Understanding Path Difference in Convex Lenses

[sp1408]

Path Difference in Lenses...

A convex lens will converge all rays parallel to the optical axis to the focus.
Now obviously different rays at different distances from the optical axis will travel different distances in reaching the focus.
So why does this not create any path difference between the rays?
Can someone please give a mathematical as well as a logical answer?

 

[Dadface]

Look up optical path difference.The rays on the outer edges of the lens travel a greater distance through the air but a shorter distance through the lens.

 

[sp1408]

Look up optical path difference.The rays on the outer edges of the lens travel a greater distance through the air but a shorter distance through the lens.

But can you give a mathematical reason for that?
I understood what you mean to say,even I thought of that...but there should be some mathematical reason or poof with that.
If you could give me any reference to this...

 

[Dadface]

Try googling thin lens formula.I wouldn't go for thick lenses yet because these are far more complicated.There are also threads in this forum that may help,search for lenses and see what comes up.If I can come up with any other good references I will send another post.

 

[sp1408]

Thanks...tried that already.
I've understood the thin lens formula...but I can't get hold of the derivation for thick lenses...I have a feeling that might be useful in proving what we want...

 

[map19]

You could thrash this out the long way.
Draw a lens. Then draw light rays to all points on the surface and down to the focus.
For n = 1.5 calc the time for each ray in air and in the glass. So that the total time for each ray is the same.
the results will give you the exact profile of the lens.

This is shown quite nicely in Feynman's book QED.

 

[sp1408]

Thanx...Ill check out feynman's book...