Resolving Power of Grating

The mercury lamp lights the slit S, and the collimator C turns the light from it into a parallel beam that falls square on the grating G on the prism table. The telescope T is first set in line with the collimator for the direct reading, then swung out to the first-order yellow pair on one side and on the other. The angle it turns through is read off the graduated circle with the two verniers.

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 (given)

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, and level the table with the spirit level.

3. 3.

   Switch on the mercury lamp and narrow the collimator jaws until the image of the slit is sharp. A wide slit widens every line in the field and merges the pair however many rulings are lit.

4. 4.

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

5. 5.

   Swing the telescope into the first-order spectrum on one side and find the yellow pair. Bring the intersection of the cross-wires onto Yellow I and note both vernier readings, then onto Yellow II and note both again.

6. 6.

   Bring the telescope round to the other side and read the same two lines there in the same way.

7. 7.

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

8. 8.

   Calculate the wavelength of each line from the grating equation, take their mean and their difference, and the resolving power follows.

   λ = e sin θ / n, dλ = λ₂ − λ₁, R = λ / dλ