How is the location of the principal plane of a negative achromatic lens calculated?

The principal plane is defined as the imaginary surface at which a lens appears to bend light rays. The focal length is the distance from the backward principal plane to the backward focal point. The principal point is the point where the principal plane hits the optical axis.

1/s´ = 1/f + 1/s

s´ is the distance from image to principal point backwards

s is the distance from object to first principal point

f is the focal length

Another helpful formula is the one for Distance to Vertex:

S x H = -r x d /[ (n-1) d + n (r₂ - r₁)]

S is the vertex plane

H is the principal plane

r is radius

d is thickness

n is refractive index of the glass substrate

Both of the above equations can be used for two lens or two element systems. Edmund Optics® also offers complete prescription information for our negative achromatic lenses. You can input the specifications we provide into a program such as Olive, or pull up our stock numbers in the Zemax lens catalog and model whatever system you require.