Diminished image of ultra small object

[eightsquare]

This may seem like a silly question, but I was studying light some time ago, and I was wondering how a diminished image(using a lens) could be formed of an 'object' consisting of two point sources of light a Planck Length away. They cannot be closer in the final image, so do they become one?

 

[Nugatory]

What is the wavelength of the light you're using to form the image?

Lenses form images only when the distances and sizes are large compared to the wavelength of the light, certainly not the case here.

 

[Bill_K]

This may seem like a silly question, but I was studying light some time ago, and I was wondering how a diminished image(using a lens) could be formed of an 'object' consisting of two point sources of light a Planck Length away. They cannot be closer in the final image, so do they become one?

Nobody understands physics at the Planck scale except them TV guys. When a quantum theory of gravity is established, we'll answer your question.

 

[eightsquare]

Ok so there's no answer? Anyway I was wondering, when radiation is emitted by a hot object, what is the minimum distance between two emitted photons? Is there a minimum distance?

 

[Nugatory]

Ok so there's no answer? Anyway I was wondering, when radiation is emitted by a hot object, what is the minimum distance between two emitted photons? Is there a minimum distance?

There is no minimum distance between photons. For that matter, there's no such thing as "distance between photons", at least in the classical way that you seem to be thinking about distance.

(BTW, if you really want to understand the behavior of electromagnetic radiation and light, your best bet is to forget that you ever heard the word "photon" while you learn the classical theory based on Maxwell's equations. You need that understanding before you can start thinking about how the classical theory is reconciled with quantum mechanics - until then, photons and Planck distances just get in the way).

 

[eightsquare]

I know that photons being bosons can be in the same state. However when the light wave hits the reflecting surface photons are absorbed and re emitted as distinct quanta, right? So what is the distance between these materializations? My original question came from a thought experiment. When I was thinking about diminished images, it seems like the same number of light waves are squeezed into a smaller space. While it seems okay that light rays from a point A and a point B, the ends of an object can come closer, I started thinking what will happen if we consider two infinitesimally close points. If a diminished image is to be formed then the light rays hitting these points have to come closer, which they can't. So what's wrong here?

 

[pbuk]

Lets assume that your model is correct; you have already said that light is absorbed and re-emitted, presumably by excitation of electrons associated with individual atoms. How can two atoms be "infinitessimally close"?

Thought experiments about macro effects such as refraction cannot tell us anything about quantum effects, and vice versa.

 

[eightsquare]

Okay. So when many rays of light hit the atom at the exact same time, they can only be reflected by electrons which have certain distance between them. What if the ray of light doesn't 'hit' an electron? Is this classical version is wrong? Does the whole electron shell reflect light?

 

[pbuk]

The classical version is not wrong at the macro level, it accurately describes how mirrors and lenses work. However it does not shed any light on what happens to individual photons.

You cannot understand interactions at this level by thinking about them, you need to do the math - Maxwell's equations for the classical picture and quantum electrodynamics when the classical model becomes inadequate.

 

[eightsquare]

I've got everything about light muddled up now, and I hope I can clear things up in a few posts. First of all, when we learn about light in the classical sense, a 'ray' of light is always mentioned. 'The angle of incidence for a ray of light on a uniform surface is equal to the angle of reflection', etc. This explains the formation of images. My first question is, what does a 'ray' of light refer to exactly?

 

[sophiecentaur]

If reflection worked by photons exciting individual atoms and then being re-emitted, the result would be scattering and not coherent reflection.
Lesson 1: forget the Hydrogen atom model for most EM problems; it's usually not appropriate. Stick to Waves when they are appropriate and consider photons when they are appropriate.

 

[pbuk]

I've got everything about light muddled up now, and I hope I can clear things up in a few posts. First of all, when we learn about light in the classical sense, a 'ray' of light is always mentioned. 'The angle of incidence for a ray of light on a uniform surface is equal to the angle of reflection', etc. This explains the formation of images. My first question is, what does a 'ray' of light refer to exactly?

