Spherical Surface

For spherical surface separating the two medium having refractive index n₁ and n₂ (Fig. 8.1.5, Fig.8.1.6) primary and secondary focal lengths f anf f ' are related as

                                                                                 (1)

Image Formation after refraction by a Spherical surface: In the case of refraction at curved surface

1. Rays traveling parallel to the axis, after refraction by a curved surface, pass through (appear to come from) the secondary focal point for a convex (concave) surface ( ray 1 in Fig.8.1.5 ,8.1.6).
2. Rays coming from (approaching to) the primary focal point, become parallel to the axis after refraction for convex(concave) surface (ray 2 in Fig.8.1.5 , 8.1.6).
3. Rays passing through the center of curvature (i.e.normal to the surface) are not deviated after refraction (ray 3 in Fig.8.1.5 , 8.1.6).

For forming the image of an object, we have to consider these three rays. If the object is a point object (not on the axis), consider any two of the three rays originating from the object. The point of intersection of these rays, gives the point, where the image is formed.