Question

A spherical mirror and a thin spherical lens have each a focal length of$-15cm.$ The mirror and the lens are likely to be

• A. both concave
• B. both convex.
• C. the mirror is concave and the lens is convex
• D. the mirror is convex, but the lens is concave.

Answer 1

The correct option is A

both concave

Explanation for the correct option

Option (A)

1. A concave is a lens that diverged parallel light rays incident on it. A concave mirror is a mirror whose reflected surface is curved inward.
2. In optics the direction of incident light is considered positive. In a concave mirror, the focus is placed at the front of the reflecting surface.
3. In the below figure, the incident ray is going in the positive direction but after reflection, it passes through the focus and takes the negative direction. So focal length of a concave mirror is negative.
4. Similarly the focus in a diverging lens is placed on the same side of the incident light. We see in the figure that refracted light rays diverged from the point $F_2$ which is the opposite side of the lens, so the focal length is negative.

Diagram

Explanation for the incorrect options

Explanation for incorrect options:

Option (B)

1. A convex lens is a lens that converges light rays after refraction, which is the same side of the incident rays.
2. In optics, the direction of incident light is considered positive. In a convex mirror, the focus is placed inside the mirror and converged from the focus which is placed inside the mirror. So, for a convex lens and convex mirror, the focal length can't be negative.

Option (C)

1. In the below figure, the incident ray is going in the positive direction but after reflection, it passes through the focus and takes the negative direction. So focal length of a concave mirror is negative.
2. For a convex both the image distance and object distance are positive, as shown in figure. lens . So, for a convex lens, the focal length can't be negative.

Option (D)

1. In optics, the direction of incident light is considered positive. In a convex mirror, the focus is placed inside the mirror and converged from the focus which is placed inside the mirror. So in both cases, the focal length is positive.
2. In optics the direction of incident light is considered positive. In a concave mirror, the focus is placed at the front of the reflecting surface. That's why the focal length of concave lens is negative.

Diagram

Therefore, option (A) is correct.