Question

The radius of curvature of a spherical mirror is $20$ cm. What is its focal length ?

Answer 1

Hint:The radius of curvature of a spherical mirror is basically the radius or the distance between the centre to the circumference of the circle of which the spherical mirror is the part of. It is twice the focal length.

Complete step by step answer:
Spherical mirror is nothing but mirrors in sphere shape or can be said to be in a circle.Spherical mirrors is of two types:
-If the reflecting surface is the outer side of the sphere, the mirror is called a convex mirror.
-If the inside surface is the reflecting surface, it is called a concave mirror.
In the question given that,
Radius of curvature, R = $20$ cm
Radius of curvature of a spherical mirror = $2 \times $ Focal length (f)
\[R=2f\]
By putting the values we get
$f=\dfrac{R}{2} \\
\Rightarrow f=\dfrac{20}{2} \\ $
$\Rightarrow f=10\,cm$
The focal length of the given spherical mirror is $cm$. The distance between the pole(P) of a mirror and the focal point(F) of a mirror is the focal length. It is donated by the symbol f(small f).

The relation between focal length and radius of curvature is proportional as given above radius of curvature is twice of focal length. The rays of light having a single frequency which are traveling in a straight line parallel to the optical axis that is O will meet at the focal point.But the rays of Light which are parallel to each other, but not to the optical axis, will meet on the focal plane.

Hence, the focal length of a spherical mirror is 10 cm.

Note: A spherical mirror has two surfaces one is the polished reflecting surface other is the coated opaque surface depending on which side is reflecting. Depending upon the type of reflecting surface we have concave and convex mirrors.