The Lens Equation

Previously we saw that the image of a distant object is formed at the focal length of the lens. What if the object isn't distant? Where is the image formed?

On this diagram we can see that the image is formed at a point beyond the focal point. At a distance v.

An experiment will reveal the relationship between between u, the object distance, and v the image distance.

Notice that:
when u is very large v is equal to f
when the object approaches the lens (u gets smaller) v increases, i.e. the image is further away.

There is an equation we can use to calculate where v will be for different values of u called The Lens Equation

Important - as distances to the right of the lens are positive then u is negative. If a question says the object is 45cm from the lens then u = -45cm

Consider this example.

Calculate the distance from the lens of an image produced by a lens f=20cm for an object 45cm from it.

1/v = -1/45 + 1/20  which is easier to put in a calculator as 1/20 - 1/45.  This gives v = 36cm.