**CBSE NOTES CLASS 12 PHYSICS **

**CHAPTER 10 WAVE OPTICS**

**Refraction of a plane wave from rarer to denser medium**

Let PP’ represent the surface separating medium 1 and medium 2. Let v_{1} and v_{2} represent the speed of light in medium 1 and medium 2, respectively. Let us take a plane wave front AB, propagating in the direction A’A, incident on the interface at an angle i. If τ be the time taken by the wave front to travel the distance BC and BC = v_{1}τ

By the time the point B on wave front travels to point C in medium 1, the point A would have travelled in medium 2, to E The new wave front will be CE and AE = v_{2}τ.

$$\mathrm{N}\mathrm{o}\mathrm{w}\mathrm{sin}\mathrm{i}=\frac{\mathrm{B}\mathrm{C}}{\mathrm{A}\mathrm{C}}={\mathrm{v}}_{1}\mathrm{}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{sin}\mathrm{r}=\frac{\mathrm{A}\mathrm{E}}{\mathrm{A}\mathrm{C}}={\mathrm{v}}_{2}\mathrm{}\mathrm{}\mathrm{}$$

$$\Rightarrow \mathrm{}\frac{\mathrm{sin}\mathrm{i}\mathrm{}}{\mathrm{sin}\mathrm{r}}=\frac{{\mathrm{v}}_{1}}{{\mathrm{v}}_{2}}$$

This is **Snell’s law**.

If r < i then the ray bends toward the normal and the speed of the light wave in the second medium (v_{2}) will be less than the speed of the light wave in the first medium (v_{1}). **This is correct and proves the corpuscular theory wrong.**

The constants

$${\mathrm{n}}_{1}\mathrm{}=\frac{\mathrm{c}}{{\mathrm{v}}_{1}}\mathrm{}\mathrm{}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{}{\mathrm{n}}_{2}\mathrm{}=\frac{\mathrm{c}}{{\mathrm{v}}_{2}}\mathrm{}$$

are called refractive indices of medium 1 and 2 respectively.

Also, ${\mathrm{n}}_{1}\mathrm{sin}\mathrm{i}=\mathrm{}{\mathrm{n}}_{2}\mathrm{sin}\mathrm{r}$

$$\mathrm{a}\mathrm{n}\mathrm{d},\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\frac{{\mathrm{v}}_{1}}{{\mathrm{v}}_{2}}=\frac{{\mathrm{\lambda}}_{1}}{{\mathrm{\lambda}}_{2}}$$