#

The ray z prime equals x sine theta prime plus z cosine theta prime in the x z plane makes angle theta prime to the z axis. The ray z double prime equals negative x sine theta double prime plus z cosine theta double prime in the z y plane makes angle theta double prime to z axis.

The text reads, from equation 8.118 a, z prime equals start fraction pi x over beta a end fraction plus z. hence, theta prime equals tangent to the power negative 1 of start fraction pi over beta a end fraction plus z. hence, theta double prime equals negative tangent to the power negative 1 of start fraction pi over beta a end fraction.