Two identical thin Plano-convex glass lenses… - NEET UG 2015 Physics PYQ

NEET UG 2015 — Physics Optics

2015mcqhard

Two identical thin Plano-convex glass lenses (refractive index $\text{1}\text{.5}$ ) each having radius of curvature of $\text{20 cm}$ are placed with their convex surfaces in contact at the center. The intervening space is filled with oil of refractive index $\text{1}\text{.7}$ The focal length of the combination is

Official previous-year question

Held on 30 Apr 2015 · Verified 9 Jul 2026.

Options

A
$-20 cm$
B
$-25 cm$
C
$-50 cm$
D
$50 cm$

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Solution

NEET 2015 Physics, Ray Optics — solution figure

Len's maker's formula

$\frac{1}{f} = (\mu -1)(\frac{1}{{R}_{1}}-\frac{1}{{R}_{2}})$

$\frac{1}{{f}_{1}}=(\mu -1)\frac{1}{ 20} \Rightarrow (1.5-1) \frac{1}{20}=\frac{1}{40}$

$\frac{1}{{f}_{1}}=\frac{1}{40}$

For lens $\frac{1}{{f}_{1}}+\frac{1}{{f}_{2}} = \frac{1}{40}+\frac{1}{40}=\frac{1}{20}$

For concave $\frac{1}{{f}_{3}}=(1.7-1) (-\frac{1}{R}-\frac{1}{R} )= \frac{-0.7\times 2}{R}$

$\frac{1}{{f}_{eq}}=\frac{1}{20}+ (\frac{-0.7\times 2}{R})$

$=\frac{1}{20} - \frac{1.4}{20}$

${f}_{eq}= -\frac{20}{0.4} =-50 cm$

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