3.2 Lateral Magnification

1.1 Refractive index of light
1.2 Types of medium

2.1 Refraction from a spherical surface

3.1 Shift due to a glass slab
3.2 Lateral Magnification

4.1 Sign convention
4.2 Some important terms
4.3 Ray tracing
4.4 Image formed by covex lens
4.5 Image formed by concave lens

5.1 Thin Lens Formula
5.2 Magnification and Power of lens
5.3 Combination of lenses
5.4 Displacement method to find focal length.
5.5 Silvering of lens

6.1 Critical angle
6.2 Application of total internal reflection

7.1 Dispersive power

8.1 Rainbow

9.1 Spectrometer
9.2 Simple microscope
9.3 Compound microscope
9.4 Astronomical telescope (Refracting type)
9.5 Terrestrial telescope
9.6 Galileo's terrestrial telescope
9.7 Reflecting type telescope

From Snell's law we can write,

$${\mu _1}\sin i = {\mu _2}\sin r$$

As angles $i$ and $r$ are very small. So,

$${\mu _1}i = {\mu _2}r\quad ...(i)$$

Also,

\[\left. \begin{gathered} \tan i = \frac{{OA}}{{MO}}\quad \& \quad i = \frac{{OA}}{{MO}} \hspace{1em} \\ \tan r = \frac{{IB}}{{MI}}\quad \& \quad r = \frac{{IB}}{{MI}} \hspace{1em} \\ \end{gathered} \right\}\quad ...(ii)\]

From equation $(i)$ and $(ii)$ we get,

$${\mu _1}\left( {\frac{{OA}}{{MO}}} \right) = {\mu _2}\left( {\frac{{IB}}{{MI}}} \right)$$

As $\left( {OA \to + h,\;MO \to - u,\;IB \to - {h_2}\;{\text{and }}MI \to + v} \right)$. So,

$$\begin{equation} \begin{aligned} {\mu _1}\left( {\frac{{{h_1}}}{{ - u}}} \right) = {\mu _2}\left( {\frac{{ - {h_2}}}{v}} \right) \\ \frac{{{h_2}}}{{{h_1}}} = \left( {\frac{v}{u}} \right)\left( {\frac{{{\mu _1}}}{{{\mu _2}}}} \right) \\\end{aligned} \end{equation} $$

The above equation is used to calculate lateral magnification $(m)$ due to refraction from a spherical surface.