Question

find the position of the object which when placed in front of a convex mirror of focal length 20cm , produce a virtual image of half the size of the object

Answer 1

Explanation:

Magnification= -v/u= -1/2

so v=u/2

1/f=2/u-1/u

so u=f

u object distance is 20 cm towards left of mirror

Answer 2

The image is located at a distance of 10 cm from the mirror.

Explanation:

Focal length of the convex lens, f = +20 cm

The mirror forms a virtual image of half the size of the object, the magnification of the mirror is,

$m=\dfrac{1}{2}=\dfrac{-v}{u}$

u = -2v

Using mirror's formula to find the position of image.

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

$\dfrac{1}{v}+\dfrac{1}{(-2v)}=\dfrac{1}{20}$

v = 10 cm

So, the image is located at a distance of 10 cm from the mirror. Hence, this is the required solution.

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Mirror's formula

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