Question

If a mirror has a focal length of \[-20\text{ cm}\]. It is a:
A. Convex mirror
B. Concave mirror
C. Plane mirror
D. Lens

Answer 1

Hint: In case of a plane mirror, the focal length is infinity as the image can be formed at infinite distance. The image in a plane mirror is formed at distance behind the mirror, equal to the distance of the object from the mirror.
A concave mirror produces an image in front of the focal point.

Complete step by step solution:
The focal length of a mirror depends on the radius of curvature of the mirror.
The focal length-radius relation is given by:
\[f=\dfrac{1}{R}\]
Where f denotes the focal length of the mirror and R denotes its radius of curvature.
R is negative for a concave surface, so the focal length is also negative, and the image formed is virtual and upright.

So, the mirror having focal length of \[-20\text{ cm}\] is a concave mirror.

Additional information:
In a concave mirror the image is virtual and erect, and is obtained on the same side of the object, whereas in a convex mirror, the image is real and inverted, and situated on the opposite side of the object.
The focal length of a convex lens is positive and that of a concave lens is negative. The focal length of a lens depends on the radius of curvature of the surface of the lens and the refractive index of the material of the lens.

Note: The focal length of both concave mirror and concave lens is negative, but in the options it is not mentioned if the lens is convex or concave.