# Multiple lenses

1. Nov 30, 2007

### indigojoker

So there are two lenses. The first lens is a converging lens and the second is a diverging lens with focal length f,-f respectively, seperated by a distance D. The question asks to show the combined effect of the lenses is focusing however, I am not getting them to be always focusing.

using: $$\frac{1}{o}+\frac{1}{i}=\frac{1}{f}$$ we see that an object placed at infinity gives i=f

Moving onto the second lens, the object is located at D-f so we get:

$$\frac{1}{D-f}+\frac{1}{i}=-\frac{1}{f}$$
$$-\frac{1}{D-f}-\frac{1}{f}=\frac{1}{i}$$
$$-(\frac{1}{D-f}+\frac{1}{f})=\frac{1}{i}$$
$$-(\frac{f+D-f}{f(D-f)})=\frac{1}{i}$$
$$-(\frac{f+D-f}{f(D-f)})=\frac{1}{i}$$
$$\frac{D}{f^2-fD}=\frac{1}{i}$$
$$\frac{f^2-fD}{D}=i$$

we see that if D>f then the image is negative, telling use that there isnt convergence

any ideas?