Question

The radius of curvature of a convex mirror is 40 cm. Find its focal length.
A. 80 cm
B. 40 cm
C. 20 cm
D. 10 cm

Answer 1

Hint:The radius of curvature of convex or concave mirror is equal to two times of the focal length of convex or concave mirror.The radius of curvature is the radius of sphere formed by the convex or concave mirror. It is also equal to the distance between the pole and centre of curvature. The sign convention for focal length and radius of curvature is the same.

Complete step by step answer:
From the question, we know that the radius of curvature of a convex mirror is,
$R=40\mathrm{c}\mathrm{m}$
We know that the relationship between the radius of curvature of convex mirror and its focal length,
$f={\displaystyle \frac{R}{2}}$
Here, $f$ is the focal length of the convex mirror.
Substitute the given value in the above equation, we have,
$$\begin{gathered} f={\displaystyle \frac{40\mathrm{c}\mathrm{m}}{2}} \\ \therefore f=20\mathrm{c}\mathrm{m} \end{gathered}$$
Thus, the focal length of the convex mirror is 20 cm and option C is correct.

Note:In convex mirror, the mirror coating is inside the spherical surface. The image formed by the convex mirror is smaller than the object; it will be upright and virtual. The image will be closer to the mirror as compared to the object whereas in concave mirror, the mirror coating is outside the spherical surface. The image formed by the concave mirror is bigger than the object; it will be upright and virtual. The image will be behind the mirror.