Name: Formation of Rainbow
Uploaded: 2019-07-19
Duration: 4 min 3 s
Description: Our joy knew no bounds when we used to see a rainbow in the sky in our childhood days. Kids! Do you know how a rainbow is formed? You can learn from this video.

Question

Using a neat labelled diagram derive the mirror equation. Define linear magnification.

Accepted Answer

Consider an object $A B$ is placed beyond the centre of curvature of a concave mirror at a distance $u$ and the image $A' B'$ is formed at a distance $v$ as shown in the diagram.

From figure the two right-angled triangles $A' B' F$ and $M P F$ are similar. Draw a line $M P$ imaginary straight line perpendicular to $C P$ .

$\frac{B^{'} A^{'}}{PM} = \frac{B^{'} F}{FP}$

$\frac{B^{'} A^{'}}{BA} = \frac{B^{'} F}{FP} (∵ PM = AB)$ ......... $(1)$

Since $∠ APB = ∠ A^{'} {PB}^{'}$ , the right angled triangles $A^{'} B^{'} P$ and $A B P$ are also similar. Therefore,

$\frac{B^{'} A^{'}}{BA} = \frac{B^{'} P}{BP}$ ............. $(2)$

Comparing equations $(1)$ and $(2)$

$\frac{B^{'} F}{FP} = \frac{B^{'} P - FP}{FP} = \frac{B^{'} P}{BP}$ ........ $(3)$

Applying sign convention, $B^{'} P = - v, FP = - f, BP = - u$

Substituting in eq $(3)$

$\frac{- v + f}{- f} = \frac{- v}{- u} \Rightarrow u v - u f = v f$

Dividing equation on both sides with $u v f$ we get,

$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$

This is the mirror equation.

Linear magnification: The ratio of the height of the image $(h_{i})$ to the height of the object $(h_{o})$ is said to be linear magnification.

$m = \frac{h_{i}}{h_{o}}$

$\Rightarrow \frac{B^{'} A^{'}}{BA} = \frac{B^{'} P}{BP} = \frac{- h_{i}}{h_{o}} = \frac{- v}{- u}$

$m = \frac{h_{i}}{h_{o}} = - \frac{v}{u}$

Using a neat labelled diagram derive the mirror equation. Define linear magnification.

Important Questions on Ray Optics and Optical Instruments

Learn and Prepare for any exam you want !