Question

A small object of length 2.5cm lies,along the principal axis of a concave mirror at a distance 1.5f.The image height is?​

Answer 1

Answer:

The magnification of the image is 1.5.

Explanation

Given that,

Focal length of the concave mirror, f = -24 cm (it is negative for concave mirror)

Let u is the object distance and v is the image distance. According to given condition, the image distance is 20 m more than the object distance,

v = 20 + u

We can find the object distance from the mirror using mirror's formula as :

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

v

1

+

u

1

=

f

1

\dfrac{1}{20+u}+\dfrac{1}{u}=\dfrac{1}{-24}

20+u

1

+

u

1

=

−24

1

u = -8 cm

Image distance becomes,

v = 20 + (-8)

v = 12 cm

The magnification of the mirror is given by :

m=\dfrac{-v}{u}m=

u

−v

m=\dfrac{-12}{-8}m=

−8

−12

m = 1.5

So, the magnification of the image is 1.5. Hence, this is the required solution