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.   

Formation of images by a concave mirror for different positions of the object.

(i) Object at infinity: When the object lies at infinity, the rays from the distant object fall on the concave mirror as a parallel beam, as shown in Fig.(a). The ray, passing through focus F becomes parallel to the principal axis after reflection from the mirror. The ray through centre of curvature C is reflected back along its own path. The two reflected rays meet at point A' in the focal plane. Hence a real, inverted and highly diminished image A'B' is formed at the focus F of the concave mirror. 


Fig. (a) Image formed by a concave mirror with object at infinity

(ii) Object beyond the centre of curvature: An object AB is placed on the principal axis of a concave mirror, beyond its centre of curvature C. A ray AM going parallel to the principal axis passes, after reflection, through the principal focus F. Another ray AN passing through focus, after reflection, parallel to the principal axis. The two reflected rays meet at point A'. Thus, image is formed at A'.

The image formed is real, inverted, diminished in size and is formed between the focus and the centre of curvature.

The ray diagram is illustrated in

Fig. (b) Image formed by a concave mirror with object beyond C.

(iii) Object at the centre of curvature: An object AB is placed at the centre of curvature C of a concave mirror. A ray AM parallel to the principal axis, passes after reflection, through the focus F. Another ray AN passing through the focus F becomes after reflection, parallel to the principal axis. The two reflected rays meet at point A'. Thus A' is the image of point A. The perpendicular A'B' drawn on the principal axis coincides with the position of AB.

Hence a real, inverted and of same size image is formed at the centre of curvature.


Fig.(c). Image formed by concave mirror with object at the centre of curvature

(iv) Object between principal focus and centre of curvature: In Fig.(d), an object AB is placed between the focus F and centre of curvature C of a concave mirror. A ray AM parallel to the principal axis, after reflection,passes through the focus F. Another ray AN passing through focus F goes, parallel to the principal axis, after reflection. The two reflected rays meet at point A'. The line A'B' drawn perpendicular to principal axis is the complete image of AB.

Hence a real, inverted and enlarged image is formed beyond the centre of curvature.

Fig.(d).  Image formed by a concave mirror with object between its F and C

(v) Object at the principal focus: In Fig.(e), an object AB, is placed at the principal focus F of a concave mirror. A ray AM parallel to the principal axis, after reflection, passes through the focus F. Another ray AM through C falls normally on the mirror and refraces its path after reflection. The two reflected rays are parallel to each other and meet at infinity.

Hence a real, inverted and highly enlarged (or magnified) image is formed at infinity.



Fig.(e). Image formed by a concave mirror with object at F

(vi) Object between the principal focus and pole: In Fig.(f) , an object AB is placed between the focus F and the pole P of a concave mirror. A ray AM parallel to the principal axis, after reflection, passes through the focus F. Another ray AN coming from C retraces it's path. Both the reflected rays appear to diverage from a common point A' behind the mirror. So A' is the virtual image of A. The normal A'B' upon the principal axis is the complete image of AB.

Hence a virtual, erect and magnified image is formed behind the mirror.


Fig.(F).  Image formed by a concave mirror with the object between F and P