Answer:
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