
5
ABERRATIONS
In developing the paraxial imaging equations in Chapters 2 and 3 with curved mirrors, sur-
faces, and lenses, we assumed that for any reection or refraction, all angles, such as those in
Figures 2.10, 2.12, and 3.4, are small, so that for any angle, represented here by θ,
sin θ = θ = tan θ and cos θ = 1. (5.1)
As a result, we obtained the lens equation, Equation 2.51 in air or, more generally, Equa-
tion 3.47, and the equation for magnication, Equation 2.54 or 3.48. Taken together, these
equations dene the location of “the image” of any point in an object. Any ray from the point
(
x, s
)
in the object passes exactly through this image