82B - Wave Properties

Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected. Mirrors exhibit specular reflection.

Anton Paar E-Learning - Introduction to reflection and refraction

Refraction is the change in direction of a wave due to a change in its transmission medium. The phenomenon exists to ensure that the law of conservation of energy and momentum are obeyed. Due to change of medium, the speed and wavelength of the wave are changed but thefrequency remains constant. This is most commonly observed when a wave passes from one medium to another at any angle other than 90° or 0° and the wavefront is seen to change direction. Refraction of light is the most commonly observed phenomenon, but any type of wave can refract when it interacts with a medium, for example when sound waves pass from one medium into another or when water waves move into water of a different depth. Refraction is described mathematically by Snell's law.

82B1 - Reflection

Here you will learn to:

Represent waves using wavefronts and rays,

Distinguish between specular and diffuse reflection,

Apply the Law of Reflection,

Draw ray diagrams to locate images for concave and convex mirrors, and

Describe applications of concave and convex mirrors.

Representing Waves

THe relationship between wavefronts and rays.

Waves can be represented in two ways: as a wavefront or as a ray. When representing reflection and refraction visually, we usually use a ray to show the wave. In experiments though, it is easier to see the wavefronts rather than the ray. For these reasons it is important to know the difference between a wavefront and a ray and the relationship between them.

A wavefront is a collection of waves all travelling in the same direction that are in phase. Being in phase means that all of the crests and troughs of each wave are lined up along the wave. The crests of each wave are represented as a series of parallel lines showing the movement of the wave. The distance between each line would represent the wavelength of the waves.

A ray is drawn perpedicular to the wave front and shows the path of a single wave in the wave front. The ray shows the direction in which the wave front is moving and is often used to show properties of waves such as reflection, refraction and diffraction.


Reflection is the abrupt change in direction of a wave front or ray at an interface between two dissimilar media so that the wave front returns into the medium from which it originated. Common examples include the reflection of light in a mirror, sound in an echo and water waves off a wall.

Types of Reflection

Specular and diffuse radiation shown
diagramatically (above) and with a laser

A typical light reflecting silver glass mirror is a piece of glass coated on its back surface with silver, which produces images by reflection. This kind of glass mirror is produced by coating a silver film on the back of the glass with two or more layers of waterproof paint over the silver to resist moisture and corrosion.

The Law of Reflection from a plane

When parallel light rays strike the smooth, silver, plane surface on the back of the mirror, the rays are also reflected parallel to each other. This type of reflection is known as specular reflection. Specular reflection will produce a clear image in the mirror. If the mirror has an uneven, irregular surface, the incident light is reflected at a variety of different angles rather than parallel. This type of relfection is known as diffuse reflection and does not produce a clear image.


Law of Reflection

Let us now consider a single light ray incident upon a smooth, shiny surface such as a plane mirror. This light ray is known as the incident ray. The angle between the normal and the incident ray will be equal the angle between the normal and the reflected ray. The normal is an imaginary line perpendicular to the surface of the mirror. The Law of Reflection states that the angle of incidence (θi) will always equal the angle of reflection (θr) for any reflected ray or wavefront.

Reflection from Curved Surfaces

Surfaces which curve inwards (like a cave) are known as concave surfaces. Surfaces which curve outwards are called convex surfaces. The focus of a curved reflecting surface is the point on the principle axis, midway between the curve and its centre of curvature.

Concave Reflectors

The image formed using a concave mirror
when when the source image is placed
between the focus and the centre of
curvature. The numbers refer to rules for
drawing rays in the text on the left.

There are some simple rules that can be used to predict the path of rays being reflecting from a concave mirror. Drawing a few rays from an object reflecting from the mirror allows us to determine where the image formed in the mirror appears and how big or small it will be compared to the original. To locate images in a concave mirror, uses these simple rules:

  1. A ray travelling parallel to the principle axis will be reflected through the focus

  2. A ray striking the mirror at the point of intersection of the principle axis will be reflected at the same angle to the normal (Law of Reflection)

Tracing these rays to the point of intersection will allow the reflected image to be located. Concave mirrors produce different types of images depending on where the source image is located in relation to the focus of the mirror. Wikipedia has more information on the types of images produced by concave mirrors.

Concave mirrors reflect light inward to one focal point and are used to focus light. It is this property of concave surfaces that makes them useful for directing light rays ahead in torches and car headlights. Concave surfaces are converging surfaces as they cause the rays to reflect and move closer together until they pass through the focus. It is this property of a concave surface which we use in solar cookers (we place the meat on a skewer at the focus) and in collecting data from radio and microwave signals from space (the receiver is suspended at the focus of the collecting dish).

