Question

The distance between a real object and its real image is 56 CM formed by a converging lens, focal length of lenses
(1) f ≤ 14
(2) f > 14
(3) f = 14
(4) f = 28

Answer 1

Given info : the distance between a real object and its real image is 56 cm formed by converging lens.

To find : focal length of lens.

Solution : let focal length of converging lens is f .

A/c to question, u + v = 56 cm [ because real image formed by converging lens just opposite of its object ]

now using formula, 1/v - 1/u = 1/f

⇒1/(56 - u) - 1/u = 1/f

⇒1/(56 - u) - 1/-u = 1/f

⇒(u + 56 - u)/(56u - u²) = 1/f

⇒56f = 56u - u²

⇒u² - 56u + 56 f = 0

Discriminant = (56)² - 4 × 56f ≥ 0

⇒56 × 56 ≥ 4 × 56 f

⇒14 ≥ f

Therefore the focal length would be f ≤ 14