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

By Shivank Goel|Updated : August 11th, 2022

Given, a distance of an object from a concave spherical mirror, u = -50 cm

Magnification, m = -1/2

We have to find the image distance to get a magnification of -1/5

For a spherical mirror,

m = -v/u

-1/2 = -v/-50

v = -50/2

v = -25 cm

By using the mirror formula,

1/f = 1/v + 1/u

Where, f = focal length

v = image distance

u = object distance

So, 1/f = 1/-25 + 1/-50

1/f = -2-1 / 50

1/f = -3/50

f = -50/3 cm

From the question,

-1/5 = -v/u

v = u/5

So, -1/(50/3) = 1/(u/5) + 1/u

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

-3/50 = (5+1)/u

-3/50 = 6/u

-1/50 = 2/u

u = -2(50)

u = -100 cm

Therefore, the required image distance is 100 cm.

Summary:

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

When an object is placed at a distance of 50 cm from a concave spherical mirror, the magnification produced is -1/2. The object is placed at a distance of 100 cm to get a magnification of -1/5.

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