 JEE Mains Previous Years Questions with Solutions

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1

JEE Main 2014 (Offline)

A thin convex lens made from crown glass $\left( {\mu = {3 \over 2}} \right)$ has focal length $f$. When it is measured in two different liquids having refractive indices ${4 \over 3}$ and ${5 \over 3},$ it has the focal lengths ${f_1}$ and ${f_2}$ respectively. The correct relation between the focal lengths is :
A
${f_1} = {f_2} < f$
B
${f_1} > f$ and ${f_2}$ becomes negative
C
${f_2} > f$ and ${f_1}$ becomes negative
D
${f_1}\,$ and${f_2}\,$ both become negative

Explanation

By Lens maker's formula for convex lens

${1 \over f} = \left( {{\mu \over {{\mu _L}}} - 1} \right)\left( {{2 \over R}} \right)$

for, $\mu {L_1} = {4 \over 3},{f_1} = 4R$

for $\mu {L_2} = {5 \over 3},{f_2} = - 5R$

$\Rightarrow {f_2} = \left( - \right)ve$
2

JEE Main 2013 (Offline)

The graph between angle of deviation $\left( \delta \right)$ and angle of incidence $(i)$ for a triangular prism is represented by
A B C D Explanation

For the prism as the angle of incidence $(i)$ increase, the angle of deviation $\left( \delta \right)$ first decreases goes to minimum value and then increases.
3

JEE Main 2013 (Offline)

Two coherent point sources ${S_1}$ and ${S_2}$ are separated by a small distance $'d'$ as shown. The fringes obtained on the screen will be A
points
B
straight lines
C
semi-circles
D
concentric circles

Explanation

It will be concentric circles.
4

JEE Main 2013 (Offline)

Diameter of a plano-convex lens is $6$ $cm$ and thickness at the center is $3mm$. If speed of light in material of lens is $2 \times {10^8}\,m/s,$ the focal length of the lens is
A
$15$ $cm$
B
$20$ $cm$
C
$30$ $cm$
D
$10$ $cm$

Explanation $\therefore$ $n = {{Velocity\,\,of\,\,light\,\,in\,\,vacuum} \over {Velocity\,\,of\,\,light\,\,in\,\,medium}}$

$\therefore$ $n = {3 \over 2}$

${3^2} + {\left( {R - 3mm} \right)^2} = {R^2}$

$\Rightarrow {3^2} + {R^2} - 2R\left( {3mm} \right) + {\left( {3mm} \right)^2} = {R^2}$

$\Rightarrow R \approx 15\,cm$

${1 \over f} = \left( {{3 \over 2} - 1} \right)\left( {{1 \over {15}}} \right) \Rightarrow f = 30\,cm$