Question

The radius of curvature of a convex mirror used as a rear view mirror in a moving car is 2.0 m. A truck is coming from behind it at a distance of 3.5 m. Calculate

1. position and
2. size of the image relative to the size of the truck.
3. What will be the nature of the image?

Answer 1

Given: The mirror is convex.

Distance of the object from the mirror u = −3.5 m

Radius of curvature of the mirror (R) = 2 cm

Focal length of the convex mirror (f) = 1 cm

a. We have to find the position of the image v and its magnification m.
Using the mirror formula, we get:

`1/f = 1/v + 1/u`

⇒ `1/1 = 1/v + 1/-3.5`

⇒ `1/1 + 1/-3.5 = 1/v`

⇒ `1/v` = 1 − 0.2857

⇒ `1/v` = −0.7143

⇒ v = `1/-0.7143`

⇒ v ≈ −8.40 m

The position of the image is 8.63 m behind the mirror.

b. Now, using the magnification formula, we get:

M = `v/u`

M = `(-8.40)/-3.5`

M = 2.4

c. Nature of the image

For a convex mirror:

1. The image is virtual (formed behind the mirror).
2. The image is diminished (smaller than the object).
3. The image is erect (upright).