All right, let's summarize the whole system then.

It turns out, the single lens imaging system is pretty darn simple.

There are a total of five independent variables that one could describe it with.

The object and image distances, the throw, the magnification, and the focal length.

There's nothing else to know.

You could replace t and t', z and z', your choice.

We have three equations which relate those variables,

the definition of throw and magnification.

And pick your favorite,

but one of the two imaging equations, the thin lens equations.

So the point is, is if you are given any 2 variables, given out of 5,

you can solve for the other 3.

So that's why I say this is a relatively simple design problem,

that's everything there is to know about it.

I just point out our common couple of forms to help with that.

Perhaps you're given the focal length and the magnification.

That's the example when using Newton's form of

the thin lens equation is quite convenient.

Because it has distances, focal lengths, and magnification in it.

So immediately, if you simply plug in the things that are given,

focal length and magnification, you have z and z'.

Sometimes you're given throw and magnification,

that would be a pretty common thing.

You don't really care about distances, you don't care what lens you're using,

just you have the external specs.

You gotta magnify so much and you get a fit in the space.

Again, a little bit of rearrangement of the equation,

starting with the definition of throw.

And you can come up with an equation for the throw, focal length, and

magnification.

Notice here, this looks bad because you always worry about things blowing up in

the denominator.

But in the single lens imaging system,

magnification can't be plus one, it can only be negative.

So this can never blow up.

So, that's everything there is to know about single lens imaging systems.

And this is a pretty important set of equations to be very,

very comfortable with.

Because we're going to build more complex things on these in future lectures.