When an object is placed at a distance of 50 cm from a concave mirror , the magnification produced is - 1/2 . where should the object be placed to get a magnification of -1/5

Let, focal length be f.

Now,

Object distance, u = -50 cm

Magnification, m = -1/2

Image distance = v

So, -v/u = -1/2

=> v = u/2 = -25 cm

So,

1/f = 1/v + 1/u

=> 1/f = -1/25 – 1/50

=> f = -50/3 cm

Now,

Magnification is, m = -1/5

So, -v/u = -1/5

=> v = u/5

Thus,

1/f = 1/v + 1/u

=> -3/50 = 5/u + 1/u

=> -3/50 = 6/u

=> u = -100 cm

So, the object must be placed at a distance 100 cm from the mirror.

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