Light passing through a lens diffraction phenomenon

[cks]

A light passing through a lens will be focused for a converging lens.

However, to look at it carefully, it'll not converge to a single point but to a certain size. The size of it and some fringes surround it is actually a diffraction phenomenon.

I don't really understand that the usual diffraction phenomenon we learn from textbook is a light source encountering an aperture or an obstacle. But the lens itself is just letting the light beam focused.

I don't really see the idea of aperture or an obstacle come into the lens that produce the diffraction pattern.

Thank you in advance for any explanations.

 

[Drakkith]

The lens has a different refractive index than the surrounding medium and will introduce diffraction effects into the light.
An interesting quote from wikipedia:

Richard Feynman[4] said that

"no-one has ever been able to define the difference between interference and diffraction satisfactorily. It is just a question of usage, and there is no specific, important physical difference between them."

It looks like it doesn't require an obstacle, IE something that blocks light, but anything that interacts with the light to cause diffraction.

 

[technician]

The lens is made of glass and causes REFRACTION to produce the focussing effect.
It is also a CIRCULAR APERTURE... the light has to pass through the lens and DIFFRACTION occurs as a result of the aperture.
The angular width of the diffraction pattern is given by ∅ = 1.22λ/D for a circular aperture where D is the diameter of the aperture.
The larger the diameter of the lens the smaller the diffraction of the image

 

[Andy Resnick]

A light passing through a lens will be focused for a converging lens.

However, to look at it carefully, it'll not converge to a single point but to a certain size. The size of it and some fringes surround it is actually a diffraction phenomenon.

I don't really understand that the usual diffraction phenomenon we learn from textbook is a light source encountering an aperture or an obstacle. But the lens itself is just letting the light beam focused.

I don't really see the idea of aperture or an obstacle come into the lens that produce the diffraction pattern.

Thank you in advance for any explanations.

As technician mentioned, the lens itself is an aperture- it has finite size. Also, the wavefront entering and exiting the lens are not perfectly spherical due to a variety of reasons: finite size of source, chromatic and monochromatic lens aberrations, etc. so most likely your focused spot isn't an Airy disk, either.

 

[sophiecentaur]

But isn't is ALL, basically, diffraction? It can all be boiled down to the result of the sum of all possible effective paths which a wave takes. It just happens that many refraction phenomena can be treated accurately enough using a 'ray' model and that many small obstacles happen to produce fringe effects which need a more complex treatment.
But there are many optical instruments where the design needs to take the effect of the transmission media into account as well as the effects of apertures.

You can even derive Newton's Laws of Reflection totally from diffraction principles - it's just a bit harder than using paper and pencil construction with lines.

 

[technician]

I like your statement sophiecentaur. Because light is a wave all behaviour results from the combination (diffraction and interference) of waves traveling different paths. The fact that reflection and refraction can be stated in simpler ways is part of the fascination of physics. Once you are familiar with the easier ways of analysing reflection and refraction it
is great to see that they can all be combined by studying wave behaviour.

 

[Claude Bile]

When solving Maxwell's equations, at no point do you say "Ah, this part is interference and this is diffraction". The solution, is just what it is; for simple cases (like a double slit) we label it "interference" or "diffraction" mainly for historical (or perhaps educational) reasons. Study the scattering of EM waves from a sphere though and it quickly becomes apparent that such distinctions are inherently meaningless.

Claude.

 

[jtbell]

But isn't is ALL, basically, diffraction?

I prefer to think of it all as basically interference. I think of interference as the fundamental phenomenon, the superposition of two or more waves. Diffraction, the "bending" of light around obstacles, is an effect of interference.

The basic two-slit pattern that everybody learns first when studying wave optics is (ideally) interference between two sources that are "point-like" in one dimension, ignoring the effects of the other dimension (the length of the slit). Other examples are thin-film interference, the Michelson interferometer, etc.

Diffraction through a single slit with non-negligible width is interference between an infinite number of sources distributed across the width of the slit.

Rectangular and circular apertures extend the analysis to two dimensions.

Inserting a lens into a circular aperture extends the analysis further so that the phase of the wave changes as it goes through the aperture, by different amounts depending on which part of the aperture it goes through.

But in the end, as Claude alluded, it really all comes down to solving Maxwell's equations with wavelike solutions, using appropriate boundary conditions.

 

[sophiecentaur]

This is semantics, mainly. Interference, imo, is what happens when a finite and well defined number of wave(let)s arrive at a location and add up. Diffraction is the pattern that is produced in space and is the result of interference from non-point sources. I would definitely disagree that diffraction is 'just' the bending of waves around corners, though.
Would anyone not describe a Hologram as a diffraction pattern, for instance?
One possible way of distinguishing between interference and diffraction could be that interference uses a ∑ where diffraction uses a ∫.

We are down to preference here, though, I think. Avoid categories where possible because some people can get obsessed with the categorising at the expense of the understanding