(a) Consider an ATR experiment with a sample having a refractive index of 1.03 at 2000 cm-1. The ATR crystal was AgCl with a refractive index of 2.00 at this wavelength. For an angle of incidence of 45°, what is the effective penetration depth of the evanescent wave? How would the penetration depth change if the angle were changed to 60°?

(b) For the same experiment in part (a) and a 60° incidence angle, find the penetration depths for sample refractive indexes varying from 1.00 to 1.70 in steps of 0.10. Plot penetration depth as a function of refractive index. Determine the refractive index for which the penetration depth becomes zero. What happens at this point?

(c) For a sample with a refractive index of 1.37 at 2000 cm-1, and an incidence angle of 45°, plot the penetration depth versus the ATR crystal refractive index. Vary the crystal refractive index over the range of 2.00 to 4.00 in steps of 0.25. Which crystal, AgCl (nc = 2.00) or Ge (nc = 4.00), gives the smaller penetration depth" Why'?

(d) An aqueous solution with a refractive index of 1.003 is measured with an ATR crystal with a refractive index of 2.8. The incidence angle is 45°. What is the effective penetration depth at 3000 cm-1, 2000 cm-1 and 1000 cm-1, Is absorption by the aqueous solvent as much of a problem in ATR as in normal IR absorption measurements" Why or why not?

(e) Work by S. Ekgasit and H. Ishida (S. Ekgasit and H. Ishida, Appl. Spec/rose., 1996, 50, 1187; Appl. Spec/rose., 1997, 51, 461) describes a new method to obtain a depth profile of a sample surface using ATR spectroscopy. Describe the principles of this new approach. Why are spectra taken with different degrees of polarization" What is the complex index of refraction?