Calculating wavelength of a laser through a diffraction pattern

Determination of wave-length laser during the leadthrough of experiment in laboratory terms by means of diagnostics of laser ray through the unique diffraction of cut. Analysis of results: length of fringe, areas and interrelation between factors.
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15

Laboratory work

Calculating wavelength of a laser through a diffraction pattern

Introduction:

The aim of this experiment was to determine the wave length of a particular light source, in //our case a red laser pointer, through single slit diffraction. Manipulating the results found through measuring the interference patterns, one can easily determine the wavelength. The expected wavelength is s=

Hypothesis:

The laser emits a ray with a wavelength л. Once it passes through a slit of width b, it forms a diffraction pattern on the diffraction plate. The distance between the diffraction plate and the endpoint is marked by L. The length of the fringe, the dark areas in the diffraction pattern, is noted by x. The relationship between all of the factors can be shown in the following ratio:

The ratio between the wavelength and the diffraction slit is equal to the one between the fringes in the diffraction pattern and the distance between the aperture and the projection plate. The bigger the aperture, the smaller the ratio between the fringes and the distance between the projection plate and slit mask, so the fringes will become smaller, as the This formula can be simplified:

According to the found ratio, the wavelength can be calculated through multiplying the fringe length by the aperture length ad dividing it by the distance between the slit and the projection plate. The resulting wavelength should fit within the accepted range between 650 nm and 750nm.

Apparatus:

Stand

Slit mask

Diffraction plate

Meter stick base

Laser pen

Projection plate

Variables:

Independent

The distance between diffraction slit and diffraction plate- with every trial the distance will be changed.

The aperture width- with every trial, the apertures will be varied in order to see how the diffraction pattern changes.

Dependent:

The resultant diffraction pattern- it will vary with every change that is made with the distance between the aperture and projection plate.

The width of the fringes- will vary with every change made to distance L and aperture width.

Controlled

The wavelength- the same laser pointer will be used for all the trials; the frequency and

The slit width for each particular trial; 3 slits will be used, each of them has a particular wave length.

The distance between the slit and the projection plate; for each trial, the diffraction window and projection plate will be held constant.

The position of the projection plate- it is fixed at the end of the meter stick, and is not moved throughout the entire experiment.

Method:

1. Assemble a stand

2. Take the meter stick base, place the Slit mask.

3. Place the projection plate behind the slit mask

4. Place the diffraction plate window on top of the slit mask

5. Adjust the slit mask and the projection plate so that they are 0.4 meters from each other.

6. Take the laser pointer, and place it on the stand, so that the pointer is at the same level as the diffraction slit window.

7. Turn on the laser pointer

8. Adjust the position of the pointer, so that the ray passes directly through the slit mask.

9. Fix the diffraction plate window, so the light passes directly through aperture A.

10. Take a ruler and measure the average width of the fringes on the projection plate/ and measure the distance between the last and first maxima, counting the fringes.

11. Record the measurement into the data table, mentioning the uncertainty.

12. Switch to aperture B.

13. Record data in the data table.

14. Switch to aperture C and record results.

15. Move the slit mask and diffraction plate window, so that they are 0.34 meters away from each other.

16. Repeat steps 9-14

17. Move the slit mask and diffraction plate window so that they are 0.54 meters away from each other.

18. Repeat steps 9-14

Data Collection and analysis

b^A=0.04mm b^B=0.08mm b^C=0.16mm

The scientist can try to measure the average width of a fringe using a ruler, but that can be proven to be a wrong and simplistic approach. Through the following calculations, this method of finding the width of a fringe will be shown to be wrong.

Trial 1

Length/m	aperture/mm	fringe/mm
0.40±0.01	0.04	2.00±0.50
0.40±0.01	0.08	1.00±0.20
0.40±0.01	0.16	0.50±0.10

A:

л= 2x10^-7m

B:

л= 2x10^-7m

C:

л= 2x10^-7m

Uncertainties:

Дл= 5.2x10^-8m

Дл= 4.25x10^-8m

Дл= 5.2x10^-8m

The average wavelength found here is 200nm±50nm. This is clearly irrelevant towards the accepted wavelength of

Trial	L/m	Slit aperture b/m	Number of fringes Y/m	D from 2nd max to last /m
1	0.50±0.005	A	4±1	0.031±0.001
	0.50±0.005	B	5±1	0.019±0.001
	0.50±0.005	C	6±1	0.012±0.001
2	0.400±0.005	A	4±1	0.030±0.001
	0.400±0.005	B	6±1	0.025±0.001
	0.400±0.005	C	7±1	0.015±0.001
3	0.300±0.005	A	5±1	0.022±0.001
	0.300±0.005	B	9±1	0.023±0.001
	0.300±0.005	C	19±1	0.024±0.001

In order to find the wave length, a calculation involving the width of a fringe between two maxima of the diffraction pattern has to be performed:

(И being the angle between the fringe width and the distance between the aperture and the projection plate)

To complete this, the width of a fringe has to be found. This can be done by directly measuring one of the fringes but the found fringe length would be very inexact and would lead to a deceiving result. Instead of that, one can measure the distance between the first and last maxima, and divide it by the number of fringes in between those two points. So the average width of a fringe would be the distance from the first maxima to the last over the number of fringes on the particular side of measurement.

So the fringe width X, would equal to this:

As the distance between the maxima Y had to be measured by the scientist manually as well as the number of fringes, this could lead to a reasonable degree of error and uncertainty. The main uncertainty would be in measuring th...