(a) Draw a ray diagram to show image formation when the concave mirror produces a real, inverted and magnified image of the object. (b) Obtain the mirror formula and write the expression for the linear magnification. (c) Explain two advantages of a reflecting telescope over a refracting telescope.

a)

a concave mirror produces a real, inverted and magnified image for the object placed between F and C
b)

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
Linear magnification
it is the ratio of the size of the image to the size of the object it is denoted by m.
$m= \frac{-v}{u}= \frac{{h}'}{h}$
where
${h}'=$ highest of the image
h = highest of the object
c)i) reflecting telescope is free from the chromatic aberration.
ii) In reflecting telescope spherical aberration is reduced by using the parabolic reflecting surface.
iii) Mechanical support is easier compared to the refracting telescope.

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