System Matrix for a Thick Lens

For glass with index of refraction nlens = n = the front surface power for lens radius R1 = m is P1 = m-1 and the back surface power for lens radius R2 = m is P2 = m-1 Lens thickness d = m (Note that for a double convex lens, the front surface radius R1 is positive and the back surface radius R2 is negative according to the Cartesian sign convention.)

The symbols used by Meyer-Arendt for the elements of the system matrix will be used. b = a = d = c =

A number of other characteristics of the thick lens may be calculated from the system matrix.

The right-hand, or equivalent focal length of the lens is just the reciprocal of matrix element a: f₂ = 1/a = m.

The distance V₂H₂ from the right vertex to the associated principal plane is given by V₂H₂= (c-1)/a = m.

The right vertex focal length (or back focal length) is given by f_v2 = c/a = m.

Note that the equivalent focal length f₂ is the sum of the back vertex focal length and the distance from the vertex to the principal plane: f₂ = f_v2 + V₂H₂. Similar relationships exist for the left-hand or front vertex.

The left vertex focal length (or front focal length) is given by f_v1 = -b/a = m.

The distance V₁H₁ from the left vertex to the associated principal plane is given by V₁H₁= (1-b)/a = m.

The equivalent front focal length f₁ is then given by f₁ = -(b/a + V₁H₁) = m.