Question

An object is placed at a large distance in front of a convex mirror of radius of curvature 40 cm.how far is the image behind the mirror?

Answer 1

The farthest point you can place an object is at infinity. So then, image is formed at the focus (behind the mirror).

R=2f
40=2*f
f=20cm

The image is 20cm behind the convex mirror.

Answer 2

Given: An object is placed at a large distance in front of a convex mirror of radius of curvature 40 cm.

To find: Distance of image behind the mirror

Solution: Let the radius of curvature be r, focal length be f, object distance be u and image distance be v.

r = 40 cm

The relation between radius of curvature and focal length is:

Radius of curvature = 2 × Focal length

=>r = 2 × f

=> 40 = 2f

=> f = 40/2

=> f = 20 cm

A convex mirror has positive focal length. Therefore, f = +20 cm

When an object is placed at a large distance from the mirror, the object distance is said to be at infinite distance.

Therefore, u = -∞(object distance is always negative)

The image distance can be found using mirror formula:

$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

$= > \frac{1}{20 } = \frac{1}{v} + \frac{1}{ - ∞}$

(since 1/∞ = 0)

$= > \frac{1}{v} = \frac{1}{20}$

=> v = 20 cm

Therefore the object is 20 cm behind the mirror.