How Does Light Intensity Vary with Distance from an Incoherent Extended Source?

In summary, the conversation discusses the topic of optics for extended sources and the difficulties in finding helpful information on the subject through Google. The speaker mentions their approach to solving the problem and asks for suggestions on an introductory text for extended sources. They also mention that the topic is covered in optics courses, but may be disguised. The other person suggests trying to approach it as a far-field diffraction pattern for an aperture with an incoherent field shaped like the source.
  • #1
reasonableman
107
8
I'm currently trying to look into the optics of extended sources. Google doesn't seem too helpful.

Anyway, I have just been thinking about it and thought that surely one of the easiest problems would be the intensity at a screen at a particular distance from an incoherent, spatial extended source.

To me it looks pretty much like an electrostatics problem, common as an undergraduate.

I'm envisioning a line of infinitesimal sources, which will each contribute some light to a point. Which assuming a Lambertian emitter will be the intensity of that infinitesimal point but taking into account the 1/r^2 drop off and the cosine of the angle of the point.

I then integrate over the whole source. However when I put this into maxima (can't do it manually) I get some horrendously long expressions.

Am I doing something wrong with my model and can anyone suggest an introductory text for extended sources?
 
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  • #2
It is covered in many optics courses, but disguised. In fact, what you are asking is the far-field diffraction pattern for an aperture, when the field aperture is not a (coherent) plane wave but an incoherent field, and the aperture is shaped like your source. Try that approach and see what happens.
 
  • #3


I would suggest approaching this problem using the principles of geometrical optics. This involves considering light as rays and using laws of reflection and refraction to determine the behavior of light from an extended source.

One way to simplify the problem is to consider the extended source as a collection of point sources, as you have mentioned. However, instead of using an integration approach, you can use the concept of radiance, which is the amount of light per unit area per unit solid angle emitted from a surface. This can be calculated for each point source and then summed up to get the total radiance of the extended source. From there, you can use the inverse square law and the cosine law to determine the intensity at a particular point on the screen.

An introductory text that covers extended sources and geometrical optics in detail is "Introduction to Modern Optics" by Grant R. Fowles. It covers topics such as radiometry, photometry, and the behavior of light from extended sources. I would also recommend consulting with a professor or colleague who is familiar with optics to discuss your approach and any possible errors.
 

FAQ: How Does Light Intensity Vary with Distance from an Incoherent Extended Source?

What is the difference between an extended source and a point source?

An extended source is one that has a finite size and emits light from multiple points, while a point source is a single point that emits light in all directions.

How does the optics of extended sources differ from that of point sources?

The optics of extended sources take into account the size and shape of the source, as well as any distortions caused by the medium it passes through. Point sources, on the other hand, can be treated as a single point of light.

What are some examples of extended sources in astronomy?

Galaxies, nebulae, and star clusters are all examples of extended sources in astronomy. These objects are made up of multiple points of light and have a finite size.

How do astronomers study the optics of extended sources?

Astronomers use various techniques such as imaging, spectroscopy, and interferometry to study the optics of extended sources. These methods allow them to capture and analyze the light emitted from different parts of the source.

What are some challenges in studying the optics of extended sources?

One of the main challenges is accurately measuring the size and shape of the source, as well as any distortions caused by the medium it passes through. Another challenge is distinguishing between different sources within a crowded field of view.

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