I How Does Diffraction Influence Shadows and Optical Observations?

[Hak]

I have a couple of doubts about diffraction I'd like to clear up anyway

The Sun's shadow cast by a tall pole embedded in the ground is less sharp at the top... How is this related to diffraction? Is it due to the presence of air? On Halliday, Resnick, Krane textbook it also says that diffraction disturbs photography much less than a telescope observation... This is also not very clear to me.

And the most important doubt: they always talk about obstacles with dimensions 'comparable' with the wavelength of the incident light (or at any rate wave) to have observable diffractive effects. This also doesn't convince me much...
Thanks in advance.

 

[sophiecentaur]

Diffraction is only one of the reasons for image aberration. In the case of the shadow thrown by a pole, diffraction is way down the list. The main reason for your blurring here is that the distance from pole to ground increases for higher parts of the pole. The fuzzy bit at the sides of the shadow are the Penumbra (Look that up) which gets wider, the further the distance from the pole to the ground. If you go far enough, there will be no actual shadow (Umbra) observable. This will be when the angle subtended by the pole is less than half a degree, which is the angle subtended by the Sun. Playing with fingers and a white wall in the Sun will show how this happens; shape shadows close in and fuzzy ones far out. (Bright Sun and no clouds or nearby white surfaces will give best results.) No diffraction at work here.

If you want to see genuine diffraction, look at light reflected on the surface of a CD. The different wavelengths of reflected light will emerge due to diffraction. Another really good experiment can be done if you look at a distant light bulb (focussing ON the bulb). Make an 'O' with thumb and a finger and (still focussing on the bulb) bring the join across the bulb you are looking at. Part finger and thumb by a tiny amount and you will see stripes appearing in the gap. Do not look at your finger.

diffraction disturbs photography much less than a telescope observation.

Not a universal rule but a valid comment.
That's because the scenes are different and angles involved are very small for many atronomical objects of interest. Resolving two stars is often limited by diffraction effects. The diffraction 'spikes' on Hubble pictures are seen due to very high contrast for very bright stars and the structure of the (Newtonian style) scope.. You still don't see them around dimmer stars. OTOH, most terrestrial scenes have less contrast and the diffraction doesn't show. But pictures of the Sun and bright lights often have diffraction patterns but the surrounding parts of the scene look fine. A greasy lens will ruin a good shot due to diffraction by the smear lines.

 

[Hak]

Diffraction is only one of the reasons for image aberration. In the case of the shadow thrown by a pole, diffraction is way down the list. The main reason for your blurring here is that the distance from pole to ground increases for higher parts of the pole. The fuzzy bit at the sides of the shadow are the Penumbra (Look that up) which gets wider, the further the distance from the pole to the ground. If you go far enough, there will be no actual shadow (Umbra) observable. This will be when the angle subtended by the pole is less than half a degree, which is the angle subtended by the Sun. Playing with fingers and a white wall in the Sun will show how this happens; shape shadows close in and fuzzy ones far out. (Bright Sun and no clouds or nearby white surfaces will give best results.) No diffraction at work here.

If you want to see genuine diffraction, look at light reflected on the surface of a CD. The different wavelengths of reflected light will emerge due to diffraction. Another really good experiment can be done if you look at a distant light bulb (focussing ON the bulb). Make an 'O' with thumb and a finger and (still focussing on the bulb) bring the join across the bulb you are looking at. Part finger and thumb by a tiny amount and you will see stripes appearing in the gap. Do not look at your finger.

Not a universal rule but a valid comment.
That's because the scenes are different and angles involved are very small for many atronomical objects of interest. Resolving two stars is often limited by diffraction effects. The diffraction 'spikes' on Hubble pictures are seen due to very high contrast for very bright stars and the structure of the (Newtonian style) scope.. You still don't see them around dimmer stars. OTOH, most terrestrial scenes have less contrast and the diffraction doesn't show. But pictures of the Sun and bright lights often have diffraction patterns but the surrounding parts of the scene look fine. A greasy lens will ruin a good shot due to diffraction by the smear lines.

Thank you for your detailed answer. Could you elaborate on the difference between Penumbra and Umbra? Thank you very much.

 

[sophiecentaur]

Thank you for your detailed answer. Could you elaborate on the difference between Penumbra and Umbra? Thank you very much.

Did you look it up? Google will be chock full of pictures and I can't be bothered to draw one. You will see that, in the penumbra, some light gets past the edge.