Chapter 9 · Question 4

Find the focal length of a convex mirror whose radius of curvature is 32 cm.

Answer Revealed

Direct Answer:

For a spherical mirror,

f = R/2

. So the focal length of a convex mirror with radius of curvature 32 cm is

32/2 = 16

cm.

Simple Explanation

The focal length is half the radius of curvature. So we divide 32 by 2 to get 16 cm.

Exam-Ready Structure

For any spherical mirror (concave or convex), the relationship between focal length (

f

) and radius of curvature (

R

) is:

f = R/2

. Given:

R = 32

cm for a convex mirror. Therefore,

f = R/2 = 32/2 = +16

cm. For a convex mirror, the focal length is taken as positive by sign convention because the focus lies behind the mirror. Answer: The focal length is +16 cm (or 16 cm behind the mirror).

Key Points

Formula: $f = R/2$ for spherical mirrors
$R = 32$ cm, so $f = 16$ cm
For convex mirror, focal length is positive (+16 cm)

Find the focal length of a convex mirror whose radius of curvature is 32 cm.