Question

an object 2 cm high when placed in front of a converging mirror produces a virtual image 3 cm high. if the object is placed at a distance of 8 cm from the pole of the mirror, calculate: 1) the position of the image 2) the focal length of the converging mirror

Answer 1

it's a concave mirror.

h=+2 cm, H=+3 cm ,u=-8 cm

H/h=v/u

3/2=v/-8

-24/2=v

-12 cm = v

now,

1/v+1u=1/f

-1/12-1/8

-8-12/96

-20/96

-10/48

f=-4.8 cm

Answer 2

Given,

Object height=2cm

Image height=3cm

Object distance=8cm

To Find,

Position of the image.

Focal length of the mirror.

Solution,

As it is a concave mirror,

h=+2 cm, H=+3 cm ,u=-8 cm

H/h=v/u

⇒3/2=v/-8

⇒-24/2=v

⇒-12 cm = v

We have the formula,

1/v+1u=1/f

-1/12-1/8=1/f

-8-12/96=1/f

-20/96=1/f

-10/48=1/f

f=-4.8 cm

Hence, focal length of the concave mirror is 4.8cm. Position of the image is behind the object at 12 cm from the mirror.