# Numerical method in spherical mirror

## Numerical Method in Spherical Mirror

### Mirror formula

Definition : The equation relating the object distance (u) the image distance (v) and the mirror focal length (f) is called the mirror formula.

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

(i)   The mirror has a small aperture.

(ii)  The object lies close to principal axis of the mirror.

(iii) The incident rays make small angles with the mirror surface or the principal axis.

### Linear magnification For spherical mirrors

Definition : The ratio of the size of the image, as formed by reflection from the mirror to the size of the object, is called linear magnification produced by the mirror. It is represented by the symbol m.

$m=-\frac{v}{u}=\frac{{height\,\,of\,\,image}}{{height\,\,of\,\,object}}$

### Power of mirror

Power of a mirror [in Diopters] = $\frac{1}{{f\,(in\,\,metre)}}$

## Summary of images by spherical mirror

 Position of object Position of Image Size of Image Nature of Image Concave mirror At infinity At focus F Highly diminished Real and inverted Beyond C Between F and C Diminished Real and inverted At C At C Same size Real and inverted Between F and C Beyond C Enlarged Real and inverted At F At infinity Highly enlarged Real and inverted Between P and F Behind the mirror Enlarged Virtual and erect Convex Mirror at infinite at focus highly diminished virtual point size anywhere on principal axis between pole & focus diminished virtual erect