Name: Sign Convention
Uploaded: 2019-07-19
Duration: 7 min 37 s
Description: All distances are measured from the optical centre of the lens. Distances measured in the direction opposite to the incident light's direction are considered...

Question

Derive the mirror equation and equation for lateral magnification.

Accepted Answer

In th above diagram an object $AB$ is placed in front of a concave mirror and its real inverted image is formed at $A' B'$ .

As $△ ABC and A' B' C$ are similar, $\frac{AB}{A' B'} = \frac{CB}{CB'}$

Again $ABP, A' B' P$ are similar hence $\frac{A B}{A' B'} = \frac{P B}{P B'}$

Combining, we have, $\frac{PB}{PB'} = \frac{CB}{CB'}$ As the distances are measured from $P$ , we have

$\frac{PB - PC}{PC - PB'} = \frac{PB}{PB'}$

Using new Cartesian sign system, we have

$PB = - u (object), PC = - R, PB' = - v$ (distance of the image), we get,

$\frac{- u + R}{- R + v'} = \frac{- u}{- v'} or + uR - uv = uv - vR or uR + vR = 2 uv$

Dividing both side by $uvR$ , we get,

$\frac{1}{v} + \frac{1}{u} = \frac{2}{R} as R = 2 f \frac{1}{v} + \frac{1}{u} = \frac{2}{2 f} = \frac{1}{f}$

This is the mirror equation

The lateral magnification is given by $m = \frac{size of the image}{size of the object} = \frac{A' B'}{AB} = \frac{PB'}{PB} = - \frac{v}{u}$

Derive the mirror equation and equation for lateral magnification.

Important Questions on Reflection of Light : Spherical Mirrors

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