. (b)) (iii) A ray passing through the centre of curvature retraces its path after reflection as it is a normal incidence. (Figure . (c)) If MP is the perpendicular from M to the principal axis, then The angles ∠ MCP = i and ∠ MFP = i From right angle triangles ∆ MCP and ∆ MFP, we can write, tan i PM PC and tan2 i PM PF As the angles are small, tan i i ≈ and tan i ≈ i , i PM PC and i PM PF Simplifying further, PM PC PM PF PF PC ; C F P M i i i 2i (a) Concave mirror M P i i i 2i F C (b) Convex Mirror Figure .
Relation between f and R - - - - Unit ray optics . . Mirror equation The mirror equation establishes a relation among object distance u , image distance v and focal length f for a spherical mirror. An object AB is considered on the principal axis of a concave mirror beyond the centre of curvature C .
The image formation is shown in the Figure . . Let us consider three paraxial rays from point B on the object. The first paraxial ray BD travells parallel to the principal axis.
It is incident on the concave mirror at D , close to the pole P . It is reflected back through the focus F . The second paraxial ray BP is incident at the pole P. It is reflected along PB ´.
The third paraxial ray BC passing through centre of curvature C , falls normally on the mirror at E. It is reflected back along the same path. The three reflected rays intersect at the point ′ B . A perpendicular drawn as ′ ′ A B to the principal axis gives the real, inverted image.
A' B' C P D E F Figure . Mirror equation As per law of reflection, the angle of incidence ∠ BPA is equal to the angle of reflection ∠ ′ ′