Ken Steel, of Dunedin, asks :-
Why do I see an array of lights when looking at a distant yellow street lamp through material used in cotton sheets?
John Campbell, who teaches physics at the University of Canterbury, responded.
What you are seeing is what we call diffraction. It occurs whenever a single type of wave meets a periodic structure whose periodicity is of a distance similar to the repetition distance (wavelength) of the wave. It applies to any type of wave and appropriate periodic structure. For example, when a wave on the surface of water approaches the periodic arrangement of piles on a pier, when X-rays fall on the regular array of atoms in a crystal, when TV waves meet the metal rods of the roof-top antenna or when light is reflected from the regularly spaced tracks on a compact disc.
In each case each element of the periodic array acts as a new source of waves which radiate in all directions. In certain directions each of these waves is exactly out of step with its neighbour and so there is no energy transmitted in that direction. In in-between directions, each wave is exactly in step with its neighbour so they reinforce each other and a maximum of energy is transmitted in that direction. So we see an array of bright images separated by dark regions.
The yellow light from the street lamp is emitted by sodium atoms. The wavelength is about half of a thousandth of a millimetre. The spacing of the threads in cotton sheets is quite a bit larger than this so the angle between bright regions is very small. The angle between the line of sight of your eye to the lamp (the central image) and its neighbouring image is determined just by the ratio of wavelength to periodic spacing of the diffracting screen. So if you use a cloth of finer weave the lamp images will appear further apart. If you take a piece of fine cloth to where you can see red and blue `neon' signs you will see the red images are about twice as far apart as the blue images because the wavelength of red light is about twice that of blue.
If we know the spacing of the diffracting screen we can accurately measure the wavelength of an unknown light source. For example, astronomers use this to determine what type of atoms are present in distant stars. If you look at the coloured image of a distant fluorescent lamp reflected off of a compact disc you will be able to see the green line which is characteristic of light emitted by mercury atoms.