Question

5) A spectrometer equips a diffraction grating with 600 grooves/mm and focal length of 33 cm. a) what is the reciprocal liner dipersion of grating? d4 pesy (b) Calculate the resolving power of the grating at first order if 5 cm is illuminated (4 pts).

Answer 1

(a) The wavelength dispersion at the exit slit of a spectroscopic instrument is usually specified as reciprocal linear dispersion, given in nm/mm. Reciprocal linear dispersion is given by: [f = focal length]

dλ/dx=-(dcosβ/nf)

where d =groove width in Angestrom.

n = order

β = differaction angle

If the incident light ray is perpendicular to the grating, you can use the following diffraction grating equation to find the directions in which the rays are diffracted:

n * λ = d * sin(β)

d (gkoor cwidth ) foul terglh 3f em 330 mm, 1X 330 ΧΙΟ d. nf OL 33Q 330 4

(b)The resolving power of a grating is a measure of its ability to spatially separate two wavelengths. It is determined by applying the Rayleigh criteria to the diffraction maxima; two wavelengths are resolvable when the maxima of one wavelength coincides with the minima of the second wavelength.

The chromatic resolving power (R) is defined by

R = λ/∆λ = nN

= 1*600grooves/mm*50mm

= 30,000

where ∆λ is the resolvable wavelength difference,

n is the diffraction order, and N is the number of grooves illuminated.