Access a simulation showing rays diagrams to locate images in a concave mirror.

Convex Reflectors

The image formed in a convex mirror.

Convex surfaces reflect rays so that their backwards extension passes through the focus of the curve. Convex surfaces are called diverging surfaces as they reflect the rays so that they travel further apart. This makes them useful in rear vision mirrors or driveway mirrors to give drivers and oncoming traffic a wider view of the area behind them or around a corner respectively.

Use the following rules to draw reflected rays and locate images formed by convex mirrors.

  1. A ray travelling parallel to the principle axis will appear to be reflected from the focus

  2. A ray striking the mirror at the point of intersection of the principle axis will be reflected at the same angle to the normal (Law of Reflection)

Convex mirrors always produce images that are virtual, upright and smaller than the actual image. A virtual image is one formed from rays that are extended behind the mirror to find the point of intersection.

Access a simulation showing rays diagrams to locate images in a convex mirror.

Stuff to Do

TutorialTutorial 82B1 - Reflection
TutorialTutorial 82B1 - Reflection - Answers
MovieKahn Academy - Specular and Diffuse Reflection 1
MovieKahn Academy - Specular and Diffuse Reflection 2
82B2 - Refraction

In this section you will learn to:

Define, explain and identify examples of refraction,

Apply Snell's Law for refraction, and

Describe the principle of total internal reflection and its application in optic fibre cables.


A wave refracting as it crosses the
boundary between air and water.

Often the light will penetrate a surface rather than being reflected from it. As most media have slightly different physical properties they will also exhibit different optical properties. The refractive index is a term which describes the ease or speed with which light moves through a substance. The higher the refractive index the slower light moves through that substance. When light enters a new substance its speed changes and this results in a change in wavelength. Since the frequency of any wave (light included) will remain the same, an increase in speed causes a corresponding increase in wavelength and vice-versa. The new speed also causes the light wave to bend or refract when it crosses the boundary at an angle to the normal.

When a wave enters a medium and is able to go faster the wave will refract or bend away from the normal and the wavelength will increase. When a wave enters a medium where it travels more slowly, it will bend toward normal and its wavelength will decrease. The corresponding change in wavelength and speed can be theorised using the wave equation (v=fλ). If speed (v) increases, the wavelength (λ) must also increase to keep the frequency the same.

Refraction is the change in speed and wavelength of a wave as it crosses a boundary where the refractive index is changing (the frequency remains constant). This will also change the direction of the wave if the angle of incidence has any value other than zero, in which case the speed will change but not the direction.

Snell's Law

Snell's law of refraction for a wave crossing the
boundary between two media with different
refractive indices.

In optics and physics, Snell's law (also known as Descartes' Law or the law of refraction), is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves, passing through a boundary between two different media, such as air and glass.

The law says that the ratio of the sines of the angles of incidence and of refraction is a constant that depends on the media. In optics, the law is used in ray tracing to compute the angles of incidence or refraction, and in experimental optics to find the refractive index of a material. Named for one of its discoverers, Willebrord Snellius (Willebrord Snel van Royen), Snell's law states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of velocities in the two media, or equivalently to the inverse ratio of the indices of refraction.


Total Internal Reflection

Total internal reflection for an air-water boundary. At angles
below the critical angle, the ray is both refracted and
reflected. At the critical angle it is totally internally reflected
along the boundary and above the critical angle it is totally
internally reflected back into the medium with the lower
refractive index.

When light moves from a more dense (higher refractive index) to a less dense (lower refractive index) medium, such as from water to air, Snell's law cannot be used to calculate the refracted angle because the resolved sine value is higher than 1. At this point, light is reflected back into the incident medium, known as total internal reflection. Before the ray totally internally reflects, the light refracts at the critical angle; it travels directly along the surface between the two refractive media, without a change in phases like in other forms of optical phenomena.

Optical fibre cabling uses total internal reflection to reflect light signals along the cable. The light signals can carry digital information and are used for IT networks to carry large amounts of data in short timeframes (high bandwidth).

Stuff to Do

TutorialTutorial 82B2 - Refraction
TutorialTutorial 82B2 - Refraction - Answers
MovieKahn Academy - Refraction and Snell's Law
MovieKahn Academy - Refraction in Water
MovieKahn Academy - Snell's Law Example 1
MovieKahn Academy - Snell's Law Example 2
MovieKahn Academy - Total Internal Reflection