Question

An object 1 cm high produces a real image 1.5 cm high, when placed at a distance of 15 cm from a concave mirror. Calculate : (i) the position of the image, (ii) focal length of the concave mirror.

Answer 1

Formula = h' u / h = v

- v = (1.5) (-15) / 1

- v = - 22.5

v = 22.5

The image is positive, therefore it is a virtual and erect image.

∴ the image is formed at a distance of 22.5 cm behind the mirror.

1 / v + 1 / u = 1 / f

1 / f = 1 / 22.5 + 1 / (- 15)

1 / f = 1 / 22.5 -1 / 15

1 /f = (15 - 22.5) / 337.5

1 / f = -7.5 / 337.5

f = 337.5 / - 7.5

f = - 45 cm

∴ the focal length of the mirror is 45 cm.

Answer 2

Now we have to find focal length.

1/v+1/u=1/f

1/22.5+1/(-15)=1/f

15-22.5/337.5=1/f

-7.5/337.5=1/f

f=337.5/-7.5

f=-45 cm