Ray Tracing with Diverging and Converging Lenses: A Quick Guide

[sltungle]

If I have an object and in front of it there's a diverging lens, and in front of that (furthest from the object) there's a converging lens can I just ignore the diverging lens when ray tracing for the image formed by the converging lens?

I figure if I were able to draw an infinite number of rays from the image of the object through the first lens (diverging lens) that at least three of the rays would pass through the three main points for the converging lens (through the centre of the lens, parallel to the optical axis, and through the near focal point). Is this correct? Does this allow me to ignore the first lens?

 

[ehild]

? How easier would it be to understand you with an attached picture...

If I understand correctly, yes, find the image with the lens closest to the object (ignoring the other lens) and then use the image as an object for the second lens, ignoring the first one.

ehild

 

[sltungle]

Yeah, sorry about that. I was trying to explain it without making it overly-complicated. Seems I failed there.

Thanks for the info, though!

Optics (ray-tracing in general) certainly isn't my favourite part of physics. I'm a lot better at relativity and quantum mechanics, but... it's part of the course nevertheless. Not to say optics isn't interesting: it is. I just find it... annoying sometimes.

 

[ehild]

So you will be able to solve problems with more than one lens?

ehild

 

[sltungle]

Most definitely. Thanks a bunch!

 

[sltungle]

One last question, I believe.

Say I have an object, and in front of it a two lens system (both converging lenses), and the first lens would cause the image of the object to form at infinity: can I just ignore that lens all together and only consider the second lens?

Again, I'm trying to use the reasoning that, if you assume the object reflects an infinite number of light rays (or simply a very high number of them), that, eventually, at least 3 of those light rays will pass through the prime points of lens 2.

 

[ehild]

Well, you can think that if the first lens produces parallel rays from those arriving from the object, these parallel rays will be collected by the second lens in its focus. But you can also solve this problem formally. Assume an object distance do(1)=x and find the image distance di(1), take the object distance for the second lens as do(2)=D-di(1) (D is the distance between the lenses) and derive the distance of the second image di(2) in terms of x, and then replace x by f1, the focal length of the first lens. Note that in case the object is very near to the focal point of the fist lens, the image is very far, so the object distance for the second lens is negative: it is a virtual object. But this does not matter, apply the lens equation.

If the object is a light source, a candle flame as old books used to show, all its points will radiate in every direction. You always can connect two points (the point of the flame with a special point of the lens) with a straight line.
The situation is similar when the object itself does not radiate light, but randomly reflects (scatters) radiation falling onto it. Or the illumination is random, arriving from every direction, so reflected in every direction too.
The problem is what happens when the object has a smooth and shiny surface which reflects light rays regularly like a mirror, and the illumination is oriented (as an example, illuminating a piece of diamond with a laser beam ) . In this case the object itself belongs to the optical system and you should trace the rays according to the laws of reflection and refraction. Then you can get the image of the light source. Sometimes you get a blurred image either of the object or the source if the object is not a "good imaging system".
I often use a torch to show imaging with a lens to my pupils. When seeing at the lighting torch, it is a round shiny circle, you can not see, what is inside. When I put it in front of lens, I will get a sharp image of the filament or a weak and somewhat blurred one of the reflector behind the filament or an even weaker one of the front glass plate.

ehild