(a) Consider an ATR experiment witha sample havinga refractive index of 1.03at 2000 em

Chapter 17, Problem 17-12

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(a) Consider an ATR experiment witha sample havinga refractive index of 1.03at 2000 em -I. The ATR crystal was AgCl witha refractive index of 2.00 atthis wavelength. For an angle of incidence of 45, what is the effective penetrationdepth of the evanescent wave? How would the penetration depthchange if the angle were changed to 60?(b) For the same experiment in part (a) anda 60 incidence angle, find thepenetration depths for sample refractive indexes varying from 1.00 to 1.70in steps of 0.10. Plot penetration depth asa function of refractive index.Determine the refractive index for which the penetration depth becomeszero. What happens at this point?(c) Fora sample witha refractive index of 1.37 at 2000 em., and an incidenceangle of 45, plot the penetration depth versus the ATR crystal refractiveindex. Vary the crystal refractive index over the range of 2.00 to 4.00 in stepsof 0.25. Which crystal, AgCl (no= 2.00) or Ge (no= 4.00), gives the smallerpenetration depth" Why'?(d) An aqueous solution witha refractive index of 1.003 is measured with anATR crystal witha refractive index of 2.8. The incidence angle is 45. Whatis the effective penetration depth at 3000 cm-', 2000 cm" and 1000 em-I.,Is absorption hy the aqueous solvent as much ofa problem in ATR as innormal 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) describesa new method toobtaina depth profile ofa sample surface using ATR spectroscopy. Describethe principles of this new approach. Why are spectra taken with differentdegrees of polarization" What isthe complex index of refraction"