We refer to light rays because they are a useful model which accurately describes the behaviour of mirrors and lenses. However when we look for these rays we find they don't really exist, and (broadly) the closer you look at what is actually going on the more complicated it gets and the LESS it helps you see the 'big picture'.

If reflection worked by photons exciting individual atoms and then being re-emitted, the result would be scattering and not coherent reflection.

Yes indeed. I wish I hadn't gone down the "assume your model is correct" path, although it seemed easier than any alternative at the time

 

[eightsquare]

Okay so rays are a useful model. In actuality the rays are waves, right? So its actually waves getting refracted and all? Now regarding waves, from what I've read, waves are oscillating electric and magnetic fields. I wanted to know, when a light wave propagates, its actually magnetic and electric fields in points of space changing, right?

 

[Drakkith]

Okay so rays are a useful model. In actuality the rays are waves, right? So its actually waves getting refracted and all? Now regarding waves, from what I've read, waves are oscillating electric and magnetic fields. I wanted to know, when a light wave propagates, its actually magnetic and electric fields in points of space changing, right?

It is the electric and magnetic field vectors that are oscillating, yes.

 

[sophiecentaur]

Okay so rays are a useful model. In actuality the rays are waves, right? So its actually waves getting refracted and all? Now regarding waves, from what I've read, waves are oscillating electric and magnetic fields. I wanted to know, when a light wave propagates, its actually magnetic and electric fields in points of space changing, right?

A ray is just an aid to constructing how an image will be formed. It is a very artificial concept but it 'works'. You can't actually produce a ray that is the same as a 'conceptual' ray because a conceptual ray has zero width and never spreads out. In real life, you can form a ray (nowadays it can be done with a laser) but even the best laser beam will spread out eventually and has a finie width.

The great thing about using rays is that you don't get bogged down with considering diffraction from the start, which is what using waves will involve. This is why rays are used in early School work. Unfortunately, photons are also introduced very early into school Science and they are taught by people who tend not to understand many of their fundamental qualities.

 

[pbuk]

Unfortunately, photons are also introduced very early into school Science and they are taught by people who tend not to understand many of their fundamental qualities.

Yes, unfortunately in the UK this is one of a number of aspects of the 21st Century Science GCSE syllabus that has not been well thought through IMHO. It seems to me that students at a lower level of ability/interest will be left confused and understanding nothing and higher level students will be left thinking they understand something which they don't. This problem is compounded by marking schemes which give credit for writing complete rubbish as long as it contains the right key words. Fortunately other syllabus options are available at GCSE which don't mention photons.

 

[eightsquare]

Okay so in this oscillating fields model higher frequency means faster changing fields, right? And what about more intense light? How is less intense light different from more intense light of the same frequency in this wave model?

 

[sophiecentaur]

Intensity would be the same as power falling on a given area. Power relates to the amplitude of the field squared.

 

[pbuk]

Okay so in this oscillating fields model higher frequency means faster changing fields, right?

Right.

And what about more intense light? How is less intense light different from more intense light of the same frequency in this wave model?

The more intense light wave has greater amplitude (the oscillations are larger).

(oops, didn't notice sophiecentaur got there first, sorry)

 

[eightsquare]

Okay so suppose in a second at a point in space the field oscillates from maximum to minimum back to maximum once in a second if the frequency is the same but the intensity is more that same point will have same maximum to minimum back to maximum oscillation but the maximum will be greater?

 

[sophiecentaur]

Have you looked in any textbooks about the basic definitions? This hyperphysics link shows the meanings of the terms used to describe waves of any kind. The more Power carried by a wave (the Energy transferred per second), the more the amplitude of the displacement will need to be.
That link is describing mechanical waves but the same thing applies to EM waves, in which the 'displacement' is in the form of Electric and Magnetic Fields. The intensity will be proportional to the Maximum value of the E field squared, whether it's light or radio waves we're describing.

 

[eightsquare]

Yes I have. Thanks for all the replies.