Name: Magnification
Uploaded: 2019-07-19
Duration: 8 min 55 s
Description: Some mirrors or lenses magnify the object's size and height. How does one calculate the measure of magnification? Let us discuss this with a suitable mathema...

Question

Find out the formulae for magnification for concave and convex mirrors. Give ray-diagrams.

Accepted Answer

The linear magnification produced by a spherical mirror is the ratio of the size of the image formed by the mirror to the size of the object. It is denoted by $m$ .

To derive the expression for the linear magnification, consider the diagram shown below.

The object of size $O O'$ has its image formed as $I I'$ , so the magnification $m$ will be $\frac{O O'}{I I'}$ .

Consider the triangles $O O' P$ and $I I' P$ which are similar. Hence, equating the corresponding ratio, we get,

$\frac{O O'}{I I'} = \frac{O P}{I P}$ .

On putting the values as per the sign convention, $O P = - u$ and $I P = - v$ , we get,

magnification $m = \frac{O O'}{I I'} = \frac{O P}{I P} = \frac{- v}{u}$

or magnification $m = \frac{- v}{u}$

Consider the following figure of a convex mirror.

From $∆ OAB, \tan θ = \frac{h_{o}}{- u}$

From $∆ OIM, \tan θ = \frac{h_{i}}{v}$

By dividing these two equations, we get, $\frac{h_{o}}{- u} = \frac{h_{i}}{v} \Rightarrow \frac{h_{i}}{h_{o}} = \frac{- v}{u}$

We know magnification is the ratio of the height of the image to the height of the object. So, $m = \frac{h_{i}}{h_{o}} = \frac{- v}{u}$

Find out the formulae for magnification for concave and convex mirrors. Give ray-diagrams.

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