Cardinal points of an optical system

• There are total six cardinal points of a lens system, which are first and second focal points, first and second principal points, and first and second nodal points.

First and second focal points (First and second focal planes)

• A pair of points lying on the principal axis and conjugate to points at infinity are known as focal points.

• A point on the principal axis in the object space so that the rays starting (or appear to start) from it become parallel to the principal axis after refraction from the lens system is known as first focal point (F₁).
• A point on the principal axis in the image space so that the rays parallel to the principal axis in the image space focus (or appear to focus) at this point after refraction from the lens system is known as second focal point (F₂).

• The plane passing through the first focal point, and perpendicular to the optic axis is first focal plane.
• The plane passing through the second focal point, and perpendicular to the optic axis is second focal plane.

First and second principal points (Principal points and Principal planes)

• Two conjugate points characterized by unit positive transverse magnification are principal planes or unit planes, and the intersection of these points on the principal axis give two points known as principal points.

• If we extend AB in forward direction and C₂F₂ in backward direction, then they intersect at M₂. On drawing a perpendicular from M₂ on optic axis, we get an intersection point on optic axis, this intersection point H₂ is second principal point.
• Similarly H₁ is first principal point.
• M₁H₁ is first principal plane, and M₂H₂ is second principal plane.

Note

• The distance of first focal point is measured from first principal point, and the distance of second focal point is measured from second principal point.
• If there is same medium on either side of lens system, then both the focal lengths will be equal, H₁F₁ = H₂F₂.
• If an object is placed on first principal plane, then its image will be equal to the size of the object, and straight and will lie on the second principal plane.
• The image of M₁ will be M₂.
• M₁H₁ = M₂H₂.
• The lateral magnification of these planes will be unit and positive.

First and second nodal points (Nodal points and Nodal planes)

• Two conjugate points on the principal axis of the optical system characterized by unit angular magnification are nodal points.
• The planes perpendicular to the principal axis and passing through the nodal points are known as nodal planes.
• The distance of nodal points are measured from focal points.