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JEE Advanced 2016 Paper 1 · Physics · Ray and Wave Optics · hard

A thin convex lens of focal length 20 cm has a small object placed 30 cm in front of it on its principal axis. A plane mirror is placed perpendicular…

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A thin convex lens of focal length 20 cm20\ \mathrm{cm} has a small object placed 30 cm30\ \mathrm{cm} in front of it on its principal axis. A plane mirror is placed perpendicular to the axis on the other side of the lens, 50 cm50\ \mathrm{cm} from the lens. Light from the object passes through the lens, is reflected by the mirror and passes through the lens a second time. Considering only this final image formed after the second refraction, it is located
  1. A. 40 cm40\ \mathrm{cm} in front of the lens (on the side of the object), real, upright and twice the size of the object
  2. B. 40 cm40\ \mathrm{cm} in front of the lens (on the side of the object), real, inverted and twice the size of the object
  3. C. 60 cm60\ \mathrm{cm} behind the mirror, virtual, inverted and of the same size as the object
  4. D. at infinity, since the rays emerge parallel to the axis
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Answer: (A) 40 cm40\ \mathrm{cm} in front of the lens (on the side of the object), real, upright and twice the size of the object

First refraction: 1v=1f+1u=120−130\dfrac1v=\dfrac1f+\dfrac1u=\dfrac1{20}-\dfrac1{30} gives v=60 cmv=60\ \mathrm{cm} with magnification m1=v/u=−2m_1=v/u=-2 (inverted, twice the size). The mirror at 50 cm50\ \mathrm{cm} intercepts the converging beam before it comes to a focus, so I1I_1 acts as a virtual object 10 cm10\ \mathrm{cm} behind the mirror. A plane mirror forms a real image 10 cm10\ \mathrm{cm} in front of it, i.e. 40 cm40\ \mathrm{cm} from the lens, with m2=+1m_2=+1. For the returning light this point is a real object at u=40 cmu=40\ \mathrm{cm}, so v=ufu−f=40 cmv=\dfrac{uf}{u-f}=40\ \mathrm{cm} on the object side, with m3=−v/u=−1m_3=-v/u=-1. The net magnification is (−2)(+1)(−1)=+2(-2)(+1)(-1)=+2: real, upright relative to the original object, twice as large. The second option forgets the inversion by the second pass. The fourth would hold only if the mirror were at 40 cm40\ \mathrm{cm}.
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Original question written in the JEE Advanced 2016 Paper 1 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake