1. A source of light and screen are separated by a distance of 50 cm . A sharp image of the source is produced by lens when placed at 2 positionsbetween the source and the screen . If the distance of the separations of the lens between 2 positions is 20 cm , find the focal length of the lens .

 where,

v=distance of image

u=distance of object

f=focal length of the lens

Now let the distance between point B and the screen is x,

Now applying the lens formula when the lens is kept at both the points A & B separately,

For point B: using proper sign conventions

u = -(50-x)

v = x

For point A: 

u = -(30-x)

v = (20+x)

Solving two above mentioned equations we can get the value of focal length of the lens.