Question

an object of 1.2 cm is placed before a convex mirrors of focal length 20cm so that a real image is formed at a distance of 60cm from it find the position and height of an object?

Answer 1

Here, Image Distance (v) = -60 cm and focal length (f) = -20 cm
Object Distance (u) = ?
By using the mirror formula,
1/v + 1/u = 1/f
1/-60 + 1/u = 1/-20
1/u = -1/20 + 1/60
By taking the LCM
1/u = [(-1*3) + 1]/60
1/u = -2/60
1/u = *1/30
u = -30 cm
So, the object must be placed between Centre of Curvature and Focus at the distance of 30 cm from the mirror.

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 .