The photodiode was attached to the travelling microscope with sellotape and was pointed directly towards the laser. The laser was placed on the flat stand 0.1m away from the travelling microscope and aimed at the photodiode, which was connected to the voltmeter in photovoltaic mode (so that a voltage was produced when light was incident on the photodiode.)
The background reading with the laser switched off so that no laser light was incident on the photodiode was measured 5 times and a mean background reading calculated and recorded.
The laser was then switched on, and the travelling microscope was adjusted to give a maximum reading on the voltmeter, which was at the centre of the laser beam. This maximum voltage was recorded. The distance of the travelling microscope was set at 0m at this point.
The travelling microscope was then adjusted until the reading on the voltmeter was equal to the background reading. This measurement was the radius of the laser beam. The experiment was repeated 5 times and the resultant diameter of the beam calculated for each repeat.
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The laser was then placed 2.5m away from the photodiode and the experiment repeated with the mean bean diameter being calculated. The divergence of the beam could then be calculated from the results.
Table showing background voltage with no laser light incident on photodiode
Maximum voltage reading (at centre of laser beam) = 0.57V
Table showing radius of laser beam at different distances from the photodiode
Distance from laser to photodiode (m)
Beam radius (m)
Table showing diameter of laser beam at different distances from the photodiode
Distance from laser to photodiode (m)
Beam diameter (m)
The angular divergence is the angle Φ shown in the diagram below.
The radius of the laser beam is increasing with distance from the laser. The angular divergence is a measure of the angle at which the radius changes.
The angular divergence θ was then calculated as shown below.
tan θ =
For voltmeter: calibration uncertainty = 0.5% ± 1unit
For max voltage, uncertainty = 0.405±((0.005x0.405) +0.001)
For travelling microscope:
Scale reading uncertainty = ± ½ smallest division
E.g. for 0.1m reading, % uncertainty = x 100 = 16.7%
Scale reading uncertainty = ± smallest division
= ± 0.001V
Uncertainty for voltage = (0.405±0.001)V
Type equation here. = 0.405V±0.25%
Random uncertainty =
For 0.1m reading: random uncertainty = = 0
For 2.5m reading: random uncertainty =
Random uncertainty is negligible, as this % uncertainty is less than of 16.7%.
Voltmeter calibration uncertainty is less than of 16.7%, as is reading uncertainty, so these too are negligible.
Total uncertainty = 16.7%
Divergence of laser beam to each side = 0.0955°±16.7%
Total divergence of laser beam =0.191°±16.7%
= (0.191±0.032) °
The experiment was not carried out in a completely dark room as such an environment was not available to use. The external light intensity may have varied, which would have an effect on the results by changing the background reading. In an ideal situation, the experiment would have been conducted in an environment of total darkness to eliminate any changes in the background reading.
It was impossible to ensure that the photodiode was perfectly perpendicular to the laser beam at all times. If the angle of the photodiode was to change during the experiment then an inaccurate value for the divergence may be calculated.
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The results show that the laser has a very small angle of divergence, which is expected as lasers theoretically should have parallel beams due to the coherent nature of the travelling photons.
Experiment 2 - Measuring the wavelength of a He-Ne laser
A laser emits photons of a single frequency, and hence a single wavelength. It is important to have a correct value for the wavelength of the photons emitted by the laser, as this value is not always indicated on the laser and this affects the tasks which the laser can be used for.
To discover the wavelength of a He-Ne laser using a diffraction grating.
The apparatus was set up as shown, with the diffraction grating held with a clamp stand at 90° to the laser beam and parallel to the screen.
The screen used was a piece of graph paper sellotaped to the wall 0.15m from the diffraction grating so that the diffraction patter was projected onto it as shown. The positions of each of the shown maxima was marked on the graph paper and the screen removed from the wall. The distance between the fringes and the central maximum was measured and recorded. The angle between each maximum, and the sine of this angle were both calculated. This was used to calculate the wavelength of the laser.
Table showing distance (m) between central maximum and other maxima in diffraction
Constant values: distance from grating to screen = 0.15m
Grating line space d =
Results are used to calculate θ (angle between n0 and nx)
e.g. tan θn1 = =
θn1 = 19.460°
The following angles were obtained using the above method.
Table showing angles (°) between central maximum and outer fringes
Table showing sinθ values of angles between central maximum and outer fringes
λ can then be calculated using λ=
Table showing wavelength calculated using above formula for each value of n
The wavelength of the laser was hence found to be 546.9x10-9m
The uncertainties for this calculation can be found in the uncertainties section for experiment 3.
It was impossible to ensure that the diffraction grating was parallel to the wall. This caused small differences between the distances from n0 to the other maxima.
The experiment was not carried out in an entirely darkened environment. If this environment had been used, more fringes may have been visible and more values for the wavelength could have been calculated.
The results were within the expected value for the laser, since the beam was green and the wavelength of green light ranges from 487-570nm. Hence the value was accepted as correct.
Experiment 3 - Measuring Thickness of Human Hair with Laser
A laser can be used as a tool for measuring very short distances such as the thickness of a piece of paper or the diameter of a human hair. By using the hair as a diffraction grating and measuring the separation of the resulting interference fringes, it was possible to measure the diameter of the hair accurately.
