A convex lens of focal length 25 cm produces images of the same magnification 2 , when an object is kept at two positions x 1 and x 2 x 1 > x 2 from the lens. The ratio of x 2 and x 1 is

Step-by-step solution

For the given convex lens, focal length, f = 25   cm Magnification of lens in terms of u and f is given by, m = f f + u = 25 25 + u                 . . . i When the image is real, then m = - 2 and u = - x 1 ∴ From Eq. ( i ) , - 2 = 25 25 - x 1 ⇒ x 1 = 75 2 Again, when the image is virtual, then m = 2 and u = - x 2 ∴ From Eq. ( i ) , 2 = 25 25 - x 2 ⇒ x 2 = 25 2 Hence, the ratio of x 2 and x 1 is ∴   x 2 x 1 = 25 / 2 75 / 2 = 1 3