Question

What is the focal length of a convex mirror that produces an image, 0.50 m behind the mirror, of a child who is 1.05 m tall standing 5.3 m in front of the mirror?

Answer 1

The focal length is f=-0.45m

Step-by-step explanation:

This problem bothers on the curved mirrors

Given data

Image distance v= 0.5m

Object distance u= 5.3m

Focal length of the mirror f=?

Applying the formula

1/v + 1/u = 1/-f

N/B the negative sign indicates a convex mirror has a virtual focus

2+0.1886=1/-f

2.188= 1/-f

f= -1/2.188

f= -0.45m

Answer 2

0.55m

Step-by-step explanation:

For a convex mirror, the nature of image formed by the mirror is virtual and upright. The image distance and the focal length of the mirror are negative.

Using the mirror formula:

1/f = 1/u+1/v

f is the focal length

v is the image distance

u is the object distance

Given u = 5.3m, v = -0.5m

-1/f = 1/5.3-1/0.5

-1/f = 0.189-2

-1/f = -1.811

f = 1/1.811

f = 0.55m

The focal length of the convex mirror is 0.55m