### Refractive index

- The value of sin
*i*/sin*r*is called the refractive index of the medium and it gives you an indication of its light-bending ability. $$\begin{array}{l}n=\frac{\mathrm{sin}i}{\mathrm{sin}r}\\ \\ n=\text{refractiveindex}\end{array}$$ - In SPM, when we say “refractive index”, what we mean is the absolute refractive index of a substance. The absolute refractive index of a substance is the refractive index where light ray travels from vacuum (or air) into the substance.

### Refractive Index and the Speed of light

$$\text{Refractiveindex=}\frac{\text{speedoflightinvacuum}}{\text{speedoflightinmedium}}$$

or

$$n=\frac{c}{v}$$
( Note that the greater the refractive index of a medium, the lower is the speed of light. The more light is slowed, the more it is bent. )

### Real and Apparent Depth

- The bending of light can give you a false impression of depth.
- Figure to the left shows two rays of light leaving a point on the bottom of a swimming pool.
- The rays are refracted as they leave the water. To the observer, the rays seem to come from a higher position, and the bottom looks closer to the surface than it really is.
- The real depth of the water and its apparent depth are marked on the diagram. These are related to the refractive index of the water by the following equation:

$$\text{Refractiveindex=}\frac{\text{realdepth}}{\text{apparentdepth}}$$ or

$$n=\frac{D}{d}$$

#### Summary:

Refractive index$$n=\frac{\mathrm{sin}i}{\mathrm{sin}r}$$

$$n=\frac{D}{d}$$

$$n=\frac{c}{v}$$