A convex lens forms a real and inverted image of a needle at a distance of `50 cm` from it. Where is the needle placed in front of the convex lens if the image is equal to size of the object ? Also, find the power of the lens.

Explanation

Here, the image distance, `v = 50 cm`, object distance, `u = ?`, power of lens, `P = ?`
As the image is of the same size as the object, therefore, object must be at a distance equal to twice the focal length of the lens. In this case, `-u = v = 2f = 50 cm`.
Thus, `u = -50 cm` and `f = 25 cm`.
As `P = 100/(f(cm)), P = 100/25 = 4 dioptre`.