A convex lens forms a real and inverted image of a needle at a distance of 50cm from it. The size of the image is same as that of the object. What is the power of the lens?

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Solution

A convex lens forms a real and inverted image of equal size only when it is kept at the center of curvature of the lens. The image is also formed at the center of curvature at the other side.
Hence, the distance of object = distance of image = 50 cm.
Now, focal length = radius of curvature / 2 = 50 cm / 2 = 25 cm = 0.25m
thus,
the power of the lens will be
P = 1/f
= 1/0.25
so,
P = 4D

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