By measuring the length a and b,
Θ1 can be obtained using the formula tanΘ =
Finally, by substituting the values of Θ1 and d
into the equation d sinθ1 = 1λ, the required
wavelength can be calculated.
Procedures
- Use the ray box with vertical filament. Place the lamp about 2 m away.
- Place two meter rules at right angles to each other as shown. Set the diffraction grating vertically at one end of the meter rule. Observe the horizontal diffraction pattern (color spectrum) of the filament by viewing through the diffraction grating.
- Ask the partner to move a long pin to the observer’s left hand side along the other meter rule until it lines up with the middle of the red band of the first order spectrum. Place the red filter in front of the lamp to helping locating the position.
- Repeat step 3 for the position on the observer’s right hand side with another pin. Find the separation, 2x, of the pins. Record the results in the table provided.
- Repeat step 3 and 4 for green and then blue.
- Determine the angles of diffraction for red, green and blue light. Hence, determine their corresponding wavelengths. Compare the results obtained with the literature values by finding their percent differences.
The diagram of the setup
Table of data
Data analysis
For the first order color spectrum, as the red light has the longest wavelength, it is diffracted the most. Hence, the separation between pins and the angle of diffraction is the biggest. As the wavelength of the light decreases form red to violet, its separation between pins and the angle of diffraction also decreases. There is a big discrepancy between the wavelength obtained in the experiment and the literature value, which leads to the large percentage difference in three sets of the data. This means that the results obtained is inaccurate because there exists errors in the experiment.
Precaution
- Use set square to ensure that the meter rules are at right angles to each other
Explanation：As the ray box and the diffraction grating are collinear to the meter rile, by ensuring the meter rules are at right angles to each other, we can sure that the incident light towards the diffraction grating is at right angle to the plane of it with zero path difference. On the other hand, when we take the date of the distance between the two meter rules or the separation of the pins, no extra length is included in it.
- Check that the two positions should be symmetrical about the lamp filament.
Explanation：To ensure that the zeroth order diffraction lies on the middle of the rule with no any displacement. And the data taken is more accurate. To keep the limitation that the path difference in two sides are almost equal.
The sources of errors in the experiment
- The environment is not relatively dark enough for the experiment to be carried out accurately. As some unwanted light existed in the surrounding will affect the spectrum formed from the diffraction grating. Maybe other unwanted color spectrums will also be formed, when the observer determines the position of the color light needed, those unwanted spectrums will make the observer confused and make the judgments wrong leading to the inaccurate data obtained.
- The human error--- As the observer needs to judge where the middle of the red band of the first order spectrum is, due to the insensitive and weak ability of the human eyes, it is really difficult to find out the position exactly. Thus, error exists as there is a big risk to take the inaccurate data.
Suggest improvement to the experiment
- Carry out the experiment in the dark back room.
- Using pins with the addition of laser bean rather than just pins to locate the position of different color of the light in the spectrum.
- Using the spectrometer to help to record the positions of the light found and collect all the data for the calculations.
Limitation of the experiment
- The whole set up of the experiment can not be exposed to an environment with a relatively high light intensity.
- The diffraction grating used should not exceed about 300-400 lines per mm
- The distance between the ray box and the clip with a diffraction grating should not be too close, it is better to place the lamp about 2 m away.
Conclusion
From the experiment, we know that light can be diffracted by a narrow slit. When many closely spaced slits (diffraction grating ) are used, interference pattern are formed. If white light is passed through the diffraction grating, color spectrum is formed. Apart from this, the white used in the experiment contains the visible light which has a composition of different wavelength of light. The longest the wavelength of the light, the largest angle it will be diffracted. On the other hand, due to the limitations and the sources of error existed in the experiment, the percentage error of the results obtained is very large, and it is difficult for us to carry out the experiment accurately.
Discussion
- Whether it is better to use pins with the addition of laser bean rather than just pins to locate the position of the light to be found.
Explanation﹕Absolutely, it is better to accept this replacement. The principle of using the pins is to move the pins along the either side of the meter rule until it lines up with the middle of the red band of the first order spectrum in order in order to find out the exact position of the required light. As using the naked eyes to judge the middle point of the red region within its wide range is already really difficult, if we just use the mechanical work (moving the pins) to match up with the observer’s observation, tremendous error will exist due to the inexact human sensate system. Thus, by using the laser bean, we can first point out the relative middle position of the light, then moving the pins along the meter rule until it coincides with the infra-red light. It is no doubt that it will increases the accuracy of the results taken.
