The distance between an object and its image formed by a diverging lens is 5.80 cm. the focal length of the lens is -2.60 cm. find (a)the image distance and (b) the object distance.

a) 1.55 cm

b) 4.25 cm

Explanation:

Given:

Distance between an object and the image = 5.80 cm

Focal length of the lens, f = -2.60 cm

let the image distance be 'v' and the object distance be 'u'

thus,

u + v = 5.80 cm

or

u = 5.80 - v

from the lens formula, we have

on substituting the values, we have

on rearranging, we get

-3.84 × (v × (5.80 - v)) = v + 5.80 - v

or

-2.23v + 3.84v² = 5.80

or

3.84v² - 2.23v - 5.80 = 0

on solving the quadratic equation, we get

v = 1.55 cm

and u = 5.80 - 1.55 = 4.25 cm

hence,

a) 1.55 cm

b) 4.25 cm