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 (a)

1. position, and
2. size, of the image relative to the size of the truck.

What will be the nature of the image?

Answer 1

Given: Radius of curvature (R) = +2.0 m

Object distance (u) = −3.5 m

a. The relation between the focal length and the radius of curvature is:

f = `R/2`

⇒ f = `2.0/2`

⇒ f = 1.0 m

By using the mirror formula:

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

⇒ `1/1.0 = 1/v + 1/-3.5`

⇒ `1/v = 1 + 1/3.5`

⇒ `1/v = 1 + 2/7`

⇒ `1/v = 9/7`

⇒ v = `7/9`

⇒ v = 0.78 m

b. By using the magnification formula:

m = `-v/u`

⇒ m = `-(7/9)/-3.5`

⇒ m = `7/(9 xx 3.5)`

⇒ m = `7/31.5`

⇒ m = `2/9`

⇒ m = 0.22

Since the magnification is positive and less than 1, the image is virtual, erect, and diminished.