## Diffraction & Gratings

Diffraction occurs whenever a wave passes an obstruction, either an aperture, a barrier or even a simple edge. The result of any diffraction is that the wave will spread out, beyond the obstruction, in to the area normally thought of as being in shadow. The amount of diffraction will depend on the both the size of the obstruction and the wavelength of the wave. Because light has such a short wavelength, compared to most everyday objects it is usually not noticed unless it is being looked for.

The following simulation tool allows students to reproduce the effect of monochromatic, visible light, passing through one or more simple slits. This experiment can of course be done 'for real' in the classroom using a laser and a variety of commercially available slits. However few schools are likely to be equipped with either variable size slits or a tunable dye laser in order to investigate altering the wavelength.

The simplest situation is when there is only one slit. The size of the slit can be set between 1 and 1000 m m (1 mm). The wavelength can also be altered between 400 and 700 nm. The distance between the slit and the screen can be set between 1 and 10 m. In order to see more detail the user can also alter the zoom and brightness settings.

When the number of slits is set to two, the pattern becomes that of Young's Double Slit experiment. Again the benefit of the simulation is that students can investigate what happens when variables are changed that are not alterable in the vast majority of school science laboratories. The slit separation can be set between 1 and 1000 m m. It cannot however be set to less than the slit size. If the slit size is increased to greater than the slit separation, the separation will increase to reflect this.

As the number of slits is gradually increased students will be able to see the improved ability to identify the positions of the maxima.

Be warned, the computational power required to simulate both the intensity curve and the actual diffraction pattern is large. Do not expect this program to run rapidly! Also, if the fringe separation on the screen approaches the screen resolution then some unexpected results may be displayed. As a teacher you have three options:

1. Note where these problems occur (i.e. when the slit separation is large and the zoom is set to low) and avoid these combinations
2. Accept that the problem occurs and treat it as an opportunity to discuss sampling frequency (the sampling frequency [in this case the screen resolution] should be at least twice that of the smallest detail you wish to measure).
3. Expand on the problems faced by professional astronomers, CCDs (as used in modern detectors, as well as in digital cameras) have a spatial resolution dictated by the size of the individual pixels. If the pixel size is too large for a given spectroscope then the data captured is misleading and vital information is lost.

It should be clear that gratings have many advantages over prisms for astronomical work. They are lighter (critical in space missions), produce a linear response to changing wavelength and can produce far greater deflection between different wavelengths and so provide a greater spectral resolution. Astronomers however, always on the lookout to squeeze the last scrap of performance out of any system frequently combine the two by etching a diffraction grating on a thin prism. These devices go under the wonderful title of 'grisms'!

Unfortunately diffraction is not always useful to an astronomer. Every telescope that has ever been made is also an obstacle and so suffers from diffraction. Whilst the amount of diffraction produced by the combination of a 10m aperture telescope and 400 nm light might be very small, astronomers attempt to squeeze every bit of information out of an image that is possible. As a result diffraction places an ultimate limit on the resolving power of a telescope.

Any point like object (such as a star) observed through a circular aperture will produce a circular diffraction, surrounded by concentric rings. This is the Airy Disc. Again the angular size of the disc depends on both the diameter of the aperture and the wavelength of the light. It is generally accepted that two stars are just resolved when the first minimum of one overlaps with the central maximum of the second. This is the 'Rayleigh Criteria' for resolution.

The following simulation tool initially allows students to investigate the size of Airy Disc that might be encountered in a school physics laboratory (aperture 0.05 - 1 mm, wavelength 400 - 700 nm). Both the wavelength and the aperture size can be controlled directly, together with the intensity of the light source. The diffraction pattern can be studied either as an intensity plot or as visible fringes. The angular size of the fringes can also be displayed.

In the second part of the simulation students can study the effect of telescope aperture and star separation on how easy it is to resolve individual stars. Aperture can be varied between 1 - 10 m and the star separation can be set anywhere below 0.2 arc seconds (1/18,000 th of one degree). Again the diffraction pattern can be studied either as an intensity plot or as visible fringes.