Editorial Feature

Primary and Secondary Principal Planes

The principal planes are two hypothetical planes found in a lens system at which all the refraction is deemed to occur. The position of the principal planes are fixed and do not depend upon the position of the object.

Primary principal planes are typically denoted by H1 and H2  and is the surface of intersection of the rays emerging from the primary focal point of the lens and the emergent parallel rays when extended to intersect each other.

The thin lens equation may be used to determine the primary principal plane, but the value of the distance between the two principal planes cannot be calculated using this equation.

Determining the Primary Principal Surface

The principal planes of a lens system are the primary and the secondary planes. These planes are computed by measuring the amount of refraction occurring at each surface of a lens.

The direction of the light ray from the lens can be deduced accurately from the computed value of refraction. The principal plane can be constructed by extending the path of the refracted ray backward into the lens to the point where it meets the path of the incident ray. All the refraction occurs at these planes. The points where these planes intersect the optical axis are called principal points.

An important observation at the principal plane is that the ray emerging from the lens appears to have crossed the rear principal plane at the same distance from the axis as the ray crosses the front principal plane. The determination of the primary principal plane is important for determining the optical properties of the lens system. The magnification of the lens system can be calculated from the principal plane calculation. Calculation of the focal length is done with respect to the principal planes.

The Secondary Principal Plane

The secondary principal plane is typically denoted by H2. The values of primary and secondary principal planes can be calculated by using the thin lens equation; this, however, will not provide the value of the distance between the planes. The secondary principal plane is the surface of the intersection of the rays emerging from the secondary focal point of the lens and the emergent parallel rays when extended to intersect each other.

Determining the Secondary Principal Plane

The secondary principal plane is analogous to the primary principal plane but it refers to a collimated beam that is incident from the left and focused onto the back focal point on the right.

The secondary principal plane is determined to measure the amount of refraction occurring at each surface of a lens. The direction of the light ray from the lens can be deduced accurately from the computed value of refraction.

The secondary principal plane can be constructed by extending the path of the refracted ray backward into the lens to the point where it meets the path of the incident ray. All the refraction occurs at these planes. The points where these planes intersect the optical axis are called principal points.

The rays in that part of the beam nearest to the axis can be considered as once refracted at the second principal surface, rather than being refracted by both lens surfaces. The determination of principal planes is important for determining the optical properties of the lens system. Computation of these surfaces is instrumental in determining the magnification and the focal length of the system.

Sources and Further Reading

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