APPENDIX A2

Beam Displacement as a Function

of Refractive Index

 

Noll (1) demonstrates that when the angle ¥è (Figure A2-1) reaches a maximum value, the index of redraction of the liwuid is related to the angle of refraction (r) by

 

(A2-1)

 

From triangle DCE in Figure A2-2, it can be seen that

 

(A2-2)

 

which can be rearranged to

 

(A2-3)

 

and from Figure 2

(A2-4)

 

 

Figure A2-1. Path of the laser beam through the reaction cell. r is the angle of refraction, and i is the angle of incidence as defined by Snell's law.

 

 

Figure A2-2. Elucudation of geometrical relationships in circled portion of Figure A2-1.

 

The distance X does not change significantly during the course of the reaction, hence

 

(A2-5)

 

Thus, the displacement measured during the course of the experiment is related to the index of refraction of the mixture by

 

(A2-6)

 

This complex relationship appears forbidding, but it turns out that for reasonable values of n (1.33 ¡Â n ¡Â 1.40) and i (60° ¡Â i ¡Â 70°), Y varies linearly with n (Figure A2-3).

 

 

Figure A2-3. Beam displacement as a function of refractive index. The solid line is calculated from equation A2-5. The dashed line is a straight line for comparison.