Question

A boy stands in front of a mirror at a distance of 40 cm from it. He sees his erect image whose height is ⅕ th of his real height. What is the nature of the mirror? Calculate its focal length.​

Answer 1

Explanation:

Only a convex mirror can produce an erect, virtual and diminished image of an object because in question it is given height of image is 51th of real height.

u−v=M<1

⟹v<−u

⟹v1>−u1

v1+u1=f1

⟹f1>−u1+u1>0

⟹f>0

⟹ Convex mirror

Answer 2

The nature mirror is a convex mirror and the focal length of the convex mirror is 10cm

Given:

Object distance = - 40cm

m = 1/5

To Find:

The nature of the mirror and the focal length of the mirror

Solution:

Since the convex mirror produces images that are diminished and erect from the size of the object, the given mirror is a convex mirror.

The image is 1/5th of the boy's height. Therefore,

m = -v/u

m = (v/40)

1/5 = v/40

v = 8cm

To find the focal length,

$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

$\frac{1}{f} = \frac{1}{8} - \frac{1}{40} \\\frac{1}{f} = \frac{40-8}{320} \\\frac{1}{f} = \frac{32}{320}\\ \frac{1}{f} = \frac{1}{10}$

f = 10cm

Therefore, the focal length of the convex mirror is 10cm.

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