Mirror Formula and Magnification

Mirror Formula and Magnification

Mirror formula gives the relationship between image distance, object distance and the focal length of the mirror and this formula is valid in all situations for all spherical mirrors for all positions of the object. Magnification produced by a spherical mirror gives the relative extent to which the image of an object is magnified with respect to the object size. It is expressed as the ratio of the height of the image to the height of the object.

For a spherical mirror:

u = Distance of object from pole,

v = Distance of image from pole,

f = Focal length,

R = Radius of curvature,

O = Size of object,

I = Size of image.

1) Mirror Formula: $$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$$.

2) Lateral Magnification: When an object is placed perpendicular to the principle axis, then linear magnification is called lateral or transverse magnification.

$$m=\frac{I}{O}=-\frac{v}{u}=\frac{f}{f-u}=\frac{f-v}{f}$$.

3) Axis Magnification: When object lies along the principle axis then its axial magnification is:

$$m=\frac{I}{O}=\frac{-\left( {{v}_{2}}-{{v}_{1}} \right)}{\left( {{u}_{2}}-{{u}_{1}} \right)}$$; If object is small, $$m=-\frac{dv}{du}={{\left( \frac{v}{u} \right)}^{2}}={{\left( \frac{f}{f-u} \right)}^{2}}={{\left( \frac{f-v}{f} \right)}^{2}}$$.

4) Areal Magnification: If 2D – object is placed with its plane perpendicular to principle axis and then its areal magnification is:

$${{m}_{s}}=\frac{Area\,of\,image\left( {{A}_{i}} \right)}{Area\,of\,object\left( {{A}_{o}} \right)}\Rightarrow {{m}_{s}}={{m}^{2}}=\frac{{{A}_{i}}}{{{A}_{o}}}$$.