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# Experimentally calculating the wavelength of an He-Ne laser by means of diffraction gratings

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Introduction

EXPERIMENTALLY CALCULATING THE WAVELENGTH OF A He-Ne LASER BY MEANS OF DIFFRACTION GRATINGS

Purpose:

To experimentally determine the wavelength of a He-Ne laser, by means of three different diffraction gratings – 600 lines/mm, 300 lines/mm, and 100 lines/mm.

Background Information:

“The deviation of light from its original path as it passes through a narrow opening or around an obstruction is called diffraction.”[1]

When light is pointed through one slit, the light is diffracted and creates an “interference pattern” on a screen a certain distance away. On this screen, various “fringes” of light are displayed through destructive interference, along with a bright vertical beam of light in the center. The fringes are less bright beams of light on either side of the central beam – the first fringes on either side are called “first order fringes,” the second fringes on either side are called “second order fringes,” and so on. Theoretically, the distances from the central beam and each of the first order fringes should be equal, as should be the distances from the central beam and each of the second order fringes, and so on.

When light is passed through two slits, the central bright beam of light is created through constructive interference of the light through the two slits. In the case of constructive interference:

dsinθ = mλ,

where d is the distance between the slits, θ is the angle at which the light is diffracted, m is the fringe order being considered, and λ is the wavelength of the light.

Middle

300 lines/mm

0.573

1.228

2.122

100 lines/mm

0.303

0.605

0.915

Note: the distance between the central beam and second/third fringes for the 600 lines/mm diffraction grating could not be found because they were too far away to practically calculate.

Qualitative Data:

As the diffraction grating spacing increases, the distance between the central beam and the first/second/third order fringes seems to decrease. Also, the distances between the central beam and the first order fringe to the left and the first order fringe to the right seem to be equal. This is the same for the second and third order fringes. However, there seems to be slightly more space between the first order fringe and the second order fringe than between the central beam and the first order fringe. Likewise, there seems to be more slightly more space between the third order fringe and the second order fringe than between the second order fringe and the first order fringe.

Data Processing and Presentation:

600 lines/mm Diffraction Grating

Calculation of λ for First Order Fringe

As mentioned before, λ can be calculated by using the equation:

λ = (dx)/(mL).

One can find d by dividing 1 by the number of lines/m:

d= 1/lines per meter

d = 1/(6.00 x 105)

d ≈ 1.67 x 10-6m

So:

λ = (dx)/(mL)

λ = ((1.67 x 10-6)(2.08))/((1.00)(4.41))

λ ≈ 7.88 x 10-7m = 788nm ± 1nm

300 lines/mm Diffraction Grating

Calculation of λ for First Order Fringe

One can find d by dividing 1 by the number of lines/m:

d= 1/lines per meter

d = 1/(3.00 x 105)

d ≈ 3.33 x 10-6m

So:

λ = (dx)/(mL)

λ = ((3.33 x 10-6)(0.573))/((1.00)(2.79))

λ ≈ 6.84 x 10-7m = 684nm ± 1nm

Conclusion

x, especially with a meter stick. One way to solve this would be to use thinner markers, so that the marks are smaller and thus length measurements can be more accurate. Yet another source of error in the experiment could have been that there is a small amount of dirt on the surface of the diffraction gratings, which would affect the path light travelled through them. The way to eliminate this chance for error would simply be to take care to thoroughly clean the gratings before they are used, so as to wash away any dirt. Of course, errors in the apparatus always exist, but the only way to solve these is to use more precise equipment, or to repeat the experiment to obtain concordant data.

[1] Giancoli, Douglas C. Physics – Principles with Applications. New Jersey: Prentice Hall, 2002.

[2] Ibid.

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