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(a) With the help of a ray diagram, show how a concave mirror is used to obtain an erect and magnified image of an object.

(b) Using the above ray diagram, obtain the mirror formula and the expression for linear magnification.

Answers (1)

From $\Delta \; A'\; B'\; F$ and $M\; F\; P$ by similarity criteria.

$\frac{A'B;}{MP}=\frac{B'F}{FP}$ Or $\frac{A'B'}{AB}=\frac{B'F}{FP}\; \; \;\; (PM=BA)$

Similarly from

$\Delta A'B'P$ and $ABP$

$\frac{B'A}{BA}=\frac{B'P}{BP}$

$\frac{B'F}{FP}=\frac{B'P}{BP}$

$B'F=v+f$

$BP=u$

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

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

Dividing throughout by v and applying sign convention

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

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

is the mirror equation.

Linear magnification

From $\Delta A'B'P$ and $ABP$

$\frac{B'A'}{BA}=\frac{B'P}{BP}=\frac{-v}{u}$

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Safeer PP

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