JEE Main 2021 · Physics · Ray and Wave Optics · hard

A plano-convex lens of refractive index 1.5 has radius of curvature 30 cm for its curved surface. Its plane face is silvered. A small object is…

Single correct option

A plano-convex lens of refractive index

1.5

has radius of curvature

30\ \mathrm{cm}

for its curved surface. Its plane face is silvered. A small object is placed

45\ \mathrm{cm}

in front of the curved face on the axis. The final image is formed

Show answer and solution

Answer: (A) $90\ \mathrm{cm}$ in front of the curved face

Light passes through the lens, reflects from the plane silvered face and passes through the lens again. Lens focal length:

\dfrac1f=(1.5-1)\dfrac1{30}\Rightarrow f=60\ \mathrm{cm}

. The plane mirror contributes zero power, so the equivalent power is

\dfrac1F=\dfrac2f=\dfrac1{30}

: the system behaves as a concave mirror of focal length

30\ \mathrm{cm}

. Mirror formula with

u=-45

f=-30

\dfrac1v=-\dfrac1{30}+\dfrac1{45}=-\dfrac1{90}

, so

v=-90\ \mathrm{cm}

, a real image

90\ \mathrm{cm}

in front of the curved face.

Original question written in the JEE Main 2021 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake