Question

If the radius of curvature of a spherical mirror is $20\,cm$, then its focal length is ___________cm.
A. $20$
B. $40$
C. $10$
D. None of these

Answer 1

Hint: A spherical mirror is a mirror that has a shape of a piece that is cut out to be a spherical surface. A spherical mirror is that mirror that has a reflecting surface inward or outward and is in the shape of a sphere. Here, we will use the formula of the radius of curvature to find the focal length of a spherical mirror.

Complete answer:
The radius of curvature of a spherical mirror is defined as the distance between the center of curvature and the pole of a spherical mirror. In the question, the radius of the curvature of the spherical mirror is $20\,cm$. Therefore, $R = 20\,cm$

The focal length is defined as the distance between the pole and the focus of a spherical mirror.Now, the focal length is also defined as half of the radius of curvature of a spherical mirror and it is given below
$f = \dfrac{R}{2}$
Now, putting the value of $R$ in the above formula, we get
$f = \dfrac{{20}}{2}$
$\therefore f = 10\,cm$

Therefore, the focal length of a spherical mirror is $10\,cm$.Hence, option (C) is the correct option.

Note:A spherical mirror is a part of the mirror, in the form of a sphere, in which the inner or outer surface is polished and non-reflecting. We can say that the curved surface is a spherical surface. A spherical mirror is of two types which are a concave mirror and convex mirror. If the surface of a spherical mirror is concave then it is called a concave mirror whereas if the surface of a spherical mirror is convex then it is called a convex mirror.