Understanding Path Difference in Convex Lenses

In summary, the path difference between light rays passing through a lens is dependent on the distance from the lens to the focus. The rays on the outer edges of the lens travel a greater distance through the air, but a shorter distance through the lens. This difference in distance creates a path difference between the rays.
  • #1
sp1408
17
0
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?
 
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  • #2


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.
 
  • #3


Dadface said:
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...
 
  • #4


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.
 
  • #5


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...
 
  • #6


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.
 
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  • #7


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

What is path difference in lenses?

Path difference in lenses refers to the difference in the distances traveled by light rays passing through a lens. It is a crucial concept in optics and is used to understand and calculate the behavior of light as it passes through a lens.

Why is path difference important in the study of lenses?

Path difference is important because it affects the behavior of light as it passes through a lens. It is a key factor in determining the image formation, focal length, and other optical properties of lenses. Understanding path difference allows scientists to accurately design and use lenses for various applications.

How is path difference calculated in lenses?

Path difference is calculated by finding the difference in the optical path lengths of two light rays passing through a lens. The optical path length is the product of the refractive index of the medium and the physical distance traveled by the light ray. By finding the difference in these lengths, we can determine the path difference in lenses.

What factors affect the path difference in lenses?

The path difference in lenses is affected by the refractive index of the lens material, the thickness of the lens, and the angle at which the light ray passes through the lens. These factors determine the speed and direction of light as it travels through the lens, thus affecting the path difference.

How is path difference used in the design of lenses?

Path difference is used in the design of lenses to ensure that the desired optical properties are achieved. By carefully controlling the path difference, scientists and engineers can design lenses with specific focal lengths, magnification levels, and aberrations. Path difference is also used in the development of advanced lens technologies, such as adaptive optics and corrective lenses.

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