Principal Points and Planes
Definition: There are two principal planes and two principal points. The first principal plane in the object space is the locus of the points of intersection of the emergent rays in the image space parallel to the axis and their conjugate incident rays in the object space. The second principal plane in the image space is the locus of the points of intersection of the incident rays in the object space parallel to the axis and their conjugate emergent rays in the image space.
Consider a thick lens or a co-axial refracting system having its principal foci F1 and F2. The ray incident at the point Q and parallel to the axis, after refraction through the lens takes the direction RF2 passing through the second principal focus F2. The incident and the emergent rays, when produced intersect at H2. A plane passing through H2 and perpendicular to the axis is termed as the second principal plane of the lens. Its point of intersection P2 with the axis is called the second principal point.
Consider another ray F1S passing through the first principal focus F1 such that after refraction it emerges along TW parallel to the axis at the same height as that of the ray incident at Q. The rays F1S and TW when produced intersect at H1. A plane perpendicular to the axis and passing through H1 is called the first principal plane and its point of intersection P1 with the axis is called the first principal point.
It is clear from figure that the two incident rays are directed towards H1 and after refraction seem to come H2. Therefore, H2 is the image of H1. Thus H1 and H2 are the conjugate points and the planes H1P1 and H2P2 are a pair of conjugate planes. Further H2P2 = H1P1. The lateral magnification of the planes is +1.
Result: (1) The two planes are known as the two conjugate planes of unit positive lateral magnification or simply unit planes. The distance P2F2 is the second principal focal length and P1F1 is the first principal focal length of the thick lens.
(2) For any incident ray intersecting the first principal plane at a given distance from the axis, its conjugate ray must intersect the second principal plane at the same distance from the axis.
(3) The rays starting from a point on the axis and cutting the first principal plane at given distances, from the axis, will have their conjugate emergent rays starting from the points in the second principal plane at the same respective distances from the axis. All these emergent rays converge to the image point on the axis.
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