JEE Physics 2023 Question with Solution

Given: focal length of convex lens is $10 \, \text{cm}$. The plane mirror is at a distance of $20 \, \text{cm}$ from the lens. The image produced by the plane mirror is $5 \, \text{cm}$ inside the mirror.

Find: the distance of the object from the lens.

Since the image formed by the plane mirror is $5 \, \text{cm}$ behind the mirror, the object for the mirror must be $5 \, \text{cm}$ in front of the mirror. Therefore, the image formed by the lens before reflection is at a distance of

from the lens.

Now apply the lens formula:

With $v = 15 \, \text{cm}$ and $f = 10 \, \text{cm}$,

So,

Therefore, the distance of the object from the lens is $30 \, \text{cm}$.

Given: the mirror forms an image $5 \, \text{cm}$ inside itself.

Find: the original object distance from the lens.

For a plane mirror, image distance behind the mirror equals object distance in front of the mirror. Hence the point from which rays reach the mirror must be $5 \, \text{cm}$ in front of it.

Since the lens and mirror are $20 \, \text{cm}$ apart, the lens must first form an image at

to the right of the lens.

Using the lens relation,

The sign indicates the usual Cartesian convention for an object on the left side of the lens, so the required distance magnitude is $30 \, \text{cm}$.

Therefore, the final answer is $30$.