Question
What is linear magnification? Obtain equation of linear magnification for mirror.
✓
Answer
$\rightarrow $ Linear magnification is the ratio of the height of the image $\left(h^{\prime}\right)$ to the height of the object $(h)$.
$\therefore m=\frac{h^{\prime}}{h}$
$\rightarrow $ As shown in figure object $AB$ is placed slight far from centre of curvature. Its image is found between $C$ and $F.$
$\rightarrow $ Here height of the object is $h$ and height of image is $h^{\prime}$.
$\rightarrow $ As per figure $\triangle ABP$ and $\triangle A ^{\prime} B ^{\prime} P$ are similar triangle.
$\therefore \frac{ B ^{\prime} A ^{\prime}}{ BA }=\frac{ B ^{\prime} P }{ BP }$
$\rightarrow $According to sign convention,
$\begin{array}{l} B ^{\prime} A ^{\prime}=-h^{\prime}, BA =h \\B^{\prime} P =- v , \quad BP =-u \\\therefore \quad \frac{-h^{\prime}}{h}=\frac{- v }{-u} \\\therefore \quad \frac{h^{\prime}}{h}=-\frac{v}{u}\end{array}$
$\rightarrow $From equation $(1),$
$m=-\frac{v}{u}$
$\therefore m=\frac{h^{\prime}}{h}$
$\rightarrow $ As shown in figure object $AB$ is placed slight far from centre of curvature. Its image is found between $C$ and $F.$
$\rightarrow $ Here height of the object is $h$ and height of image is $h^{\prime}$.
$\rightarrow $ As per figure $\triangle ABP$ and $\triangle A ^{\prime} B ^{\prime} P$ are similar triangle.
$\therefore \frac{ B ^{\prime} A ^{\prime}}{ BA }=\frac{ B ^{\prime} P }{ BP }$
$\rightarrow $According to sign convention,
$\begin{array}{l} B ^{\prime} A ^{\prime}=-h^{\prime}, BA =h \\B^{\prime} P =- v , \quad BP =-u \\\therefore \quad \frac{-h^{\prime}}{h}=\frac{- v }{-u} \\\therefore \quad \frac{h^{\prime}}{h}=-\frac{v}{u}\end{array}$
$\rightarrow $From equation $(1),$
$m=-\frac{v}{u}$
| No. | Type of mirror | Image type and size | Magnification |
| $1$ | Plane | Virtual, erect and same as of object | $+1$ |
| $2$ | Concave | Real, inverted and same as of object | $-1$ |
| $3$ | Concave | Real, inverted and magnified | $> 1$ and negative |
| $4$ | Concave | Real, inverted and diminished | $< 1$ and negative |
| $5$ | Concave | Virtual, erect and magnified | $> 1$ and negative |
| $6$ | Convex | Virtual, erect and diminished | $< 1$ and positive$ |
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