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JEE Advanced 2023 Paper 1 · Physics · Ray and Wave Optics · medium

A thin plano-convex glass lens (refractive index 1.5) has its curved surface of radius of curvature 30 cm facing a small point object on the axis, 20…

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A thin plano-convex glass lens (refractive index 1.51.5) has its curved surface of radius of curvature 30 cm30\ \mathrm{cm} facing a small point object on the axis, 20 cm20\ \mathrm{cm} from the lens. The plane surface of the lens is silvered. Treating the lens as thin, the distance in centimetres of the final image from the lens is
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Answer: 60

Light enters through the curved surface, reflects from the silvered plane surface and leaves through the curved surface again. The lens, mirror, lens combination acts as a single mirror of power P=2PLP=2P_L (two passes through the lens, the plane mirror adding no power). The focal length of the lens is given by 1fL=(μ−1)1R=0.530\dfrac1{f_L}=(\mu-1)\dfrac1R=\dfrac{0.5}{30}, so fL=60 cmf_L=60\ \mathrm{cm} and the equivalent mirror has focal length F=fL/2=30 cmF=f_L/2=30\ \mathrm{cm}, concave. With the object at u=−20 cmu=-20\ \mathrm{cm} and f=−30 cmf=-30\ \mathrm{cm} the mirror equation gives 1v=1f−1u=−130+120=160\dfrac1v=\dfrac1f-\dfrac1u=-\dfrac1{30}+\dfrac1{20}=\dfrac1{60}. So v=+60 cmv=+60\ \mathrm{cm}, a virtual image 60 cm60\ \mathrm{cm} behind the silvered surface. Since the object lies inside the focal length, the image is virtual and magnified, as expected. The distance from the lens is 60 cm60\ \mathrm{cm}.
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