Determination of Wavelength of Sodium Light using Plane Diffraction Grating
Plane Diffraction Grating
(with known grating constant)
Sodium Vapor Lamp
(as monochromatic light source)
Spectrometer
(with collimator and telescope)
Reading Lens
(for accurate readings)
Spirit Level
(for proper alignment)
Laboratory Stand
(for mounting apparatus)
Experimental Setup Diagram
📷 Insert image of diffraction grating setup showing:
- Sodium lamp positioned at collimator
- Diffraction grating mounted on spectrometer table
- Telescope positioned to observe diffracted orders
- Angular positions marked for measurements
When monochromatic light passes through a diffraction grating, it undergoes diffraction and produces a series of bright and dark fringes. A diffraction grating consists of a large number of parallel slits of equal width separated by equal distances.
The condition for constructive interference (bright fringes) in a diffraction grating is given by the grating equation:
Where:
- d = grating spacing (distance between adjacent slits)
- θ = angle of diffraction
- n = order of diffraction (n = 0, ±1, ±2, ±3, ...)
- λ = wavelength of light
The grating spacing is related to the number of lines per unit length by:
where N is the number of lines per unit length
The wavelength of sodium light can be calculated using:
For first order diffraction (n = 1):
The angle θ is calculated from the angular positions:
where θR and θL are right and left angular positions
Step 1: Set up the spectrometer and ensure it is properly leveled using the spirit level.
Step 2: Adjust the collimator to produce parallel rays by focusing on a distant object.
Step 3: Place the sodium vapor lamp in front of the collimator slit and allow it to warm up.
Step 4: Mount the diffraction grating on the spectrometer table with the grating perpendicular to the incident light.
Step 5: Adjust the telescope to view the direct (zero-order) image clearly and note its position.
Step 6: Rotate the telescope to locate the first-order diffracted image on the right side and record the angular position.
Step 7: Similarly, locate and record the angular position of the first-order diffracted image on the left side.
Step 8: Repeat the measurements for second and third-order diffractions if visible.
Step 9: Record all observations in the observation table and calculate the wavelength for each order.
Given: Number of lines per mm (N) = _______ lines/mm
Grating spacing (d): d = 1/N = _______ mm = _______ m
| Order of Diffraction (n) |
Angular Position |
2θ = θR - θL |
θ (degrees) |
sin θ |
λ = (d sin θ)/n (m) |
λ (nm) |
| Right (θR) |
Left (θL) |
| 1 |
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| 2 |
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| 3 |
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Sample Calculation (for n = 1):
Given:
- Grating spacing, d = _______ m
- Right angular position, θR = _______°
- Left angular position, θL = _______°
Calculation:
Mean wavelength:
The wavelength of sodium light determined experimentally:
λexperimental = _______ nm
The theoretical wavelength of sodium D-line: λtheoretical = 589.3 nm
Percentage Error:
Percentage Error = _______%
⚠️ Optical Alignment: Ensure the spectrometer is properly leveled and the grating is perpendicular to the incident beam.
⚠️ Light Source: Allow the sodium vapor lamp sufficient time to warm up for stable, bright illumination.
⚠️ Grating Handling: Handle the diffraction grating carefully to avoid scratches or fingerprints on the surface.
⚠️ Angular Measurements: Take readings carefully to minimize parallax errors and ensure accuracy.
⚠️ Multiple Readings: Record observations for multiple orders to improve accuracy through averaging.
⚠️ Cross-hair Alignment: Ensure the telescope cross-hairs are properly aligned with the diffracted images.
⚠️ Room Lighting: Minimize ambient light to clearly observe the diffracted patterns.
Q1: What is a diffraction grating?
A diffraction grating is an optical component with a periodic structure that diffracts light into several beams traveling in different directions. It consists of many parallel slits of equal width separated by equal distances.
Q2: What is the difference between transmission and reflection gratings?
Transmission gratings allow light to pass through and observe diffracted orders on the same side, while reflection gratings reflect light and diffracted orders are observed on the opposite side of the incident beam.
Q3: Why do we use sodium light in this experiment?
Sodium light is nearly monochromatic (single wavelength) with a dominant yellow line at 589.3 nm, making it ideal for precise wavelength measurements and clear diffraction patterns.
Q4: What happens if we use white light instead of monochromatic light?
White light would produce a continuous spectrum for each diffraction order, with different colors diffracted at different angles, making it difficult to measure a specific wavelength.
Q5: Why do higher-order diffractions become dimmer?
Higher-order diffractions have lower intensity because the energy is distributed among multiple orders, and the intensity decreases according to the sinc function envelope.
Q6: What is the resolving power of a grating?
Resolving power is the ability to distinguish between two close wavelengths. For a grating, R = λ/Δλ = nN, where n is the order and N is the total number of illuminated lines.
Q7: What are the advantages of diffraction grating over prism?
Gratings provide: (1) Higher resolving power, (2) Linear dispersion, (3) Multiple orders, (4) Better suited for UV and IR regions, (5) More precise wavelength measurements.
Q8: What is the maximum number of diffraction orders possible?
The maximum order is limited by the condition sin θ ≤ 1, so n_max = d/λ. For smaller grating spacing or larger wavelength, fewer orders are visible.
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