5. In Figure 10 of this section, ray 1 is incident on the inside surface of the glass fibre at an angle less than the critical angle. (a) What is the critical angle for this fibre if the index of refrac- tion for the glass is 1.50? (b) With what maximum angle relative to the normal of the fibre’s end can it strike the end of the fibre without later escaping? Applying Inquiry Skills 6. Design an experiment to determine whether light will undergo DID YOU KNOW ? total internal reflection within gases, for example, when travelling ϭ ϭ Medical Application of Total in carbon dioxide (n 1.000450) toward air (n 1.000293). What Internal Reflection is the critical angle of light in carbon dioxide, according to Snell’s law? How will this affect the design of your experiment? An endoscope is a device that transmits images using bundles of fibres. Endoscopes Making Connections probe parts of the body that would otherwise 7. Research which fields, other than communications, have been require exploratory surgery. greatly affected by the use of fibre optics. 9.7 Applications of Refraction Geometric optics is a good model of light for explaining many natural optical phenomena. Recall that a point is perceived by the eye when a cone of diverging light enters the eye. The diverging light is traced backward and where the rays meet, an image of the object is perceived. Atmospheric Refraction For many purposes, we assume the index of refraction of air to be 1.000. Although variation of the index of refraction of air from this value is just a small fraction of a percent, it is this small fraction that causes many optical effects. The atmosphere’s index of refraction varies, especially along vertical lines. Refractive effects such as mirages and shimmering are due to variations in the index of refraction caused by temperature variations. Twinkling and Shimmering DID YOU KNOW ? Earth’s atmosphere consists of flowing masses of air of varying density and tem- perature; therefore, the refractive index varies slightly from one region of the Observing the Sky atmosphere to another. When light from a star enters the atmosphere it is Most large telescopes are located high on refracted as it moves from one mass of air to another, and, since the variable mountains where there is less of Earth’s masses of air are in motion, the star seems to twinkle. atmosphere between them and the stars, and Under conditions of constant pressure, warm air has a slightly lower index where the air is more uniform in temperature. of refraction than cold air. When light passes through a stream of warm air, as it This minimizes distortions caused by atmos- does above a hot stove or barbecue, it is refracted away from the normal. This pheric refraction. Astronomers find that cold refraction is not uniform because the warm air rises irregularly, in gusts. Light winter nights are usually best for celestial observation since vertical temperature varia- from objects seen through the warm air is distorted by irregular refraction, and tions are minimized. Any atmospheric distor- the objects appear to shimmer. You can see the same effect over hot pavement in tions are corrected using specialized software. the summer or at an airport as jets go by. 346 Chapter 9 9.7 Mirages Two types of mirages can occur, depending on the temperature variation. An inferior mirage occurs when cooler layers of air lie above warmer layers. The viewer sees an image displaced downward. Inferior mirages are most often asso- ciated with deserts, but can occur over any hot, flat surface, such as a road on a summer day (Figure 1). As the light from the sky nears the ground it is progres- sively refracted by successive layers of warmer air, each with a lower index of refraction (Figure 2). The angle of incidence to the boundaries of these layers keeps increasing. Eventually, the light is totally internally reflected upward from one of the layers. What your eye sees is a virtual image of the sky below the road. It just appears that there is a layer of water on the road because you perceive that there is a reflecting surface. objectdirect light through air of uniform refracted index eye Figure 1 cool air Sometimes, what seems to be a sheet of warm air hot air water appears on the highway a short dis- tance ahead of you, but you never reach it. hot flat pavement image Figure 2 An inferior mirage A superior mirage occurs when optically denser layers of air lie below less dense layers. The viewer sees an image displaced upward, as in Figure 3(a). In this case, light refracts toward the denser air (Figure 3(b)). (a) Figure 3 (a) A complex mirage of the Alaska Range with Mt. McKinley on the far right, (b) less dense air 250 km away. In this photograph there image are no clouds. This mirage is a result of a temperature inversion: layers of cold air lie beneath layers of warmer air. more dense air (b) Light refracts toward denser air. A virtual eye object image is perceived. Light Rays, Reflection, and Refraction 347 When the Sun is very close to the horizon, the light from the lower part of the Sun is refracted more than the light from the upper part (Figure 4). This gives the impression that the Sun has a flattened bottom, making it appear oval rather than round. Try This Activity Mirages A mirage can be set up in a laboratory setting using solutions of dif- Figure 4 ferent densities and an empty fish tank. The shape of the Sun appears to change as it Materials: a fish tank, solutions with different densities, and a simple approaches the horizon. line drawing. • Pour the densest solution into the fish tank first. • To prevent mixing, pour the second solution slowly onto a board that is placed on the first solution. The second solution will float on top of the denser first solution. • At the end of the fish tank place a simple line drawing. Look at the drawing through the other end of the fish tank. Compare what you see through the fish tank with what you see at the same distance dispersion: the spreading of white light without the fish tank in place. into a spectrum of colours • Repeat the previous two steps by adding a third liquid, less dense than the other two. (a) If you see a mirage, is it an inferior or superior mirage? Explain. • Demonstrate the device to your class. Dispersion and Rainbows The ancient Egyptians were probably the first to discover that fragments of clear, colourless glass and precious stones spread, or disperse, the colours of the rainbow when placed in the path of a beam of white light. We now know that the index of refraction of a medium changes according to the colour of light that is entering the medium. These changes in the index of refraction are the source of dispersion. A rainbow is the Sun’s spectrum produced by water droplets in the atmos- Figure 5 phere (Figure 5). Light enters the spherical rain droplets, where it is refracted, This photograph shows a rainbow over the onetime home of Sir Isaac Newton. When dispersed, and reflected internally. The violet and red rays intersect internally, watching the dazzling colours of a rainbow, emerging with violet at the top, red at the bottom, and the other colours of the you likely make two basic observations. First, spectrum in between. If the rays that enter your eye are traced backward, you can rainbows consist of the same colours of the see an image called the primary rainbow (Figure 6). Other orders of rainbows, spectrum as produced by a prism, with red on which are much more difficult to observe than a primary rainbow, occur when the outside of the bow and blue and violet on the light is internally reflected more than once. For instance, a secondary the inside. Second, whenever you see a rainbow, which is located higher in the sky than the primary (Figure 5), occurs rainbow, the Sun is at your back. This is why after two internal reflections. you see rainbows in the western sky in the morning and in the eastern sky before sunset. A rainbow arc appears at certain points in the sky because droplets of water Both of these observations can be explained along that arc reflect the spectrum at just the right angle into the eye of the by the concepts of dispersion, refraction, and observer. The angle is approximately 42° to the horizontal sunlight. total internal reflection. primary rainbow: the rainbow of visible spectral colours that results from a single internal reflection in rain drops 348 Chapter 9 9.7 sunlight 42° water droplets 40° Figure 6 Formation of a primary rainbow. Looking at millions of drops, you see the spectrum in an arc of a semicircle with red on the outside and violet on the inside. Activity 9.7.1 Modelling Atmospheric Refraction There is a continuous decrease in the index of refraction of air as you move from the ground to the outermost layer of the atmosphere. Although the decrease in temperature increases the index of refraction, the decrease in pressure as you move up through the atmosphere has a greater effect on the index of refraction. This effect is simplified by representing the atmosphere by layers (Figure 7). Figure 7 1 The indexes of refraction of the layers of the atmosphere. (Layers not to scale.) 2 n = 1.0000 exosphere n = 1.000 024 thermosphere n = 1.000 026 mesosphere n = 1.000 028 stratosphere n = 1.000 03 tropopause and troposphere ground actual light observer from the Sun Procedure 1.