Question

A object is placed 15 cm from (a) a converging mirror (b) a diverging mirror,
of radius of curvature 20 cm. Calculate the image position and magnification in each case.

Answer 1

U= -15

Case of converging mirror

2f=r

F=20 /2

F= 10 therefore f= -10

Mirror formula

1/f = 1/ v +1/u

1/v = -1/10 + 1/15

1/v = -1/30

V= 30

M= -v/u

M = -(-30 )/ -15

M= -2

Case of diverging mirror

U=-15

F= 10

1/ v = 1/f -1/ u

1/v = 1/6

V= 6

Magnification = -(-v) /u

M= -(6) / - (15 )

M = 0.4

Answer 2

Explanation:

(a) u = -15cm,

R = -20cm (Converging mirror)

f = R/2 = -10 cm

1/v + 1/u = 1/f

1/v + 1/-15 = 1/-10

⇒ 1/v – 1/15 = -(1/10)

⇒ 1/v = 1/15 – 1/10 = (2 -3)/30 = - (1/30)

∴ v = - 30 cm

The image is formed 30 cm in front of the mirror.

m = - (v/u) = - (-30)/(-15) = -2

(b)  u = -15cm,

R = 20cm (Diverging mirror)

f = R/2 = 10 cm

1/v + 1/u = 1/f

1/v + 1/-15 = 1/10

⇒ 1/v – 1/15 = 1/10

⇒ 1/v = 1/15 + 1/10 = (2 + 3)/30 = 5/30

∴ v = 6 cm

The image is formed 6 cm behind the mirror.

m = - (v/u) = - (6)/(-15) = 0.4