Intersections of the Conic and Receiving Slit Boundary

For the sides x = l j2 that lie parallel to the equatorial plane the quadratic equation ayX + byX + = 0 has the coefficients  

In a special case there is only one intersection of the line and the conics. This can occur if the line is parallel to the main axis of the conic (in the case of a parabola), or the line is parallel to the asymptote of the hyperbola. Only the intersection points x y, lying on the receiving slit boundary are of interest. 

The conditions -l 2 Xi l j2 and -fi n,/2 y, d j2 should be met. Care should be taken at the Bragg and scanning angles near 90° to ensure the intersection points lie on the proper branch of the hyperbola. 

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Suppose points = xi,yi,0 and Xj = x2,y2,0 represent the intersections of the conic and receiving slit boundary. The registered intensity is proportional to the dihedral angle 4> between two planes containing points Ai, A2, Xi and A, 2, This angle is the angle between the two normals Ni and N2 to the plane in question ... 

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