Refraction

This follows the pages about understanding light (what is light ?, light leaving surfaces, light and vision) then introducing a ray-diagram of image formation within the eye.

What is Refraction and why study it ?

Refraction is an important concept describing how electromagnetic waves (including visible light) change direction when passing from one medium to another. Examples of different media include air, water, glass and transparent plastics. Biological examples include the transparent parts of the eye, such as the cornea, aqueous humour, lens and vitreous humour.

As mentioned on the previous page: Refraction is an important means by which the eye controls and re-directs in such a way as to produce the good-quality clear images on the retina that are essential for good vision / eyesight, the light it receives from objects in the person's field of view. Summary from previous page: The previous page states that ray-diagrams can be used used to show how light from an object outside the body passes into the eye and forms an image at the back of the eye. The ray-diagram shows light leaving the object in all directions, so not all of the light travelling (in straight lines) away from the object reaches the eye. Considering a simple object defined by just two (2) points, it is possible to see an example of image formation on the retina by tracing just four (4) rays through the eye. Rays representing light travelling in straight lines from the object to the eye change direction on entering the eye through the cornea. More detailed consideration of the optical path through the eye would include further re-direction of light passing through the lens of the eye. In general, the changes of direction of light passing through the eye to produce an image on the retina are largely due to the effect of refraction.

The Principle of Refraction:

Some people remember how refraction works using this simple statement, which is explained below:

e.g. when travelling from air into water, or from air into glass.

1. The normal is a theoretical line (i.e. it is not present in real objects but is often drawn on diagrams) at right-angles to the tangent to a surface at the position at which a ray of light crosses that surface between media. This means that the normal to a plane surface is at right-angles to the surface - as shown opposite.

   The normal is usually drawn as a dashed line.

2. Refraction is concerned with the refractive index
   (a form of "optical density") of materials, rather than with actual density (density = mass / volume).

   However, use of the idea of density may be helpful to convey and remember the basic concept of refraction - and loosely applies for the simple examples of light passing from air into water, or water into glass etc..

The opposite is also true, i.e. light bends away from the normal when moving into a less dense medium.

e.g. when travelling from water into air, or from glass into air.

Another way to remember this is to note that:

A more detailed explanation including the significance of refractive index is included below and is important for numerical examples (calculations) and when considering different types of glasses, as necessary for opticians and optical physicists.

The Law of Refraction:

The Law of Refraction is also known as Snell's Law, as Descartes' Law, and (less usually) as The Snell–Descartes Law.

Knowledge of the mathematics of the Law of Refraction is not necessary for an introductory-level understanding of how the eye works but it is interesting and essential for more advanced study. The Law of Refraction is more useful than the simple "Principle of Refraction" (above) because the Law of Refaction is quantitative, hence enables calculations to be made.

The change in direction of a wave (e.g. green light) that is known as refraction is due to the change in speed at which that wave (e.g. green light) travels through one medium compared with another medium - or sometimes even through different areas of the same medium such as areas of different temperatues.

An equation is a simple way to summarise the relationship between the angles (which, together, describe the change in direction of the wave) and the speeds at which the wave (e.g. green light) travels through the different media.

In the following equation:

There are also two other terms in the equation form of the Law of Refraction.

They are n₁ and n₂, which represent the refractive indices of the two materials:
n₁ represents the refractive index of Material (1), and n₂ represents the refractive index of Material (2).

Strictly, one would specify the refractive index of a material for a particular wavelength (or frequency, as the wavelength and frequency of electromagnetic radiation are related). However, the variation of the refractive index of most common materials/substances with wavelength (within the visible spectrum) is sufficiently small that in non-specialist situations a value of refractive index for a single (specified) wavelength is usually given and used for the visible range of wavelengths generally. Exceptions to this simplification apply in cases of advanced high-specification optical design, and when considering wavelengths from different parts of the electromagnetic spectrum e.g. IR, UV, radio waves, etc..

Refractive Index

There are equations defining the refractive index of materials in terms of other properties of the material (including e.g. the phase velocity, relative permittivity, and relative permeability of the material) but those equations and their explanations are beyond the knowledge necessary to understand how the structures of the human eye operate to form good quality inverted images on the retina.

Lenses and Refraction

The above descriptions of refraction indicate that there are important parameters controlling how light is refracted (i.e. re-directed) at surfaces between different media. These parameters are:

1. The refractive indices of the materials on either side of the surface (e.g. the refractive indices of air and glass).

   The mathematics in the equation form of the Law of Refraction means that, generally, the bigger the difference in refractive index between the two materials, the larger the change in direction (i.e. the bigger the difference between the angle of incidence and the angle of refraction).

   and

2. The angle of incidence at the interface between the two media.

   The extent to which light bends (changes direction) at a surface also depends on the angle at which the light reaches that surface (i.e. the angle of incidence).

One way to control the direction of travel of light using the effect of refraction is by the use of lenses.

The material from which a lens is made determines its refractive index. For a lens at a specific location and orientation, the curvature of the surfaces of the lens determine the range of angles of incidence of light arriving at the lens from any particular point in space.

Lenses are very important components in optical physics. A basic understanding of lenses is also necessary to explain how the human eye works.

The next page is a very simple introduction to lenses (e.g. the lens in the eye is a convex lens).

Note: Understanding of parts of the nervous system (such as the eye / visual system) are required for many exams - e.g. GCSE Physics, GCSE Biology, and AS and "A"-Level Biology and Human Biology.