Images Formed by Concave and Convex Mirrors and Determination of Focal Length

Images Formed by Concave and Convex Mirrors

For concave mirror

S.no.	Position of object	Position and nature of image formed
1.	At infinity,	Image is real, inverted, small size and forms at principle focus.
2.	Beyond C,	Image is real, inverted and smaller size. Image is formed between F and C.
3.	At C,	Image is real, inverted and equal in size. Image is formed at C.
4.	Between F and C,	Image is real, inverted and magnified. Image is formed beyond C.
5.	At F,	Image is real, inverted and highly magnified. Image is formed at infinity.
6.	Between pole P and F,	Image is virtual, erect and magnified. Image is formed behind the mirror.

For Convex Mirror

S.no.	Position of object	Position and nature of image formed
1.	In front of a convex mirror at any position,	Image is erect, virtual, diminished and forms at other side of the object.
2.	If a converging beam is incident on convex mirror,	Image is real, inverted and in front ofmirror.

Determination of Focal Length of Spherical Mirrors

1. Focal length of concave mirror by double in (u – v) method

   It consists of a concave mirror two pins and three stands for pins and the mirror. The arrangement of pins and mirror on stands are adjusted as shown in figure.
   First of all, the rough focal length of the mirror is found out by focusing a distance object on wall or in paper and measuring the distance between the mirror and sharp image.
   
   Now, the object pin is placed at a distance 2 f from or at centre of curvature C of the mirror and an inverted image will be formed by the mirror which lies at the position of the object. Exact positions are determined by moving the pin towards or away from the mirror removing parallax. Now, as the object is placed within pole P and C, the image will be formed beyond C and when an object is placed beyond C and when an object is placed beyond C, an image will be formed with in P and C. In each case, a real inverted image will be formed, the position of which is determined by using second pin on which the image inverted touching the tips of each other as shown in the figure. Hence it is noted as we move our eyes across the mirror object and image must be together. Thus we obtain a pair of object distance and image distance and on substituting in mirror formula we can determine focal length of the mirror.

2. Focal length of convex mirror by plane mirror method

   It consists of a convex mirror mounted on a stand, and a plane mirror and a pin are adjusted on other two stands as shown in the figure. The plane mirror is held in front of the convex mirror with the top of the mirror lying on the principle axis of the convex mirror. An object pin is held in front of two mirrors and its position is adjusted such that there is no parallax between the image and the object seen through the two mirrors. The position of object pin, plane mirror and convex mirror are noted and we can determine
   \begin{align*} \text {Object distance,} \: u &= PO \\ \text {Image distance,}\: v &= -PI = -(MI – PM) \\ &= (MO – PM) \\ \end{align*}
   as MO = MI or u = v in plane mirror. Substituting these values, we can determine focal length of convex mirror.

Uses of Mirrors