CD Diffraction

Purpose:

            The primary purpose of this experiment is to use a simple apparatus to determine the spacing of the lines within a compact disk. This experiment will explore the properties of diffraction gradients using everyday items and a laser of known wavelength. The laser will be used to measure the spacing of the lines by using the relationship learned of light diffraction. Once the spacing have been determined, the obtained results will be compared to the factory requirements of 1600nm and evaluated. In addition to the CD, a DVD will also be evaluated and its spacing will also be compared to the factory specifications of 740nm.

Procedure:

            First, the following supplies were gathered: CD, DVD, piece of paper, meter stick and a laser. The paper was first taken and a hole was placed in the middle of it. Once that was done, the laser was placed on the table so that the beam would strike through the hole created. On the opposite side of the paper, the CD was placed so that the beam would reflect off and bounce diffractively back at the paper. 

Once this was completed, the spacing of the dots were measured and recorded. The length from the CD to the paper was also recorded to be used in later calculations. This entire process was then repeated with the DVD to determine the differences.

Data Analysis:

CD:

            The following data chart displays the raw recorded data for the CD measurements with x representing the distance to the first maxima, l indicating the distance from the paper to the CD, and lambda representing the wavelength of the laser:

Trial	x(cm)	l(cm)	λ(nm)
1	11.5 ± .5	24.3 ± .5	633
2	14.8 ± .5	32.4 ± .5	633
3	16 ± .5	34.8 ± .5	633

The following sample calculation represents the work done to determine the spacing between each line for the CD:

Sinθ = λ/a = x/(x²+l²)^1/2

a = λ(x²+l²)^1/2/x

a = (633nm)(11.5cm²+24.3cm²)^1/2/11.5cm

a = 1480nm

The proceeding table includes the calculated spacing for all three trials:

Trial	Spacing(nm)
1	1480
2	1520
3	1520

DVD:

            Unfortunately, the DVD experiment was only done once due to time restraints. The following table represents the raw data achieved for the DVD, again the same values represent the same quantities as the CD observations:

Trial	x(cm)	l(cm)	λ(nm)
1	9.1  ± .5	5.5  ± .5	633

Using the same calculations as for the CD, the spacing for the DVD is as followed:

Trial	Spacing(nm)
1	739  ± 89

Conclusion:

            After completing all necessary calculations, the spacing for both the CD and DVD were found. The computed spacing of the CD were found to be 1480 nm and 1520 nm. When these values were compared to the factory standard of 1600nm, the range of errors ranged from 5.0% to 7.5%. Considering the small amounts of distances being evaluated, these numbers are rather large. It would be recommended that the factory consider the way their CDs are produced to ensure that the standards are more closely achieved. As for the DVD, the spacing was found to be close to 740nm. When comparing this to the standard of 760nm, the error of 2.6% is not as far off as from the CD. It would not be recommended to the factory to consider the manufacturing process of their DVDs since the error is relatively small.