Diffraction Grating Experiment: Calculating Wavelengths
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Diffraction Grating Experiment
Subject:
Calculate the d-spacing (d) of diffraction grating and determine wavelengths of different light sources.
Planning:
A diffraction grating is an optical component that separates light into its constituent wavelengths. There are two main types of diffraction gratings: reflection gratings and transmission gratings. A diffraction grating consists of a surface with a series of closely spaced parallel lines or slits. These can be etched onto a flat metal surface (reflection grating) or a glass plate (transmission grating). When monochromatic light (light of a single wavelength) is incident on a diffraction grating, the emerging waves interfere constructively at specific angles, resulting in a pattern of constructive interference. This occurs when:
d * sin(θ) = ± mλ (where m = 0, 1, 2, ...)
Procedure:
Use a rotation torque sensor to measure the angular displacement of a rotating disc. Use a light sensor to determine the positions of maximum light intensity for different diffraction orders. First, conduct the experiment using laser light, and then repeat it with white light.
Use DataStudio to record and display the data in a graph. Determine the angular variation (θ) from the data to calculate the wavelength (λ) of the light for both laser light and each spectral color of white light.
For each measurement:
- Determine the angular variation (Δθ) using the Smart Tool and the initial angle. In the white light experiment, the initial angle is 0.
- Transfer the results to a table in the laboratory report.
Table format:
| Color | θ1 | θ2 | Δθ | λ = d * sin(Δθ) / m |
|---|---|---|---|---|
| Laser Light | 6.45 | 31.78 | 25.32 | 7.13 * 10^-7 |
| Red | 0 | 24.014 | 24.014 | 6.79 * 10^-7 |
| Orange | 0 | 22.253 | 22.253 | 6.32 * 10^-7 |
| Yellow | 0 | 21.234 | 21.234 | 6.04 * 10^-7 |
| Green | 0 | 20.574 | 20.574 | 5.86 * 10^-7 |
| Blue | 0 | 16.611 | 16.611 | 4.77 * 10^-7 |
| Violet | 0 | 15.621 | 15.621 | 4.49 * 10^-7 |
Calculation of d:
The maximum value of m = 1
d = (1 / 600) / 1000 = 1.67 * 10^-6 m
Conclusions:
- Compare the measured wavelength values with reference values.
- What is the range of wavelengths in the visible electromagnetic spectrum?
- If a nitrogen laser (λN = 337 nm) is used, what distance from the center would the minimum of order 2 be observed?
- Is this wavelength within the visible spectrum?
Answers:
- The measured values for violet, blue, and red are within the expected range. The other colors have a small margin of error, possibly due to distortions during data collection.
- Based on our data, the visible electromagnetic spectrum ranges from 4.49 * 10^-7 m to 6.79 * 10^-7 m.
- d * sin(θ) = mλ => 1.67 * 10^-6 * sin(θ) = 2 * 337 * 10^-9 => sin(θ) = 0.4 => θ = 23.57 degrees
- The nitrogen laser wavelength (337 nm) is not within the visible spectrum, as it is shorter than the wavelength of violet light, which is the shortest wavelength visible to the human eye.