A grating has 40,000 rulings spread over 76 mm. (a) We have to estimate the dispersion in for sodium light in the first three orders; and (b) the resolving powers in these orders.

Solution: Click For PDF Version (a) The dispersion of a grating is defined by the relation
where is the order of the spectrum and d is the spacing of the grating rulings. As 40,000 rulings are spread over 76 mm, the grating spacing is
The angles from the incident normal at which the lines in the first, second, and third orders for wavelength will be observed are as follows; (1) (2) and (3) The dispersions in the first, second, and third orders for the sodium light in this grating can be calculated from the relation
(1) (2)
(3)
(b) The resolving power of the grating in the first, second, and third orders can be determined from the definition
As , the resolving power of this grating in the first, second, and third orders will be 40,000, 80,000, and 120,000, respectively.
