A NIR (near infrared) spectrometer is
commonly used in medicine, law enforcement
and forensics to determine the presence and
concentration of specific chemicals. It works
by measuring the absorption of a solution as a
function the frequency of light shining through
it; a simplified version of the apparatus is
shown to the right. The light source is usually
a hot object (filament) that glows across the
infrared spectrum.
Grating equation: sin(θ)=mλ/d
Speed of light: c=λf=3x108m/s
a) How long does it take light to get from the filament to the sample if the distances from the filament to
the grating and from the grating to the sample are 80 cm?
b) The spectrum to the right shows b) the infrared spectrum of
methamphetamine, which has a distinctive absorption peak at
a wavenumber of 2696 cm-1 (the wavenumber refers to how
many wavelengths there are per cm—in this case, 2696 full
wavelengths of the light fit into 1 cm). What are the
wavelength and frequency the light with this wavenumber?
c) If the analyzing grating has 200 lines per mm, at what angle should the sample arm (exit slit, sample
and photodiode) be placed to measure this absorption peak using the first order diffracted beam?
(hint: the ‘order’ of a diffracted beam refers to m in the equation above—the difference in the number of
wavelengths of light that fit into paths through neighboring grating lines).
d) One problem with using the grating as the only dispersive (i.e., color-spreading) element is that other
frequencies may be sent down the same path, diffracted at different orders, and there is no way to tell
which one is being absorbed. If the filament produces light up to the visible red (λ = 800 nm), what other
wavelengths will be diffracted through the same angle as the 2696 cm-1 peak?
e) In practice, frequency scanning over a small range is usually done by
changing the angle of the grating, which is easy, rather than the angle of the
sample. If the grating is rotated by 20 degrees with respect to the incident
beam, at what angle should the sample arm be placed so that the first order
diffracted beam at 2696 cm-1 peak is still passing through the sample? (Hint:
remember that the total path length difference for light going through
neighboring grating lines must still be exactly λ; the figure to the right shows
two such paths and may help. Note that in this figure, the angle of the sample arm is θ1+θ2).