Mirror Formula and Magnification - Light Reflection and Refraction, Class 10, Science | EduRev Notes

Magnification:

Power of a mirror:

The power of a mirror is defined as

Convex mirrors give erect, virtual and diminished image.

In convex mirror, the field of view is increased as compared to plane mirror.

It is used as rear-view mirror in vehicles.

Concave mirrors give enlarged, erect and virtual image, so these are used by dentists for examining teeth. Due to their converging property concave mirrors are also used as reflectors in automobiles head lights and search lights.

A real image can be taken on a screen, but a virtual image cannot be taken on a screen.

As focal length of a spherical mirror  depends only on the radius of mirror and is independent of wavelength of light and refractive index of medium so the focal length of a spherical mirror in air or water and for red or blue light is same.

Mirror formula:

The relation between the distance of the object from the pole of the spherical mirror (u), the distance of the image from the pole of the spherical mirror (v) and its focal length (f) is given by the mathematical formula :

It must be remembered that focal length (f) of a spherical mirror is half the radius of curvature (R).

Thus, (i) R = 2f, (ii) f =

Important points in using the mirror formula : 

(i) Put the correct signs of known variables according to the sign convention.

(ii) Do not put the sign of an unknown variable. The sign will be automatically appeared during calculations.

(iii) If the calculated sign turns out to be positive, then the variable calculated is behind the mirror. However, if calculated sign turns out to be negative, then variable is to be in front of the mirror.

Linear magnification produced by spherical mirrors :

The ratio between the height of the image produced by the spherical mirror to the height of the object is called the linear magnification.

where m = magnification

h_i  = height of the image

h_o = height of the object

Linear magnification when the image is real: 

As we normally take the object above the principal axis, therefore, h₀ is always positive. The real image is always inverted and is formed below the principal axis.
Therefore, h_i is always negative. Thus, Linear magnification for real images =   is always negative.

Linear magnification when the image is virtual : 

In case of virtual image. it is erect and formed above the principal axis. Thus, h₀ and h_i are both positive.

The linear magnification produced by a spherical mirror is equal to the ratio of the distance of the image from the pole of the mirror (v) to the distance of the object from the pole of the mirror (u) with a minus sign.

Linear magnification,

Thus Linear magnification,  =  

 Important points in using magnification formula :

(i) Put the correct signs of known variables according to the sign convention.

(ii) If 'm' is known, take the sign for virtual image positive and for real image negative.

(iii) Do not put the sign of unknown variables. The sign will automatically come up during calculations.