Verified Solution • 2025–26 Session moderate

QJEEM22Ph303a: JEE Main 2022 Physics - Class 12 JEEM22Ph303a Solution: For an object placed at a distance 2.4 m from a lens, a sharp…

For an object placed at a distance 2.4 m from a lens, a sharp focused image is observed on a screen placed at a distance 12 cm from the lens. A glass plate of refractive index 1.5 and thickness 1 cm is introduced between lens and screen such that the glass plate plane faces parallel to the screen. By what distance should the object be shifted so that a sharp focused image is observed again on the screen?

Multiple Choice Options

  • A 0.8 m
  • B 3.2 m
  • C 1.2 m
  • D 5.6 m

Step-by-Step Verified Solution

The shift produced by the glass plate is

d=t(1−1μ)=1×(1−11.5)=13d = t\left( {1 - {1 \over \mu }} \right) = 1 \times \left( {1 - {1 \over {1.5}}} \right) = {1 \over 3} cm

So final image must be produced at (12−13)\left( {12 - {1 \over 3}} \right) cm =353= {{35} \over 3} cm from lens so that glass plate must shift it to produce image at screen. So

112−1−240=1f=135/3−1u{1 \over {12}} - {1 \over { - 240}} = {1 \over f} = {1 \over {35/3}} - {1 \over u}

1u=335−112−1240{1 \over u} = {3 \over {35}} - {1 \over {12}} - {1 \over {240}}

or u=−560u = - 560 cm

so shift =5.6−2.4=3.2= 5.6 - 2.4 = 3.2 m

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