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Experiment - 3

To measure the wavelength of light with a grating.


EQUIPMENT:
Spectrometer, Mercury lamp, transmission grating.



THEORY: When a beam of light is incident on a grating, diffraction takes place. Figure shows the process of diffraction
The governing equation when the incident beam is incident normally on the grating is

d sin θm = m λ

m=0, ±1, ±2, ±3, ……


where d is the period of the grating, qm is the angle of diffraction for the order. Obviously the incident beam is diffracted in several orders and hence many spectra are formed. For m=0, there is no wavelength dependence and hence there is no dispersion. The diffraction pattern is symmetric about the grating normal, which is also the direction of incident beam.

PROCEDURE :

    1. Set the spectrometer as outlined for the experiment with prism: the collimator is adjusted to give a collimated beam, telescope is adjusted to receive a collimated beam and turntable surface is horizontal.
    2. Mount the grating on the turn table and adjust it to be normal to the incident beam as shown in the Figure.
    3. Bring the telescope in line with the collimator, and adjust the telescope such that the slit image is on the crosswire. Adjust the slit width so that its image is narrow and adequately bright. Take the vernier readings (Vd1, Vd2).
    4. Capture the first order spectrum by rotating the telescope, say first to the right of the grating normal and take vernier readings for all spectral lines by bringing the crosswire on a line with fine motion screw.
    5. Rotate the telescope to capture the second order spectrum and again take vernier readings on all the spectral lines. It may be difficult to see third order spectrum.
    6. Carry on the measurements on the left side of the grating normal in the first and second orders.

     

     

     

     

     

     

    S.No.

    Telescope to the right

    Telescope to the left

    2q=(Vr1-Vl1)

    2q=(Vr2-Vl2)

    Wavelength

     

    (Vr1)

    (Vr2)

    (Vl1)

    (Vl2)

     

     

     

                   
                   

     

     

     

     

     

     

     

     

  1. Calculate the wavelength for different spectral lines using the formula λ = d sin θ /m
  2. Compare your values with the standard values given and obtain percentage error.

    Question:

    1. What is responsible for the dispersion, i.e. the formation of spectrum?
    2. Bring out the differences between grating spectrum and prism spectrum for the same input radiation.
    3. What limits the order of diffraction?
    4. Obtain the intensity distribution in the spectrum formed by a grating having N grooves.

   
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