Question

The radius of curvature of a convex mirror used as a rear view mirror in a moving car is 12.0 m. A truck is coming from behind it at a distance of 3.54 m. Calculate (a)

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 = −3.54 cm

Radius of curvature of the mirror R = 12 cm

Focal length of the convex mirror f = 6 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`

⇒ `1/6 = 1/v + 1/-3.5`

⇒ `1/6 + (- 1)/3.54 = 1/v`

⇒ `1/v = 0.1667 - 0.2825`

⇒ `1/v = -0.1158`

⇒ `v = 1/-0.1158`

⇒ v ≈ −8.63 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 = (-8.63)/-3.54`

M = 0.244

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).