While designating the sign conventions for reflection by spherical mirrors we have to consider the pole P of the mirror as origin O and the principal axis as the X axis of the Cartesian coordinate system.
The sign conventions for reflection by spherical mirror are as follows:
- All the distances are measured from the pole P of the mirror.
- All the distances measured to the right of pole are taken as positive while the distances measured to the left of pole are taken as negative.
- Distances measured above & normal to principal axis are taken as positive.
- Distances measured below & normal to principal axis are taken as negative.
- If the image is real then image distance is taken as negative.
- If the image is virtual then the image distance is taken as positive.
- Focal length of concave mirror is negative while the focal length of convex mirror is positive.
- The fig.given below explains the sign conventions in case of spherical mirrors
Mirror Formula and Magnification:
Above Fig. representation of sign conventions in Cartesian coordinate system for spherical mirror
Object distance (u):
The distance of object from the pole of the spherical mirror is called object distance.
It is denoted by u.
Image distance (v):
The distance of image from the pole of spherical mirror is called as image distance.
It is denoted by v.
The mirror formula gives the relationship between object distance, image distance & focal length of spherical mirror which is given by,
1/v + 1/u = 1/f
i.e. 1/image distance + 1/ object distance = 1/ focal length
Magnification:
Magnification is the ratio of height of image to the height of object & it is denoted by m.
m = height of the image/ height of the object =h’ /h
Magnification in terms of image distance & object distance is given as
Magnification m = h’/h = -v/u
Magnification gives the relative extent of magnified image with respect to the original object size.
Note: When m is negative, then image is real.
When m is positive, then image is virtual.
Questions:
- Find the focal length of concave mirror where radius of curvature is 30cm.
- What are the main point of differences in concave and convex mirror on the basis of their applications?