An optical system is located in air. Let `OO`' be its optical axis, F' and F' are the front and rear focal points, H and H' are the front and rear principle planes, `P` and P' are the conjugate points. By means of plotting find:
(a) the position `F'` and `H`' (Fig.),
(b) the position of the point `S`' conjugate to the point `S` (Fig.),

(c) the positions `F, F`', and `H`' (Fig. where the path of the ray of light is shown before and after pasing through the system).

Explanation

(a) Draw `P'X` parallel to the axis `OO'` and let `PE` intensity it at `X`. That determines the principle point `H`. As the medium on both sides of the sytem is the same, the principle point conicides with the nodal point. Draw a ray parallel to `PH` through `P'`. that determines `H'`. Draw a ray `PX'` parallel to the axis and join `P'X'`. That givens `F'`.

(b) We let `H` stand fro the principle point (on the axis). Determine `H`' by drawing a ray `P'H` passing through `P'` and parallel to `PH`. One ray (conjugate to `SH`) can be obtained from this. To get the other ray once needs to know `F` or `F'`. This is easy because `P` and `P'` are knows. Finally we get `S'`.

(c) From the incident ray we determine `Q`. A line parallel to `OO'` through `Q` determines `Q` and hence `H' H` and `H'` are then also the normal points. A ray parallel to the incident ray thorugh `H` will emerge parallel to itself through `H'`. That determines `F'`. Similarly a ray parallel to the emergent ray through `H` determines `F`.