pHYSICS

Experiment 6

Aim of the Experiment

To determine the wavelength of Monochromatic source using diffraction gratings.

Principle

When waves pass through a gap, which is about as wide as the wavelength they spread out into the region beyond the gap, it is called diffraction. Huygens considered each point along a wave front to be the source of a secondary disturbance that forms a semi-circular wavelet. Diffraction is due to the superposition of such secondary wavelets. The secondary wavelets spread out and overlap each other interfering with each other to form a pattern of maximum and minimum intensity. The pattern formed on a screen consists of a broad central band of light with dark bands on either side. The dark bands are caused when the light from the top half of the slit destructively interferes with the light from the bottom half. Diffraction grating is an arrangement of large number of equidistant and parallel slits. One of the techniques to manufacture diffraction grating is to rule the equidistant lines on glass plate. Typical diffraction gratings consist of 15000-20000 lines per inch (this number can reach up to 100000 lines per inch).

The wavelength λ, of any spectral line can be calculated by the formula

(a + b )sinӨ = nλ

Where,

(a + b) =Grating element =1/N = 1/15000 lines/inch

Ө = Angle of diffraction

n = Order of the spectrum

Materials required

A diffraction grating, spectrometer, mercury lamp & reading lens.

Procedure

1. Set up apparatus as shown in diagram.

2. Adjust the spectrometer as follows:

- make sure cross threads are in focus and upright

- focus on a distant object to ensure parallel beams

- illuminate the slit and focus on slit

- adjust the width of the slit to get a narrow beam

- level the turntable

3. Place the diffraction grating vertically in the holder.

4. Look through the eye-piece which is straight in front of the grating to find the zero order image. At this stage ensure the vernier scale is zeroed.

5. Move the telescope to the left and right to find the 1st order image.

6. Measure and record the readings on the circular scale/vernier scale (θ1).

7. Repeat steps 5 and 6 for the corresponding 1st order image on the right.

8. Measure and record the readings on the circular scale/vernier scale on this right side (θ2)

9. Repeat step 6-8 to find the 2nd order image.

10. Find the mean value of θ and calculate the value of wavelength λ using the given formula.

Observations:-

Least count of main scale, x = .....degree

No. of division of vernier scale, n = ……

Least count (L.C.) of vernier scale x/n = …….degree

Observation Table

Calculation

Grating element (a+b) = 2.54/15000 cm

The wavelength of various spectral lines can be calculated by

(a + b )sinӨ = nλ

Result

Observed value of wavelength λ of monochromatic light = ………Å

Standard value of λ = 5893 Å

% Error = ……….. %

Reference Material

J E Lorrimer et al 1976 Phys. Educ. 11 42 (https://doi.org/10.1088/0031-9120/11/1/004)

Questions

1. What is diffraction grating?

2. On which principle diffraction grating works?