Reflection From Mirrors

Reflection From Mirrors

RULES FOR IMAGE FORMATION BY SPHERICAL MIRROR AND RAY DIAGRAM
The intersection of at least two reflected rays give the position of image of the point object.  Any two of the following rays can be considered for locating the image.
1.  A ray parallel to the principal axis, after reflection, will pass through the principal focus  in case of a concave mirror or appear to diverge from the principal focus in case of a convex mirror.


2.    A ray passing through the principal focus of a concave mirror or a ray which is directed towards the principal focus of a convex mirror, after reflection, will emerge parallel to the principal axis.
 
3.    A ray passing through the centre of curvature of a concave mirror or directed in the direction of the centre of curvature of a convex mirror, after reflection, is reflected back along the same path. The light rays come back along the same path because the incident rays fall on the mirror along the normal to the reflecting surface.
 
4.    A ray incident obliquely to the principal axis, towards a point P (pole of the mirror), on the concave mirror or a convex mirror, is reflected obliquely. The incident and reflected rays follow the laws of reflection at the point of incidence (point P), making equal angles with the principal axis.
 
Remember that in all the above cases the laws of reflection are followed. At the point of incidence, the incident ray is reflected in such a way that the angle of reflection equals the angle of incidence.
Focal length is equal to half of the radius of curvature (f = R/2 or R = 2f):

\( \begin{gathered} \text{From the figure}\tan \theta = \frac{{BP}} {{CP}} \Rightarrow \theta = \frac{{BP}} {{CP}} = \frac{{BP}} {R} \hfill \\ \text{ (}\because \text{for small angles tan}\theta \text{ = }\theta \text{)} \hfill \\ \text{tan2}\theta \text{ = }\frac{{BP}} {{FP}} \Rightarrow 2\theta = \frac{{BP}} {{FP}} = \frac{{BP}} {f} \hfill \\ \text{Hence from the above 2}\frac{{BP}} {R} = \frac{{BP}} {f} \hfill \\ \Rightarrow \frac{2} {R} = \frac{1} {f} \Rightarrow R = 2f(or)f = R/2 \hfill \\ \end{gathered} \)
Formation of Image by a concave mirror: Formation of image depends upon the position of the object. There are six possibilities of the position of object in the case of concave mirror.

Formation of image by a convex mirror:
There are only two possibilities of position of object in the case of a convex mirror, i.e. object at infinity and object is between infinity and pole of a convex mirror.