Rules for drawing images formed by spherical mirrors: The position of the image formed by spherical mirrors can be found by considering any two of the following rays of light coming from a point on the object.
(i) A ray proceeding parallel to the principal axis will, after reflection, pass through the principal focus in the case of a concave mirrors [Fig.(a)], and appear to come from focus in the case of a convex mirror [Fig.(b)].
Fig.(a). A ray parallel to the principal axis through F after reflection from a concave mirror
Fig.(b) A ray parallel to the principal axis appears to come from F after reflection from a convex mirror.
(ii) A ray passing through the principal focus in the case of a concave mirror [Fig.(c)], and directed towards the principal focus in the case of a convex mirror will [Fig.(d)], after reflection, become parallel to the principal axis.
Fig. (c) A ray through F becomes parallel the principal axis after reflection from a concave mirror
Fig.(d) A ray directed towards F becomes parallel to the principal axis after reflection from a convex mirror
(iii) A ray passing through the centre of curvature in the case of a concave mirror [Fig.(e)] and directed towards the centre of curvature in the case of a convex mirror [Fig. F] falls normallly (∠i = ∠r = 0°) and is reflected back along the same path.
Fig.(e) A ray passing through C is reflected back along of same path after reflection from a concave mirror
Fig.(F) A ray directed towards C is reflected back along same path after reflection from a convex mirror
(iv) A ray incident obliquely to the principal axis, towards the pole P, on the concave mirror [Fig.(G)] or a convex mirror [Fig.(H)] is reflected obliquely, following the laws of reflection at the point of incidence, i.e., the incident and reflected rays make equal angles with the principal axis.
Fig.(G) Incident and relfected rays follow the laws of reflection
By drawing ray diagrams, explain the formation of image when an object is placed on the principal axis of a concave mirror at the following positions:
(i) At infinity.
(ii) Beyond the centre of curvature.
(iii) At the centre of curvature.
(iv) Between the centre of curvature and the focus.
(v) At the principal focus.
(vi) Between the pole and the focus.
(i) Pole: It is the middle point P of the spherical mirror.
(ii) Centre of curvature: It is the centre C of the sphere of which the mirror forms a part.
(iii) Radius of curvature: It is the radius R (= AC or BC) of the sphere of which the mirror forms a part.
(iv) Principal axis: The line passing through the pole and the centre of curvature of mirror is called its principal axis.
(v) Linear aperture: It is the diameter AB of the circular boundary of the spherical mirror.
(vi) Angular aperture: It is the angle ACB subtended by the boundary of the spherical mirror at its centre of curvature.
(vii) Principle focus: It is a point F on the principal axis where a beam of light parallel to the principal axis either actually converges to or appears to diverge from, after reflection from a mirror.
Fig. Principal focus of (a) a concave mirror (b) a convex mirror
As shown in Fig.(a), when a beam of light is incident on a concave mirror parallel to its principal axis, it actually converges to a point F on the principal axis. So a concave mirror has a real focus and it is called a converging mirror also. As shown in Fig.(b), when a beam of light is incident on a convex mirror parallel to its principal axis, after reflection it appears to diverge from a point F (lying behind the mirror) on the principal axis. So a convex mirror has a virtual focus and it is called a diverging mirror also.
(viii) Focal length. It is the distance f (= PF) between the focus and the pole of the mirror.
(ix) Focal plane. The vertical plane passing through the principal focus and perpendicular to the principal axis is called focal plane. When a parallel beam of light is incident on a concave mirror at a small angle to the principal axis, it is converged to a point in the focal plane of the mirror.
Note: A line joining any point of the spherical mirror to its centre of curvature is always normal to the mirror at that point.