Question

A boy is standing in front oftwo big mirrors $P$ and $Q$ fitted side by side on a wall. He can see the erect image of his face in both the mirrors, the size of his face in mirror $P$ remains the same but it goes on increasing in mirror $Q$. which one of the following is correct?

• A. Mirror $P$ is convex and $Q$ is concave.
• B. Mirror $P$ is plane and $Q$ is concave.
• C. Mirror $P$ is plane and $Q$ is convex.
• D. Mirror $P$ is concave and $Q$ is plane.

Answer 1

The correct option is B Mirror $P$ is plane and $Q$ is concave.

In a plane mirror, the images is that the dimensions of the image are the same as the dimensions of the object. They do not change.

In a concave mirror, there is a relationship between the object distance and object size and the image distance and image size. Starting from a large value, as the object distance decreases (i.e., the object is moved closer to the mirror), the image distance increases; meanwhile, the image height increases. At the center of curvature, the object distance equals the image distance and the object height equals the image height. As the object distance approaches one focal length, the image distance and image height approaches infinity. Finally, when the object distance is equal to exactly one focal length, there is no image. Then altering the object distance to values less than one focal length produces images that are upright, virtual and located on the opposite side of the mirror. Finally, if the object distance approaches $0$, the image distance approaches $0$ and the image height ultimately becomes equal to the object height.

In this case, the size of the boy's face in mirror $P$ remains the same but it goes on increasing in mirror $Q$.

Therefore, the mirror $P$ is a plane mirror and the mirror $Q$ is a concave mirror.