Experiment 10 · Setup Diagram

Diffraction Grating

A parallel beam W-W' falls square on the grating A-B. Each slit sends out secondary wavelets, and in the directions where the path difference between neighbouring slits is a whole number of wavelengths they arrive in step. The lens gathers each such parallel bundle to a point: the bundle at θ forms the first-order image P₁, and the undeviated bundle forms the direct image P₀ on the axis.

Observations

Lines on the grating, N

15000 per inch

Grating element, e = 2.54/N

1.6933 × 10⁻⁴ cm

Order of the spectrum, n

1

One main-scale division

0.5° = 30′

Vernier scale divisions

30

Least count

1′

Procedure

1. 1.

   Adjust the spectrometer for parallel light by Schuster's method, or on a distant object. The collimator then delivers a parallel beam and the telescope is focused for it.

2. 2.

   Mount the grating on its table with its ruled surface perpendicular to the incident parallel beam.

3. 3.

   Unlock the telescope and bring it in line with the collimator so the white image of the slit falls on the cross-wires. Note the reading of the position of the telescope. This is the direct reading.

4. 4.

   Start from the violet line in the first-order spectrum on the L.H.S. Bring the intersection of the cross-wires onto it and note the readings of both verniers. Do the same for the green line and for each yellow line.

5. 5.

   Bring the telescope round to the R.H.S. and record the vernier readings in the first-order spectrum for the violet, green and yellow lines in the same way.

6. 6.

   Take the difference between the corresponding readings on the two sides to get 2θ for each colour, then average the value from vernier I with the value from vernier II.

7. 7.

   Halve the mean to get θ and calculate the wavelength from the grating equation.

   λ = e sin θ / n, e = 2.54 / N cm

Formula

e sin θ = n λ

λ = e sin θ / n