Question

The distance between an object and its image formed by a diverging lens is 8.20 cm. The focal length of the lens is -3.70 cm. Find (a) the image distance and (b) the object distance.

Answer 1

Solution-

d + d' = 8.20 cm   ................... (1)
using lens equation ,
                            1 / f = (1/d)+(1/d')
focal length f = dd' / (d + d')
               dd' = f (d + d')
                     = (-3.70 cm)(8.20 cm)
                     = -30.34 cm2
(d +d')^2 + (d - d')^2 = 4dd'

(8.2)^2 + (d - d')^2 = 4(-30.34)

d - d' = 7.36 .................. (2)

adding eq (1) & (2) , we get

d = 7.78 cm    (object distance)

this value substitute in eq (1) , we get

   d' = -0.42 cm  

for diverging lens image distance must be negative.

image distance d' = 0.42 cm

answers :

a )

image distance d' = 0.42 cm

b)

object distance d = 7.78 cm