Question

an object of height 20 cm is kept at a distance of 48 cm in front of a mirror of focal lenght 12 cm ,if the mirror forms a virtual ,diminished image of the object the calculate the distance of the image from mirror and its magnification .​

Answer 1

v=-16cm (1/v=1/12-1/48)

&h=-60cm

Answer 2

The distance of the image from mirror and its magnification is 9.6 cm and 0.2 respectively.

Explanation:

Given that,

Height of the object, h = 20 cm

Object distance, u = -48 cm

As it forms virtual ,diminished image of the object, this is a case of convex mirror, so, f = +12 cm

Let v is the location of the image. It can be calculated as :

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

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

$\dfrac{1}{v}=\dfrac{1}{12}-\dfrac{1}{(-48)}$

v = 9.6 cm

So, the image will be formed at a distance of 9.6 cm from the mirror. The magnification of the mirror is given by :

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

$m=\dfrac{-9.6}{-48}$

m = 0.2

Hence, this is the required solution.

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