WAVES    RAY MODEL OF LIGHT    REFLECTION and REFRACTION    DISPERSION A great deal of evidence suggests that light is a wave and under a wide range of circumstances, light travels in a straight line. For example, sunlight casts sharp shadows. Another example is refraction where light passes from one transparent medium into another (figure 1).  Such observations, has led to the ray model of light.  A ray is an idealization that represents an extremely narrow beam of light.   According to the ray model, we see an object because light reaches our eyes from each point on the object. Although the light leaves a point on the object in all directions, only a small bundle enters your eye. The ray model of light has been very successful in explaining many aspects of the behaviour of light such as reflection, refraction, dispersion, and the formation of images by mirrors and lenses.   Fig. 1.  We can use a ray model to explain the straight line propagation of light. How do we see? A small bundle of light rays come from each single point on an object and enters your eye.  A pencil in water looks bent even when it isn’t.   When a ray of light of is obliquely incident upon a medium of different refractive index, the ray is bent. The relationship between the angle of incidence and angle of refraction is described by Snell’s Law          (1A)               (1B)                  (1C)                       Refraction is responsible for several common optical illusions. When you look into a lake and see a fish – where is the fish located?        Fig. 2.   Where is the fish located?

 Thinking Exercise When you watch a person standing in waist-deep water, it appears that their legs are shorter. Explain this observation using a scientific annotated ray diagram.

 Figure 3 shows a ray of light that emerges from a rectangular slab of glass such that the direction of the beam of light is unchanged.        Fig. 3.   Light passing through a glass slab.   Why does a diamond sparkle? The refractive index of glass is 1.5 whereas for diamond it is  2.42. The critical angle for glass is 41o and the critical angle for diamond is 24.4o which is smaller than for any other common substances. (Check the calculations for the critical angles for diamond and glass). When light enters a cut diamond, the large refractive index compare with air results in the strong dispersion of the light and this dispersed light is mostly incident on the sloping backsides of the gem at angles greater than 24.4o, hence most of the light is totally internally reflected. Further dispersion occurs as the light exists through the many facets of its face. Hence, we see flashes of a wide range of colours, but with only one eye are they noticeable at any one time – these narrow flashes are what makes diamond “sparkle”.     Why do we see the Sun after it has set? Because of refraction, when the Sun is near the horizon, it appears higher in the sky than it actually is. So, if you watch a sunset, we see the Sun for several minutes after it has sunk below the horizon and thus, slightly more daylight each day. The Earth’s atmosphere is more dense towards the ground and light travels faster in the thinner atmosphere further from the ground, so the light from the sun does not travel in a straight line, but travels in longer and higher path in penetrating the atmosphere.  Since the density of the atmosphere changes gradually, the light also bends gradually to propagate in a curved path. When the Sun (Moon) is near the horizon, the rays from the lower edge are bent more than the rays from the top edge – this produces a reduction in the vertical diameter causing the Sun (Moon) to appear flatten like a pumpkin.   MIRAGES A mirage is an optical phenomenon that creates the illusion of water or an inverted reflection and results from the refraction of light through a non-uniform medium.     You may see a mirage when driving along a hot road – the distant road appears to be wet, yet it is dry. Why?   The air near the surface of the road is hot and much cooler above. Light travels faster through the thin hotter air then it does through the denser and more cooler air. So, instead of the light travelling in a straight line, it travels in a curved line – the wetness on the road we observe is a reflection of the sky. The bending of light is simply refraction and is a consequence of light having different speeds in different media.

 VISIBLE SPECTRUM and DISPERSION Visible light is part electromagnetic spectrum to which our eyes are sensitive and falls within the range of wavelengths from ~ 400 nm to ~ 750 nm. The colour of light is related to its wavelength (or frequency). Fig. 4.   Electromagnetic spectrum. There is no “white” light. When different colours (fixed wavelengths) are mixed together in certain combinations, our eye perceives the light to be white.     A glass prism separates “white” light into a rainbow of colours. This occurs because the index of refraction of a material depends upon the wavelength of the light – the shorter the wavelength, the higher the refractive index.   Fig. 5.   Index of refraction as a function of wavelength for some transparent solids. N.B. the shorter the wavelength, the higher the refractive index.   White light is a mixture of all the visible wavelengths, so when the white light enters the glass prism, different wavelengths (colours) will be bent through different angles (refraction). Because violet light is bent the most and red light the least, the white light is separated into its component colours and this phenomenon is called dispersion.        Fig. 6.   White light dispersed by a glass prism into the visible spectrum.   Rainbows are a spectacular example of dispersion caused by reflection and refraction from droplets of water. You observe a rainbow by looking at falling water drops with the Sun at your back. The red light is bent the least and is observed higher in the sky, whereas violet light is bent the most and is observed lower in the sky.   Fig. 7.   Rainbows are formed by reflection and refraction of sunlight from falling water droplets.

 If you have any feedback, comments, suggestions or corrections please email: Ian Cooper   School of Physics   University of Sydney ian.cooper@sydney.edu.au