Question
What is linear magnification? Obtain equation of linear magnification for mirror.
✓
Answer
→Linear magnification is the ratio of the height of the image $\left(h^{\prime}\right)$ to the height of the object $(h)$.
$\therefore m=\frac{h^{\prime}}{h}$
→As shown in figure object AB is placed slight far from centre of curvature. Its image is found between C and F.
→Here height of the object is $h$ and height of image is $h^{\prime}$.
→As per figure $\triangle ABP$ and $\triangle A ^{\prime} B ^{\prime} P$ are similar triangle.
$\therefore \frac{ B ^{\prime} A ^{\prime}}{ BA }=\frac{ B ^{\prime} P }{ BP }$
→According to sign convention,
$\begin{array}{l} B ^{\prime} A ^{\prime}=-h^{\prime}, BA =h \\B^{\prime} P =- v , \quad BP =-u \\\therefore \quad \frac{-h^{\prime}}{h}=\frac{- v }{-u} \\\therefore \quad \frac{h^{\prime}}{h}=-\frac{v}{u}\end{array}$
→From equation (1),
$m=-\frac{v}{u}$
$\therefore m=\frac{h^{\prime}}{h}$
→As shown in figure object AB is placed slight far from centre of curvature. Its image is found between C and F.
→Here height of the object is $h$ and height of image is $h^{\prime}$.
→As per figure $\triangle ABP$ and $\triangle A ^{\prime} B ^{\prime} P$ are similar triangle.
$\therefore \frac{ B ^{\prime} A ^{\prime}}{ BA }=\frac{ B ^{\prime} P }{ BP }$
→According to sign convention,
$\begin{array}{l} B ^{\prime} A ^{\prime}=-h^{\prime}, BA =h \\B^{\prime} P =- v , \quad BP =-u \\\therefore \quad \frac{-h^{\prime}}{h}=\frac{- v }{-u} \\\therefore \quad \frac{h^{\prime}}{h}=-\frac{v}{u}\end{array}$
→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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