Show that a convex lens produces an N times magnified image when the object distances from the lens have magnitudes `(f+- f/N)` Hence, find the two values of object distance for which a convex lens of power 2.5 D will produce an image that is 4 times as large as the object ?

Explanation

We know that magnification produced by a lens is given by `m=v/u = f/(u +f)`
Hence, in present case `+- N =f/(u+f)` signs are used for virtual and real images respectively]
`u+f =+- f/N rArr u =-f +- f/N` or `|u| =f+- f/N`
In present numerical problem `P = +2.5 D`, hence, `f = 1/P = 1/2.5 m = 40 cm`, and magnification `N=+-4`
`therefore u=f +-f/N = 40 +- 40/4 = 40 +- 10 = 50 cm` or 30 cm