The Thin Lens Equation

We can find the position of the image of a lens mathematically as there is mathematical relation between the object distance, image distance, and focal length.

where
u = object distance [cm]
v = image distance [cm]
f = focal length of lens [cm]

When applying the equation, take note of the following:
1) The object distance,u, is always positive.

2) If the image on the same side of the lens as the light leaves the lens. Then v is positive and the image is real .

3. If the image on the same side of the lens as the light rays enter the lens. Then v is negative
and the image is virtual.

Worked example :

1. An object of height 3 cm is placed
(a) at 30 cm
(b) at 5 cm
from a convex lens of focal length 10 cm. determine the position and the size of the image in each case.

solution :
given ,
u= 30 cm, f = 10 cm

find v=?

1/f = 1/u + 1/v
1/10 = 1/30 + 1/v
v= +15 cm
(a positive sign shows that the image is real )


m = image height / object height = v/u
image height / 3 = 15/30
==> image height =1.5 cm

The image is real and at the distance of 15 cm from the lens on the opposite side of the object. the height of the image is 1.5 cm.