Measurement of the wavelength of monochromatic light

When monochromatic light is passed through a diffraction grating a number of bright lines (fringes) are formed as a result of diffraction and interference. A spectrometer, which must first be adjusted, is used to allow a parallel beam of light to fall on a diffraction grating and to view the fringes. The angles at which the fringes are produced can then be measured. In this simulation a grating with 400 lines per mm (see analysis) scatters red light. Other options are also available. When the angles have been measured for each fringe (n = 1, .. up to 4) the wavelength of the light can be calculated using the formula:

wavelength = [spacing].[sin(angle)] / n

Procedure:

Note: The telescope can be moved by dragging with the mouse when the pointer is on the orange coloured strip

1. Drag the telescope down until the red line (1st. order image) is lined up with the vertical cross-wire.
2. Press the "Show Angle" button and record the angle.
3. Drag the telescope up to the first order image on that side and again record the angle.
4. Repeat for the second, third and fourth (if present) order images.
5. When all relevant angles have been recorded, note the number of lines on the diffraction grating.
6. Repeat the entire experiment with a different grating or with light of different wavelength (green light)
 Order of image n Reading of angle on left Reading of angle on right Average angle Left + Right / 2 Wavelength (m)

Analysis:

The spacing between the lines on the diffraction grating = 1 / no. of lines per metre, eg the spacing between the lines in a grating with 400 lines / mm is 1 / 400 000 metre. Find the average value of the angle ((angle on the left + angle on the right) / 2) for each bright fringe. Use the formula given above to calculate the wavelength of the light.

Precautions:

• Ensure that the slit, collimator, table, telescope and eyepiece are properly adjusted before using the spectrometer, use a narrow slit
• Ensure that the bright fringes are exactly centered on the vertical cross-wire when readings are taken
• Measure angles on both sides of the n = 0 position and take the average of the two readings