Two Objects A and B, When Placed In Turn In Front Of A Concave Mirror Of Focal Length 7.5 Cm Give Images Of Equal Size. If A is Two Times The Size OfB and Is Placed At A Distance Of 15cm From The Mirror, Find The Distance OfB from The Mirror

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Question

Two objects A and B, when placed in turn in front of a concave mirror of focal length 7.5 cm give images of equal size. If A is two times the size ofB and is placed at a distance of 15cm from the mirror, find the distance ofB from the mirror

diffcult

Solution

Correct option is

11.25 cm

For a mirror (concave or convex)

We have

And magnification

For object A: u = – 15cm, f = – 7.5 cm

If y₁ is the size of the object A and y₂ the size of the image, then the magnification is

For object B: size of object B = y₁/2 (given) and size of the image of B = – y₁ (inverted)

or c = 2u

from mirror formula, we have

The object B is a distance of 11.25 cm in front the mirror.

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