Question

a 5 cm tall object is placed at a distance of 30 cm from a convex mirror of focal length 15 cm. find the position, size and nature of the image formed.

Answer 1

height of object , h = 5cm
object distance from the convex mirror, u = -30 cm
focal length of convex mirror, f = +15cm

now, use formula 1/v + 1/u = 1/f

or, 1/v + 1/-30 = 1/15

or, 1/v = 1/15 + 1/30 = 3/30

or, v = +10cm

hence, position of image is 30cm right side from the pole of convex mirror.

magnification = -v/u

height of image/height of object = - (+10)/(-30) = +1/3

height of image/5cm = 1/3

height of image = 5/3cm = 1.67cm

hence, virtual image is formed by the convex mirror and the size of image is smaller than size of object.

Answer 2

Given u=-20cm

f=-30 cm

H1=5cm

I/v+1/u=1/f

1/v=1/-30+1/20

1/v=-2+3/60

I/v = 1/60

V=60cm

H2/H1=-v/u

On solving

H2=15 cm