Question

An object of height 1.2m is placed before a concave miror of focal length 20 cm so that a real image is formed at a distance of 60m from it .find the position of an object .what will be the height of the image formed

Answer 1

height of the object h=-1.2cm. [since real image ]
focal length f =-20 m
image distance v=-60m
let u be the position of the object
using mirror formula
1/V+1/u=1/f
1/u=1/f-1/V
1/u=(1/-20)-(1/-60)
1/u=1/60-1/20
1/u=1-3/60
1/u=-2/60
1/u=-1/30
u=-30m
the image is formed at a distance of 30m
from the concave mirror
let the height of the image formed =H
H/h=-V/u
H=-V x h/u
H=-(-60x-1.2)/-30
H =-72/-30
H=+2.4m
hence the image is virtual and erect and it height =+2.4m

Answer 2

Answer:

u = 30 cm

$\display \text{h _i = 2.4 cm}$

Explanation:

We have given :

Focal length = 20 cm

Image distance =  60 cm

We have to find object distance .

We know :

1 / f = 1 / v + 1 / u

Since image formed is real :

f = - 20 cm and v = - 60 cm

1 / u = 1 - 3 / 60

u = - 30 cm

Hence object distance is 30 cm .

Also given object height = 1.2 cm

We know :

h_i / h_o = - v / u

h_i / 1.2 = - 60 / 20

h_i = - 2.4 cm

Hence image height is 2.4 cm .