# 0.1 Geometrical optics - grade 10  (Page 5/14)

 Page 5 / 14

When light travels from one medium to another, it will be bent away from its original path. When it travels from an optically dense medium like water or glass to a less dense medium like air, it will be refracted away from the normal ( [link] ). Whereas, if it travels from a less dense medium to a denser one, it will be refracted towards the normal ( [link] ).

Just as we defined an angle of reflection in the previous section, we can similarly define an angle of refraction as the angle between the surface normal and the refracted ray. This is shown in [link] .

## Refractive index

Which is easier to travel through, air or water? People usually travel faster through air. So does light! The speed of light and therefore the degree of bending of the light depends on the refractive index of material through which the light passes. The refractive index (symbol $n$ ) is the ratio of the speed of light in a vacuum to its speed in the material.

Refractive Index

The refractive index of a material is the ratio of the speed of light in a vacuum to its speed in the medium.

## Interesting fact

The symbol $c$ is used to represent the speed of light in a vacuum.

$c=299\phantom{\rule{0.277778em}{0ex}}792\phantom{\rule{0.277778em}{0ex}}485\phantom{\rule{0.166667em}{0ex}}\mathrm{m}·{\mathrm{s}}^{-1}$

For purposes of calculation, we use $3×{10}^{8}\phantom{\rule{0.166667em}{0ex}}\mathrm{m}·{\mathrm{s}}^{-1}$ . A vacuum is a region with no matter in it, not even air. However, the speed of light in air is very close to that in a vacuum.

Refractive Index

The refractive index (symbol $n$ ) of a material is the ratio of the speed of light in a vacuum to its speed in the material and gives an indication of how difficult it is for light to get through the material.

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

where

 $n$ = refractive index (no unit) $c$ = speed of light in a vacuum ( $3,00×{10}^{8}\phantom{\rule{0.166667em}{0ex}}\mathrm{m}·{\mathrm{s}}^{-1}$ ) $v$ = speed of light in a given medium ( $\phantom{\rule{0.166667em}{0ex}}\mathrm{m}·{\mathrm{s}}^{-1}$ )

## Refractive index and speed of light

Using

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

we can also examine how the speed of light changes in different media, because the speed of light in a vacuum ( $c$ ) is constant.

If the refractive index $n$ increases, the speed of light in the material $v$ must decrease. Light therefore travels slowly through materials of high $n$ .

[link] shows refractive indices for various materials. Light travels slower in any material than it does in a vacuum, so all values for $n$ are greater than 1.

 Medium Refractive Index Vacuum 1 Helium 1,000036 Air* 1,0002926 Carbon dioxide 1,00045 Water: Ice 1,31 Water: Liquid ( ${20}^{\circ }$ C) 1,333 Acetone 1,36 Ethyl Alcohol (Ethanol) 1,36 Sugar solution (30%) 1,38 Fused quartz 1,46 Glycerine 1,4729 Sugar solution (80%) 1,49 Rock salt 1,516 Crown Glass 1,52 Sodium chloride 1,54 Polystyrene 1,55 to 1,59 Bromine 1,661 Sapphire 1,77 Glass (typical) 1,5 to 1,9 Cubic zirconia 2,15 to 2,18 Diamond 2,419 Silicon 4,01

## Snell's law

Now that we know that the degree of bending, or the angle of refraction, is dependent on the refractive index of a medium, how do we calculate the angle of refraction?

#### Questions & Answers

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Source:  OpenStax, Maths test. OpenStax CNX. Feb 09, 2011 Download for free at http://cnx.org/content/col11236/1.2
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