MEASURING REFRACTION INDICES— POLARIZING MICROSCOPES 201 



readily that the path difference between Z^ and iT^, equates at M the 

 product ad. If the path difference I is not zero. Fig. 7.28 shows that 

 the path difference at M becomes J f ad. When A = 0-565 ^i, the 

 first order purple is obtained between crossed polarizers, in the areas Bh., 

 and B'C. Since the path difference at M has not the same value, 



^C 



I, 



A I2 



Fig. 7.28. Owing to the slope a the path difference at M is A- ad. 



the tint is different and characterizes the slope a of the wave-surface 

 as the side shift ^ is a constant of interference microscope. The tints 

 in the areas Bb.y and M are identified by means of Newton's scale. 

 Let a and h be the correlated path differences, i.e. in microns. 

 Then : 



A = a 



A + ad = b (7.12) 



whence the slope a: 



a=(b-a)ld. (7.13) 



As shown later, connecting a to the index n is readily achieved. 

 The shift d is set in a definite direction in relation to the microscope. 

 To make equations (7.12) and (7.13) applicable, the steeper fine 

 of the object, i.e. BB' in the present instance, must be parallel 

 to the direction of duplication. To do this, after securing the first- 

 order purple, in the area B., the specimen is rotated (by means of 

 the stage) until the tint in the area Bb.y is farthest from the purple 

 in Newton's scale. If this adjustment is not achieved, the duplication 

 in equations (7.12) and (7.13) is not d but dcos(^ where /? is the angle 

 formed by the direction of actual duplication and projection of the 

 steeper slope BB' to the horizontal plane (stage plane). If the pro- 

 jected steeper-slope line BB to the horizontal plane is at right angles 

 to the direction of duphcation, then: fi = n;/2 and dcosfi = 0. The 

 object's slope is invisible since the path difference is the same at Bbo 

 and BB' {a -= b in equation (7.12)). 



