Question

For an object placed at distance of 20cm from the pole of the mirror , an image is formed 40 cm further away from the object at the same side

find..

1. Focal lenght

2. The image is real or inverted

3. What is the nature of the mirror

Answer 1

1. We have, u= -20cm
As image formed at same side, so v= -40cm
Using morror formula, 1/f = 1/v + 1/u
1/f = (1/-40) + (1/-20)
1/f = (-1-2/40)
=(-3/40)
f = -40/3 = -13.34
focal length is 13.34cm

2.Image is formed at same side of mirror, so image is real.

3.Negative sign of focal length indicates the mirror is concave.

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Answer 2

Focal length, f = -13.34 cm

Real image

concave mirror

Explanation:

It is given that,

Object distance, u = -20 cm

Image distance, v = -40 cm (at the same side)

(1) Let f is the focal length of the mirror. Using mirror's formula to find it as :

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

$\dfrac{1}{f}=\dfrac{1}{-40}+\dfrac{1}{-20}$          

f = -13.34 cm

(2) It is mentioned that the image is formed at the same side of the object. The formed image is real.

(3) The focal length of concave mirror is negative. It is a concave mirror.

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