The validity of ray optics in telescopes

[esha]

the largest telescope in the world has an aperture of 10 m. According to the fresnel distance this makes ray optics valid for it, for a wavelength of lightsay 500 nm, uptil a distance of 2 * 10^7 m. I have read that after the fresnel distance, diffraction tends to dominate. But telescopes tend to help us look at objects much farther than that. So this means ray optics isn't valid beyond that. So how do scientists figure out the distance and all other stuff we do with ray optics at that time??

 

[sophiecentaur]

I think the first answer to that is that ray optics are fine for most purposes but that diffraction is considered when, for instance, you are trying to determine the relative sizes / brightnesses / magnitudes and separation of two objects that you can only just resolve.
I think your statement that ray optics is not valid for large distances is a bit off beam (no pun unintended). Ray optics is only an approximation for all distances and the diffraction effects are much easier to calculate for large distances where the rays can be considered as being parallel. But that may well only apply for parts of an optical system; light from a distant point source can be said to have parallel rays but. for a large aperture telescope in particular, the focussed rays are far from parallel.

 

[esha]

u can check out the fresnel distance... which deals with the validity of ray optics

 

[Khashishi]

The resolution of astronomical images are usually limited by diffraction, I think. So, instead of a dot for a star, you see an Airy disk. You also have aberrations due to the atmosphere gradients and stuff.
You can still use ray optics to figure out the approximate positions of stuff. For example, you can draw a line from the telescope to the center of the Airy disk.

 

[esha]

oo.. so the star looks like a blur... m i right??

 

[sophiecentaur]

oo.. so the star looks like a blur... m i right??

Actually, what you see is stars of different apparent sizes and their edges seems fairly sharp. The bright ones look bigger and the less bright look smaller. The very dim ones tend to look fuzzy. There are thousands of astro image links http://www.redorbit.com/reference/stellar-astrophysics/. The brightest stars in this picture have cross patterns which is because of the diffraction caused by the support of the secondary mirror on a Newtonian telescope. The cross patterns for fainter stars are there but too faint to see.

 

[Drakkith]

the largest telescope in the world has an aperture of 10 m. According to the fresnel distance this makes ray optics valid for it, for a wavelength of lightsay 500 nm, uptil a distance of 2 * 10^7 m. I have read that after the fresnel distance, diffraction tends to dominate. But telescopes tend to help us look at objects much farther than that. So this means ray optics isn't valid beyond that. So how do scientists figure out the distance and all other stuff we do with ray optics at that time??

After looking around a bit I think I understand this. Someone correct me if I'm wrong please.

Illuminate a circular aperture with a collimated bundle of rays such that the aperture is smaller than the bundle and blocks some of the light. The remaining light passes through the aperture and at some distance $d$ we place a screen. According to ray optics, the ray bundle should remain the same diameter as the aperture as it travels. This would result in an illuminated spot on the screen (the image) that is equal in diameter to the aperture.

However, if we were to perform this experiment in real life, we would find that the image is larger in diameter than the aperture, and moving the screen towards or away fro the aperture would change the size of the image, with the image becoming smaller as we moved it closer and larger as we moved the screen away. The Fresnel distance is the distance from the aperture at which ray optics stops being a good approximation and you are forced to use wave optics. The formula I've seen is $\frac{zλ}{α}$, where $λ$ is the wavelength of the light, $α$ is the diameter of the aperture, and $z$ is the distance from the aperture. It is not about subsequently capturing that bundle of light with an optical system like a telescope. This is because the aperture of the telescope immediately constrains the size of the wavefront so that we don't have to even bother using ray or wave optics to calculate it. We already know it.

After that, the choice of whether to use ray or wave optics depends on the size of the optical system and how accurate you want to be. Ray optics gives a good approximation for rough calculations when your system is the size of a regular camera or telescope. However you are forced to use wave optics if you really want to get good predictions about how the system will behave in real life. Optical design programs are usually programmed to do both ray and wave optics, so you can use ray optics to get the rough dimensions and spacings of the different elements of the system, and then switch to wave optics when you want to know exactly how the light is focused at different points in the focal plane at the micrometer and nanometer scale.

 

[sophiecentaur]

According to the fresnel distance this makes ray optics valid for it, for a wavelength of lightsay 500 nm, uptil a distance of 2 * 10^7 m

You seem to be after some sort of cast iron limit and there really isn't one. A microscope which seldom involves more than a few tens of mm cannot be designed with ray optics alone - if you want a half decent picture.

 

[esha]

okk