412 H. S. TJhler — Deviation Produced by Prisms. 



altitude rj 1 and the prism angle ft. Each of the curves a, b, c, 

 d, and e is characterized by a different value of ft, and also 

 each curve represents the intersection of the plane 7! = 90° 

 with the corresponding *ij\ x D surface. In other words, for the 

 chosen values of the prism angle, figure 6 shows the distribu- 

 tion of deviation along the great-circle arc KT of figure 1. As 

 before, n = 1*5. The values of ft for the curves a, b, c, d, and 

 e are 9° 42', 20°, 43° 37' 58", 60° 47' 39", and 77° 42', in the 

 order named. The ordinate of each point along the coordinate 

 axis OD signifies the deviation at grazing incidence in a prin- 

 cipal plane corresponding to the associated value of the prism 

 angle. That is, the line OD is the locus of D 1 when ft varies. 

 From the same point of view, the complete curve t passes 

 through all points pertaining to simultaneous grazing incidence 

 and emergence, or, it is the locus of Z> 2 when ft assumes all 

 possible values. The greatest value of the prism angle consist- 

 ent with transmission is given by ft=2c. In this limiting case the 

 only ray possible corresponds to simultaneous grazing incidence 

 and emergence in a principal plane, e = D A = Z> 2 = 180° — 2c, 

 the Xy/I) and y^^D surfaces degenerate into single points, 

 and the small-circle arcs of figure 1 become tangent, so that 

 A and B coincide. For n = 1*5 the limiting values are 

 ft = 83° 37' 14" and D = 96° 22' 46". Figure 6 shows very 

 clearly that the greatest deviation which can be produced by a 

 prism having a given index of refraction is obtained when 

 ft = 2c. This follows from the fact that when both ft and c 

 are fixed the greatest deviation corresponds to grazing inci- 

 dence, and figure 6 has y x = 90° and c = constant throughout. 

 [See pages 393 and 405.] For the curves a, b, and c, ft is less 

 than tan" 1 (2 tan c), hence each complete locus has two discrete 

 minima and one maximum which corresponds to grazing 

 incidence in a principal plane. [Only one-half of each curve 

 is shown in the figure since OD is the axis of symmetry.] The 

 line c satisfies condition (50), namely, 



cos f /5 — cot c sin i/? = 0, 



hence the ordinates at the extremities of the plotted curve are 

 equal, (D, = 7) 2 ). The condition tan ft — 2 tan c is fulfilled 

 by curve d, hence the discrete minima coincide with the maxi- 

 mum and produce a resultant minimum in the principal plane. 

 Thus, as ft increases from 0, the curve d is the first one to 

 have a minimum at grazing incidence and zero altitude. One- 

 half of the locus of discrete minima, as ft varies from to 

 tan -1 (2 tan c\ is shown by curve m. Line e shows the type 

 of curve when ft lies within the limits tan -1 (2 tan c) and 2c. 

 At the points of intersection of the constant-/^ curves with the 



