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}$

Assumptions made :

(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