PrepRung
Sign inSign up free

JEE Main 2017 · Physics · Ray and Wave Optics · easy

A double convex glass lens (μg = 1.5) has focal length 20 cm in air. It is completely immersed in water (μw = 4/3). Its focal length in water is

Single correct option

A double convex glass lens (μg=1.5\mu_g = 1.5) has focal length 20 cm20\ \mathrm{cm} in air. It is completely immersed in water (μw=4/3\mu_w = 4/3). Its focal length in water is
  1. A. 40 cm40\ \mathrm{cm}
  2. B. 60 cm60\ \mathrm{cm}
  3. C. 80 cm80\ \mathrm{cm}
  4. D. 120 cm120\ \mathrm{cm}
Show answer and solution

Answer: (C) 80 cm80\ \mathrm{cm}

Lens-maker's formula: 1f=(μgμm−1)(1R1−1R2)\dfrac1f = \left(\dfrac{\mu_g}{\mu_m} - 1\right)\left(\dfrac1{R_1} - \dfrac1{R_2}\right). In air: 120=0.5 K\dfrac1{20} = 0.5\,K. In water: μgμw=1.54/3=1.125\dfrac{\mu_g}{\mu_w} = \dfrac{1.5}{4/3} = 1.125, so 1fw=0.125 K\dfrac1{f_w} = 0.125\,K. Dividing, fw20=0.50.125=4\dfrac{f_w}{20} = \dfrac{0.5}{0.125} = 4, so fw=80 cmf_w = 80\ \mathrm{cm}. The lens becomes four times weaker because the relative refractive index drops from 1.51.5 to 1.1251.125.
Report a mistake

Original question written in the JEE Main 2017 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake