They fall on the mirror very close to the pole. On the other hand, the marginal rays are the rays which travel far away from the principal axis and make large angles with it . They fall on the mirror far away from the pole. These two rays behave differently (get focused at different points) as shown in Figure .
. In this chapter, we shall restrict our studies only to paraxial rays. As the angles made by the paraxial rays are very small, we can make good approximations. C F Marginal rays Paraxial rays Principal axis P Figure .
Paraxial and marginal rays . . Relation between f and R Let C be the centre of curvature of the mirror. Consider a ray of light parallel to the principal axis is incident on the mirror at M.
It passes through the principal focus F after reflection. The geometry related to this is shown in Figure . (a). The line CM is the normal to the mirror at M .
Let i be the angle of incidence and the same will be the angle of reflection. - - - - Unit ray optics PF is focal length f and PC is the radius of curvature R . R R (or) ( . ) Equation ( .
) is the relation between f and R . The construction is shown for convex mirror in figure . (b) . .
Image formation in spherical mirrors The image formed by spherical mirror can be found by ray construction called image tracing. To locate an image point, a minimum of two rays must meet at that point. We can use at least any two of the following four rays as shown in Figure . .
C F P (a) C F P (c) C (b) F P C F P (d) Figure . Image tracing (i) A ray parallel to the principal axis after reflection will pass (or appear to pass) through the principal focus. (Figure . (a)) (ii) A ray passing (or appear passing) through the principal focus, after reflection will travel parallel to the principal axis.