Total Internal Reflection

Total internal reflection is the reflection of light incident at the boundary of a medium back into the medium whence it came. A varying proportion of the incident light may be totally internally reflected depending on the angle of incidence of the light and the critical angle of the medium.
Physics - Waves - Reflection, Refraction and Diffraction 


This article is part 3 of the series 'Reflection, Refraction and Diffraction'. Prior knowledge may be required. If you have difficulty with this article, read its precursor here: http://exploringgcses.blogspot.com/2012/01/refraction-of-light.html

Total internal reflection occurs alongside refraction, and only in the passage of light from a more optically dense material to a less optically dense material. When the light is incident at the boundary of the medium in this case, most of it is refracted, but a small proportion is reflected back into the medium.

The proportion of light reflected back remains small until the light is incident at an angle greater than the critical angle. Once this happens, all of the light is totally internally reflected. When a light ray incident at exactly the critical angle, the refracted ray runs perpendicular (at 90 degrees) to the normal.

If the angle of incidence increases such that it is greater than c, all of the light will be totally internally reflected.

The value of c depends not only on the optical density of the first medium, but also on the optical density of the medium that the light would be refracted to. In other words, it relies on the density of the materials either side of the boundary. This is important to remember.

The equation sin(c) = 1/n relates a medium's refractive index to its critical angle in air.


Total internal reflection has several uses. It can be used to carry optical signals along bundles of optical fibres because the light inside just reflects against the side continuously as it moves forwards. It is used in periscope prisms as well: because the critical angle for glass is 42 degrees, it will be totally internally reflected in a periscope arrangement because it will be incident to the boundary at 45 degrees, which is greater than c.


Read part 4 of this series, 'Diffraction', http://exploringgcses.blogspot.com/2012/01/diffraction.html

Refraction of light

Refraction describes the change in direction of a ray of light as it travels from one medium to another medium with a different optical density. The change in direction happens as a result of the change in velocity of the light as it travels into this other medium.
Physics - Waves - Reflection, refraction and diffraction


This article is part 2 of the series 'Reflection, Refraction and Diffraction'. Prior knowledge may be required. If you have difficulty with this article, read its precursor here: http://exploringgcses.blogspot.com/2011/12/reflection-of-waves.html

The optical density (also called absorbance)  of a medium (a material through which light can travel) describes the speed at which light travels in it. For example, a vacuum (a space with no matter of any kind in it) has an optical density of 0. This is because there is absolutely nothing to slow it down, the vacuum is completely empty. The 'speed of light' (300 million m/s) actually means the speed of light in a vacuum because that's where it travels fastest.

The refractive index of a medium is derived from the optical density of that medium. The optical density defines how much the light's speed changes, and that in turn defines how much it is refracted. How much it is refracted is the refractive index; it is easy to see that these two terms are closely linked. Looking ahead, the refractive index is calculated using Snells' Law, which says that:

the ratio sin(i) : sin(r) is constant

where i = angle of incidence and r = angle of refraction

If these terms are difficult to understand, read on and return to the equation later

To look up the refractive index of a material, try this website: http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=5f7039b1bb628805481cb58560a1208b&title=Index%20of%20Refraction&theme=red&i0=glass&podSelect=&showAssumptions=1&showWarnings=1

Now that all of the terminology has been explained, we will explore the trends of refraction. Whenever light travels from one medium to another medium that has a different optical density, refraction will occur*. When light travels from a less optically dense medium to a more optically dense medium, the light is bent towards the normal. When it travels from a less optically dense material to a more optically dense material, it bends away from the normal. Look at the diagram: light is refracted twice, once from air to glass and once from glass to air. Glass is more optically dense, and since the dotted lines represent the normals, you can see the rules being applied. First, the light bends towards the normal, and then away from it.


Notice that the ray leaving the glass is travelling in the same direction as the ray entering the glass, but has just been moved down. We say that it has been subject to parallel displacement. This will only happen if the light leaves the 2nd medium back into the same medium it started in.

*There is an exception: if the light enters the second medium along the normal (perpendicular to the new material's surface) then no refraction will occur.

Now we can return to the rule: the ratio sin(i) : sin(r) is constant. We can derive from the equation
 n = sin(i)/sin(r) with n being the refractive index. We can use this to find i, r, or n by substituting know values into the equation and simplifying.


Dispersion occurs when white light is refracted through a prism to give a spectrum of light. White light is composed of 7 different colours of visible light, which all have different wavelengths. As a result of this, the prism has a different refractive index for each colour. This means that the direction of each colour is changed by a different amount, and a spectrum or band of colours spreads out from the other side of the prism. This is not an exception to refraction, only an interesting application of it.

To summarise: refraction is the change in the direction of light as a result of the change of the medium in which it is travelling. When light travels into a more optically dense material, it bends towards the normal, and vice versa. The sine of the angle of incidence divided by the sine of the angle of refraction is equal to the refractive index, n. The magnitude of the refration is defined by the refractive index of the new medium.


The next post in the series is 'Total Internal Reflection' http://exploringgcses.blogspot.com/2012/01/total-internal-reflection.html