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To measure the diameter of a human hair using the diffraction pattern produced by a He-Ne laser when diffracted by the hair.
Custom - built human hair holder
100mm digital callipers
Low power LED
Diffraction bands from edge B
Diffraction bands from edge A
The whole experiment was carried out in a dark room, so that the maximum possible number of fringes could be seen. The lab pack and low power LED lamp were used to illuminate the ohmmeter to allow the reading to be seen in the dark without affecting the results.
The human hair in the holder was placed as close as possible to the laser beam with the hair at the very centre of the laser beam. The distance from the hair to the laser (L) was measured using callipers and the screen placed perpendicular to the laser beam and the hair so that a diffraction patter was observed on the screen. A spirit level was used to make sure that the laser was sitting horizontally.
The distance from the hair to the screen (D) was then measured using a metre stick.
The distance from the central maximum of the laser to the middle of each of the first 5 diffraction bands on each side of the maximum was then measured, and the distance recorded. This was repeated five times and the mean distance calculated. The diameter if the hair (d) was then calculated.
Table showing distance (mm) between central maximum and centre of fringe
Side from centre
Average distance from central maximum to n for each fringe
sin θ1= 2.716x10-3
sin θ2=7.716 x10-3
sin θ3=12.871 x10-3
sin θ4=17.961 x10-3
sin θ5=23.012 x10-3
dsin θ=nλ λ=546.9 x10-9
d= = = 2.01x10-4mm
Using this method, five values were calculated for d
Mean value for d = 1.42 x10-4mm
random uncertainty in d = (2.01-1.19) x10-4
D=(7.007±0.0005)m = 7.007m ±7.136x10-3 %
L=(0.00886±0.00001)m = 0.00886m ± 0.113 %
Uncertainty in D is less than 1/3 of uncertainty in L so is disregarded.
Reading uncertainty is less than 1/3 of random uncertainty so is disregarded.
Electronic callipers were used to measure the very small distance between the fringes. This gave a more accurate value for the distance and decreased the uncertainty in the results compared to the uncertainty in using a steel rule.
The room was not completely dark when the experiment was carried out. In a repeat of the experiment, a completely dark room could have been used so that more fringes were visible, giving a more accurate result.
Evaluation of investigation
The overall purpose of the investigation was to investigate the properties of lasers, and to investigate their use as a measuring device for distances of nanometre magnitudes. All these aims were successfully carried out with the wavelength and divergence of laser being calculated before the laser was used to measure the diameter of a human hair.
The laser used in the investigation was a He-Ne laser. This is a laser which uses a gain medium which is a mixture of helium and neon in the ratio 10:1, and was a common type of laser used in barcode scanners in the past. Today however, many other types of lasers such as Argon lasers which emit photons of a different frequency exist. Has these lasers been accessible, and if the time required to investigate their properties had been available, the experiments could have been repeated using different types of lasers to see if their properties differed.
Five readings were taken in each of the experiments and the mean value calculated. This increased the reliability of the results and ensured that random uncertainty was reduced. Time constraints did not allow more repeats of the experiment to be carried out, but this was not deemed to be a problem as the random uncertainty was very low in each experiment.
A completely dark room was unavailable for the duration of the investigation. If one was available, it would have been used to allow more fringes to be measured in experiment 3. The room was made as dark as possible during the experiments by blacking out the windows with blinds and covering any large cracks with masking tape. However, due to the nature of the room it was impossible to create a completely dark room and hence some of the fringes could not be detected.
At first, reading the voltmeter in the darkened room was problematic. This problem was solved by setting up a low power LED lamp which was bright enough to allow the voltmeter reading to be seen, but not bright enough to affect the results of the experiment. A screen was set up to prevent light from the lamp from affecting the results. This allowed the voltage to be read easily without the results of the experiment.
The results showed that the properties of lasers can be easily identified. This shows that organisations which use lasers can test the properties with relative ease in order to ensure than the laser suits the purpose they are being used for. This ensures that the correct laser is used for the correct purpose.
The results of experiment one showed that lasers have a very low divergence. This is significant as it means that lasers have a very straight beam, which allows them to be used as a concentrated point source of light. If the divergence was measured and found to be very high, this would have made them unsuitable for many of their purposes.
The results of experiment 2 showed that the wavelength of the laser could be calculated easily. This is significant since the wavelength is required when using the laser as a measuring device. Hence, since the wavelength can so easily be calculated, the laser can easily be used as a measuring device.
The results of experiment 3 showed the diameter of a human hair. It is important to be able to measure very short distances, e.g. for the production of microchip components. The method detailed in the investigation is very easy to accomplish and easily allowed distances of nanometre magnitude to be measured.
Hence all three aims of the investigation were successfully completed, with all the procedures working as intended after a few small modifications. Had more accurate measuring equipment been available, such as more accurate digital callipers, the uncertainties in the measurements could have been reduced, allowing the properties of the laser to be more accurately determined. The most accurate tools in the lab were used, which gave fairly low uncertainties.
If more time had been available, the coherency of the laser would have been determined through experimentation, to check whether or not the photons were actually emitted in phase as they should be. This could ensure that the laser was functioning correctly.