Q 12-09-112JEE MainJEE Main 2023 (25 Jan, Shift 2)Medium
An object is placed on the principal axis of convex lens of focal length $10\ \text{cm}$ as shown. A plane mirror is placed on the other side of lens at a distance of $20\ \text{cm}$. The image produced by the plane mirror is $5\ \text{cm}$ inside the mirror. The distance of the object from the lens is ______ cm.
Numerical value type. Enter your answer.
Answer: 30
The mirror's image is $5\ \text{cm}$ behind it, so the lens image (the mirror's object) is $5\ \text{cm}$ in front of the mirror, i.e. $v=20-5=15\ \text{cm}$ from the lens.
$$\frac1{15}-\frac1u=\frac1{10}\ \Rightarrow\ \frac1u=-\frac1{30}\ \Rightarrow\ u=-30\ \text{cm}$$
The object is $30\ \text{cm}$ from the lens.
Solution by Sreeraj P, M.Sc Physics