Question

(b) An object of height 20 cm is kept at a distance of 48 cm in front of a mirror of
31
focal length 12 cm. If the mirror forms a virtual, diminished image of the object
then calculate
the distance of the image from the mirror.
(ii) its magnification.

Answer 1

Given that,

Height of an object is 20 cm

Object distance from a mirror is 48 cm

Focal length of the mirror is 12 cm  

To find,

Image distance and its magnification.

Solution,

The mirror forms a virtual, diminished image of the object, it means that the mirror is convex. Using mirrors formula to find the image distance as :

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

v is image distance

$\dfrac{1}{v}=\dfrac{1}{f}+\dfrac{1}{u}\\\\\dfrac{1}{v}=\dfrac{1}{(12)}+\dfrac{1}{(-48)}\\\\v=16\ cm$

So, the distance of the image from the mirror is 16 cm.

Magnification of the mirror is :

$m=\dfrac{-v}{u}\\\\m=\dfrac{-(16)}{-48}\\\\m=+0.34$

So, the magnification of the mirror is 0.34 and image distance is 16 cm.

Learn more,

Mirror formula

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