(a) Using the necessary ray diagram, derive the mirror formula for a concave mirror.

(b) In the magnified image of a measuring scale (with equidistant markings) lying along the principal axis of a concave mirror, the markings are not equidistant. Explain.

 

 
 
 
 
 

Answers (1)
S safeer

a)
 
Triangle A 'B' F and MPF are similar
Therefore,

\frac{{B}'{A}'}{PM}= \frac{{B}'F}{FP}
or   \frac{{B}'{A}'}{BA}= \frac{{B}'F}{FP} \; \left ( \because PM= AB \right )---(1)
Since < APB= < {A}'PB, the right-angled triangle {A}'{B}'P and ABP are also similar, Therefore,
\frac{{B}'{A}'}{BA}= \frac{{B}'P}{BP}---(2)
From equation (1) and (2)
\frac{{B}'{F}}{FP}= \frac{{B}'P-FP}{FP}= \frac{{B}'P}{BP}---(3)
Apply the sign convention
That is {B}'P= -V
FP= -f
BP= -u
using the relation equation (3) become
\frac{-v+f}{-f}= \frac{-v}{-u}
\frac{v-f}{f}= \frac{v}{u}
\frac{1}{v}+\frac{1}{u}= \frac{1}{f}
This relation is known as mirror equation
where, v = image distance
          u = object distances
          f = focal length

b) Magnification is different for different object distances. 

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