# Why is a diffraction grating required in optics

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### The CD as a reflection grating - determination of the track spacing

As we have seen before, if the grating constant is known, the wavelengths of the light used can be determined.

If, on the other hand, the wavelength (or the wavelengths) of the light used is known, the grating constant of the grating used can be determined from this.

A CD has a continuous, spiral-shaped groove like that of a long-playing record. When light falls on the underside of a CD, it acts like a reflection phase grating: the pits and lands (depressions and elevations) in a single track groove reflect the light (reflective layer on the CD top side!), So a track looks like the groove when viewed in a longitudinal section a diffraction grating as a coherent point light source.

The tracks of a CD run at a fixed distance, which therefore corresponds to our lattice constant.

We now want to determine this track spacing approximately.

In the following we want to simplify the case of a perpendicular incidence of light. As can be seen from the sketch, the following applies again as usual for the diffraction maxima of a fixed wavelength:

For our experiment we only need a commercially available audio CD (used here: Papa Roach, "Infest"), a desk lamp (or another narrow white light source) and preferably a metal measuring tape. If you feel like it and have the opportunity, just try this yourself!

First we position the desk lamp at a height as precisely as possible above the center of the CD, which we place on the desk with the underside up. Now we look almost vertically (the lamp is in the way!) At the CD and look for the first-order diffraction spectrum by slowly increasing our viewing angle. We want to use the red end of this spectrum immediately afterwards - note its appearance or the approximate viewing angle at which it appears.

Work order

To help you find this diffraction order more easily, watch the following video.

Now go with your eyes to the level of the light source and look for the distance to it, below which the red end of the first diffraction spectrum is just visible at the inner edge of the CD (see illustration). In this position, measure the distance to the light source as precisely as possible (we received a value of).

The diameter of the inner edge of the CD is. From this it follows for the angle at which we see the red end of the spectrum: With a wavelength of (which roughly corresponds to the "red end" of the spectrum) results again from (for): The actual track spacing is, of course not to be forgotten It is allowed that our experiment is bursting with sources of error which have a negative impact on the accuracy of the result. For example, measuring the distance is very error-prone. The estimation of the wavelength of the red end of the spectrum is of course very imprecise, since we do not have a single, defined spectral line available.

Of course, this experiment could have been carried out in the laboratory with a monochromatic laser beam, which would have led to much more precise results.

However, preference should be given to a low-cost, everyday variant, in order to simply show how one can get by with relatively little resources when it comes to estimating orders of magnitude - such as the track spacing of a CD.