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 in size to the object? Also find the power of the lens.
(i) In this case needle is the object. Since the image is real, inverted and of same size as the needle (or object), the needle must be at the same distance (50 cm) in front of lens, as the image is behind the lens. Thus, the needle is placed at a distance of 50 cm from lens in the front.
(ii) When the image formed by a convex lens is of the same size as the needle (or object), then the distance of needle from the lens is 2f (twice the focal length).
In this case: focal length, f = 50/2cm
Thus, the focal length of this convex lens is +25 cm. This is equal to (+25)/100m or +0.25m. Now, Power, P= 1/(f(in meters)) = 1/(+0.25) = +4.0 D
So, the power of this convex lens is +4.0 diopters.