The pathlength of a cell for infrared spectroscopy can be measured by counting interference fringes (ripples in the transmission spectrum). The following spectrum shows 30 interference maxima between 1 906 and 698 cm[1]1 obtained by placing an empty KBr cell in a spectrophotometer.

The fringes arise because light reflected from the cell compartment interferes constructively or destructively with the unreflected beam.

If the reflected beam travels an extra distance λ, it will interfere constructively with the unreflected beam. If the reflection pathlength is λ/2, destructive interference occurs. Peaks therefore arise when m λ = 2b and troughs occur when m λ/2 = 2b, where m is an integer. If the medium between the KBr plates has refractive index n, the wavelength in the medium is λ/n, so the equations become mλ/n = 2b and mλ/2n = 2b. The cell pathlength can be shown to be given by

where N maxima occur between wavelengths λ₁ and λ₂. Calculate the pathlength of the cell that gave the interference fringes shown earlier.

Wavelength (um) 5 7 8 10 12 14 16 100 1 906 cm 698 cm 90 12345 10 15 20 25 rir 80 1 200 1 000 Wavenumber (cm-1) 2 000 1 800 1 600 1 400 800 600 Transmittance (%) CO