Question

An object 3 cm high is placed at a distance of 10 cm in front of a converging mirror of focal length 20 cm. Find the position, nature, and size of the image formed.

Answer 1

Given:

The height of the object h_i = 3 cm

object distance u = −10 cm

focal length f = −20 cm

Now,

Finding the distance of the image:

According to Mirror formula,

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

`1/v = 1/f − 1/u`

`1/v = 1/(−20) − 1/(−10)`

`1/v = (−1 + 2)/20 = 1/20`

v = 20 cm

Finding the height of the image:

Magnification is the ratio of the height of an image with respect to the height of an object.

`m =−v/u = h_i/h_0`

`(−20)/(−10) = h_i/3 cm`

⇒ h_i = 6 cm

The nature of the image is virtual. (as image distance is on the right side of mirror.)