So let's lay out our problem.

Let's say we'd like to do a ray trace of a single lens imaging system,

a nice simple type problem to start off with.

We'll represent the lens as a flat surface and

the two little arrowheads here represent the lenticular, the pointy bits of a lens.

If this was a negative lens, I use an arrow that's pointed the other way,

the little triangle here is inverted.

We'll label the front and back focal distances with, I like to use circles,

but you can use whatever symbol you like.

Be careful, make these the same distance, that's important.

Precision is actually important here.

Remember, you're solving a differential equation.

And finally, we'll put an object on the diagram.

The object we'll draw is just an arrow, and

the tip of the arrow will be the place we'll launch rays from.

This is a radiating, spherical wave, it's our field point.

And we'll use an arrow so we can keep track of what's up, because at some point,

it might point down, and that'll be important.

So first rule, a ray that comes off of the object and goes through

the center of the lens, the place the lens intersects the optical axis.

Comes out the other side of the lens without bending, it's undeviated.

The reason for this is, if you think of the shape of a lens,

on the axis the surfaces are actually perpendicular to the axis.

And so the lens is actually right near the axis, basically a plate of glass.

And if you've ever looked through a plate of glass, you know the rays don't bend.

Snell's law tells you you refract in, but

then n sine theta is conserved, and you refract right back out at the same angle.

So rule number one, and

you always should do this ray first because it's the easy one.

You should ray right towards the center of the lens, and

it comes right on out the other side without changing direction.

That's cool, and notice by the way, we've labeled the ray height.

I'm sorry, the object height, and

the object distance just to start getting in the habit of the coordinate system.

And again, the object distance is -t here because, from the perspective of the lens,

the object is at a negative distance in this example.