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Ray Optics — JEE physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceJEE physicsRay Optics1 Mark
MCQ
Shown in the figure here is a convergent lens placed inside a cell filled with a liquid. The lens has focal length $+20 \mathrm{~cm}$ when in air and its material has refractive index $1.50.$ If the liquid has refractive index $1.60,$ the focal length of the system is
Image
  • A
    $+80 \mathrm{~cm}$
  • B
    $-80 \mathrm{~cm}$
  • C
    $-24 \mathrm{~cm}$
  • ✓
    $-100 \mathrm{~cm}$
✓

Answer

Correct option: D.
$-100 \mathrm{~cm}$

$\frac{1}{f_1}=(1.6-1)\left(\frac{1}{\infty}-\frac{1}{20}\right)=-\frac{0.6}{20}=-\frac{3}{100} $
$ \frac{1}{f_2}=(1.5-1)\left(\frac{1}{20}-\frac{1}{-20}\right)=\frac{1}{20} $
$ \frac{1}{f_3}=(1.6-1)\left(\frac{1}{-20}-\frac{1}{\infty}\right)=-\frac{3}{100} $
$\Rightarrow \frac{1}{F}=-\frac{3}{100}+\frac{1}{20}-\frac{3}{100}$
$ \Rightarrow F=-100\ cm$

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