What is really happening in collimation of rays?

[baseballfan_ny]

Ok so if an object is placed at the focal point of a convex lens, it will have it's rays collimated -- which I assumed to mean that all rays would end up parallel to each other.

But then, I saw this diagram of a simple compound microscope from Hecht "Optics" 5th ed:

And I noticed that all the various rays emerging (I think they do that because of Huygen's principle?) from the bottom of the image at the field stop (the one I've circled in the diagram above, it's effectively an object for the eyepiece) end up collimated with an angle of 0 degrees with respect to the vertical. However, the various rays emerging from the top of that same image are also collimated but they are at an angle (maybe 30 to 40 degrees eyeballing it) with respect to the vertical. So that means when rays of an object are collimated, not all of them end up parallel to each other? Only the ones that are "Huygen's diverging" from the same point on the object end up parallel to each other? I had interpreted it that collimation would mean all rays from all across the object would be parallel to each other but I'm pretty sure that's not right and I'm not sure if my new understanding is right either.

 

[Andy Resnick]

Ok so if an object is placed at the focal point of a convex lens, it will have it's rays collimated --

Not exactly- a *point source* located in the focal plane of a lens will generate *plane waves*. If the source is finite-sized, the wavefront generated will not be a perfect plane wave.

 

[sophiecentaur]

in my experience, the word 'collimation' can be used as a general process to make light rays 'behave themselves'. This can involve making them parallel or lining the optics up so that the path through an instrument produces an optimum image. etc. etc. The word needs to be taken in its context.
When you "collimate" a pair of binoculars, you adjust them so that both images are aligned correctly so that the eye doesn't need to struggle to see it properly. When you collimate a Newtonian telescope, you make sure that the image of a star ends up on the axis of the eyepiece, to minimise distortions by lining up the two mirrors optimally. etc. etc.

 

[tech99]

Not exactly- a *point source* located in the focal plane of a lens will generate *plane waves*. If the source is finite-sized, the wavefront generated will not be a perfect plane wave.

Before the invention of the laser it was very difficult to obtain an approximately parallel beam because a point source always had a finite size and so our beam diverged. I still have this problem teaching school children about optics. The condenser lens in front of a lamp is supposed to form a parallel beam but it is only an approximation.

 

[sophiecentaur]

The condenser lens in front of a lamp is supposed to form a parallel beam

As I understand it, the reflector and condenser in a projector are arranged to produce an image of the lamp that's in the projector lens. The illumination optics are separate from the optics of projecting the object / slide on a screen. This gets the most light through the projector lens and the brightest image.

 

[hutchphd]

Not exactly- a *point source* located in the focal plane of a lens will generate *plane waves*. If the source is finite-sized, the wavefront generated will not be a perfect plane wave.

True but I have two rules for teaching classical optics:
(1) Never talk about waves unless you are worried about diffraction limits
(2) remember the three rays: center, parallel in (out thru focus), parallel out (in thru focus)
That takes care of most situations.

And I noticed that all the various rays emerging (I think they do that because of Huygen's principle?) from the bottom of the image at the field stop (the one I've circled in the diagram above, it's effectively an object for the eyepiece) end up collimated with an angle of 0 degrees with respect to the vertical

That is certainly not true. Look at the ray labelled "chief ray" on the diagram. I do not know Hecht but have heard less than glowing comments...that diagram is terrible IMHO. Unfortunately I do not know a really good text.( I never actually took an "optics" course although I have designed a lot of optics. ) The purpose of any focusing optic is to provide a one to one map of the image plane to he object plane and vice-versa (subject to certain constraints)

 

[baseballfan_ny]

Not exactly- a *point source* located in the focal plane of a lens will generate *plane waves*. If the source is finite-sized, the wavefront generated will not be a perfect plane wave.

Ah okay. What exactly is generated then? Is a finite sized object some sort of a superposition of point sources ... so that if you place such an object at the focal plane of a lens you get a ton of different plane waves from each point source that makes up the object?

That is certainly not true. Look at the ray labelled "chief ray" on the diagram.

Okay. I see that the chief ray, originating from the top of the original object passes through the top of the circled image. Then it refracts through the eyepiece and corresponds to an infinite image with its rays at a slight angle wrt the vertical. At the same time, it really looks like to me that the rays from the bottom of the image at the field stop (the ones I've circled below) end up aligned wrt the vertical. How do we make sense out of this?

 

[Andy Resnick]

Ah okay. What exactly is generated then? Is a finite sized object some sort of a superposition of point sources ... so that if you place such an object at the focal plane of a lens you get a ton of different plane waves from each point source that makes up the object?

Basically, yes- that is the idea behind "angular spectrum" analysis of optical systems. There is a wrinkle, tho- the result varies depending on the spatial coherence of the extended source. That is to say, the total optical field will depend on whether the individual plane wave components of the optical field are mutually coherent, mutually incoherent, or partially coherent.