1)(1R−1∞)=(μ−1)R...(2)\begin{matrix}\dfrac{1}{{f}^{'}} & = & (\mu -1)\left(\dfrac{1}{R}-\dfrac{1}{\infty }\right) \\ & = & \dfrac{\left(\mu -1\right)}{R}...\left(2\right)\end{matrix}
Hence, the ratio of the powers for both the lenses can be given by
P′P=1f′1f=ff′=(μ−1)R2(μ−1)R=12⇒P′=P2...(3)\begin{matrix}\dfrac{{P}^{'}}{P} & = & \dfrac{\dfrac{1}{f'}}{\dfrac{1}{f}} \\ & = & \dfrac{f}{f'} \\ & = & \dfrac{\dfrac{\left(\mu -1\right)}{R}}{\dfrac{2\left(\mu -1\right)}{R}} \\ & = & \dfrac{1}{2} \\ & \Rightarrow & P'=\dfrac{P}{2}...\left(3\right)\end{matrix}
Substitute the value of the known parameter into equation (3) to calculate the required power.
P′=10D2=5D\begin{matrix}P' & = & \dfrac{10D}{2} \\ & = & 5D\end{matrix}

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.
See it move: Lens ray diagram simulationDrag the sliders and watch the numbers in this question change.Revise Ray Optics firstFormula sheet, solved examples and the traps students fall into.

More Physics practice

JEE Main Physics practice question on Ray Optics (Lens Formula, Refraction of light from curved surface), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.