Question

The distance between an object and its image formed by a diverging lens is 51.7 cm. The focal length of the lens is -235 cm.
a.) Find the image distance
b.) Find the object distance.

Answer 1

Let the image distance be "v" and the object distance be "u". Then

  ........................................(1)

Focal Length of diverging lens, f= -235cm

then using Equation of lens,

Using equation 1 in above,

  

  

  

solving for the quadratic,

  

  

  

  

considering positive value first,

now considering the negative value,

then using equation 1,

if object distance is u₁ then

image distance,

if object distance is u₂ then

image distance,

But Since its a diverging lens thus it always form the virtual image for the real object. Hence image distance will be always negative and object distance will always be positive for diverging lens.

hence Image distance, (ANS) (negative sign of image distance denotes virtual image formed towards the left of lens)

and Object Distance, (ANS) (positive sign of object distance denotes the real object towards the left of lens only)