Question

do the following sum

an object is placed at a distance of 30 cms from a convex lens . the image is formed at a distance of 45 cms . find the focal length of the lens and write the position of object and image

Answer 1

Convex lens: f is positive.  u is negative.    u = - 30 cm

We donot know if real or virtual image is formed.

1) Assume a real image is formed. v = +45 cm
   $\frac{1}{f} = \frac{1}{v} - \frac{1}{u} \\ \\ = \frac{1}{45} + \frac{1}{30} \\ \\ = \frac{5}{90} \\ \\ f = 16 cm$

  Let us say that the object is at 30cm from the lens on the left side then
    image is formed inverted on the right side of lens at 45cm.

2) Assume a virtual image is formed v = -45 cm

   $\frac{1}{f} = \frac{-1}{45} + \frac{1}{30} \\ \\ f = 90 cm$

     image is formed erect and on the same side as the object wrt to lens