Monday, October 27, 2008

Homemade CD spectroscope - Part 1

wavelength_measurementThe photo to the right is the experimental set-up for the measurement of the wavelength of red laser light from a pound shop laser pointer, using a reflecting diffraction grating, some measurements and a bit of basic geometry and trigonometry.

What's a reflecting diffraction grating? A reflecting surface with many equidistant parallel lines, so close together that the distance between them is in the same order of magnitude as the wavelength of visible light. Due to a phenomenon known as positive interference, such a grating will reflect light with a specific wavelength at angles depending specifically on the angle of incidence of the incoming beam of light, the wavelength of the light and the distance between two adjacent lines on the diffraction grating.

And why use laser light and not ordinary light? Laser light has some remarkable properties, among them that it's highly collimated (it's a narrow beam of highly parallel light waves) and that it's strictly monochromatic; it's composed of one single wavelength only. These are two very important properties when carrying out this type of experiment.

While diffraction gratings used to be slightly outside of the envelope of most home experimenters, the advent of CD ROMs (and CD-Rs) has changed that: the data tracks of these storage devices are so closely together that they rival specialist diffraction gratings and are suitable for use in homemade spectroscopes and spectrometers.

In the set-up above, in the left hand bottom corner (point B) is the source of laser light, top middle (point O) a piece of CD ROM (at right angles to the line OO'), on the right hand side the reflected light for a 0-order spectrum (n = 0, arriving at point A) and the 1st order positive interference (n = 1) arriving at point C.

It can be shown easily that a simple relationship exists between the wavelength of the incoming laser light (λ - lambda), the angle of incidence (β - beta), the angle of reflection (α - alpha) when positive interference occurs and the distance between two adjacent lines on the diffraction grating (D) according to:

n λ = D ( sin β - sin α )

where n is the order of the positive interference (n = 0, 1, 2, 3, ...)

(Note that α is only positive when C falls between O' and A, it is negative when C falls between O' and B.)

By varying the angle of incidence β and measuring the corresponding angle α for non-0 order positive interferences, the wavelength λ can be calculated, provided the constant D and the order n are known.

For ordinary CD ROMs, D = 1.6 μm (micrometer, 10-6 m) and for DVD-R (single layer, 4.7 GByte storage capacity) it is 0.74 μm and so, armed with two pieces of diffraction gratings, one cut out from a CD-ROM and one from a DVD-R, I set about conducting two sets of 9 measurements (total number of measurements 18).

Although the angles β and α can be measured directly, I prefer the easier and more precise measurement via three distance measurements per data point, good old Pythagoras and some elementary trigonometry.

It can be shown easily that sin β = O'B / OB (where O'B is the distance between O' and B and OB the distance between O and B) and that OB = √(O'B2 + OO'2).

Similarly, sin α = O'C / OC and OC = √(O'C2 + OO'2).

Thus by recording O'B, O'C and OO' for the 18 data points, λ = D ( sin β - sin α ) / n can be calculated for each data point, from the three measured distances. An average value of 659 nm (nanometer, 10-9 m) with a sample standard deviation of σn-1 = 9 nm was obtained. This is entirely plausible as there is a deep red light laser diode used for the cheapest laser pointers that's in the 670/650 nm range.

But the fact that at constant angle of incidence β the angle of reflection α depends only on the wavelength λ of the light (for a given order of positive interference and given D) points to the possibility of separating light according to its wavelength, commonly known as spectroscopy or spectrometry. And that's the object of one of my next posts...

Part 2 of this essay on home spectroscopy can be found here.


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