Cardinal Points

Focal Points
If a parallel beam of light incident on a lens parallel to the principal axis then it will converge to a single point F2 on principal axix as shown in the figure. This point is known as focus or second focal point. Similarly a diverging beam from point F1 when incidented on lense then it will travel along a parallel direction to principal axis and the point is know as first focal point
Principal points
Let us consider a lense having principal focus f1 and f2. Consider a ray of light AB parallel to principal axis be incident on lens. Then it will refreact along BC and finally emerge out along CF2 i.e principal focus II. Now Producing AB in initial direction and CF2 in backward direction. Then they will intersect in one point H2. A plane passing through H2 and perpendicular to principal axis is called principal plane and point of intersection betweeb this principal point and principal axis is called 2nd principal point
Similarly if we consider a ray of light F1D from first principal plane be incidented on lens and refract along DE and emerge along EG parallel to principal axis. Then point of intersection H1 producing F1D and EG in backward direction. A plane passing forn H1 and perpendicular to principal axis is called first principal plane. The Point of intersection of first plane and principal axis is called as first principal point

Nodal Point
NOdal point are pair of Conjugate points having unit angular magnification. This ,eans when an incident ray be incident on lense directed to either of nodal points and parallel to initial direction
By definition, Q1=Q2
So that P1N1=P2N2
H1H2=N1N2