How far should be the object be placed from the pole of converging mirror of 20 cm to form a real image of the size exactly 1/4th of the size of object?

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Solution

We have,

Focal length, f = -20 cm

Let object distance be u and image distance be v.

Magnification is, m = -v/u = -1/4 (for real image m is negative)

Therefore, v = u/4

Now,

1/f = 1/v + 1/u

=> -1/20 = 4/u + 1/u

=> -1/20 = 5/u

=> u = -100 cm

Thus, the object must be placed at a distance 100 cm from the pole of the concave mirror.

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