Download 8.3 -‐ Critical Angle, Total Internal Reflection and Electromagnetic

8.3 -­‐ Critical Angle, Total Internal Reflection and Electromagnetic Radiation Critical angle and total internal reflection When light is incident upon the boundary between two media, reflection, transmission and absorption may occur. Light travelling from water into air • As the angle of incidence is increased, the angle of refraction also increases. • This continues until the angle of refraction will be almost 90 and the transmitted ray travels just along the surface of the water • This incident angle is called the critical angle, ic, • The critical angle can be found for any boundary between two media by using Snell’s law. If the incident angle is equal to the critical angle, i.e. i= ic , then r= 90. Then Snell’s law becomes 𝑠𝑖𝑛 𝑖! 𝑛!
= 𝑠𝑖𝑛90 𝑛!
sin 𝑖! =
𝑛!
𝑛!
The critical angle for light travelling from water into air is approximately 49o. If the incident angle is greater than 49o total internal reflection occurs. Worked example 8.3A An underwater light shines upwards from the centre of a swimming pool that is 1.50 m deep. Determine the radius of the circle of light that is seen from above. (nair 1.00, nwater 1.33) Total internal reflection is used in many optical instruments, including cameras, periscopes and binoculars. When light reflects from a mirror there is always some loss in the intensity of the incident light, and reflection can occur from both the front and rear surfaces of the mirror, causing problems. By contrast, almost no loss of intensity occurs with total internal reflection. Since the refractive index for glass is about 1.5, the critical angle for light travelling from glass to air is approximately 42, and a glass prism with internal angles of 45 can be used as a mirror in the applications discussed above. 1 Electromagnetic waves 1860s investigations being carried out on different forms of electromagnetic radiation led to the finding that visible light itself is just one of the many forms of electromagnetic radiation (EMR) Electricity and magnetism were once considered to be separate subjects. However, moving charges create magnetic fields. Similarly a changing magnetic field can be used to create electricity. In 1864 James Clerk Maxwell used mathematical equations to describe how charges moving periodically in a conductor would set up alternating electric fields and magnetic fields in the nearby region. Maxwell knew that the magnetic and electric fields travelled through space. He calculated their speed and found it to be 300 000 km s-­‐1, exactly the same as the speed of light! Also, he devised mathematical expressions to describe the magnetic and electric fields. The solution to these expressions was found to be the equation of a wave. Maxwell had shown that light is an electromagnetic wave. Today we know that the electromagnetic spectrum includes a wide range of frequencies (or wavelengths). All electromagnetic waves are created by accelerating charges which result in a rapidly changing magnetic field and electric field travelling out from the source at the speed of light, as shown in Figure 8.35. The many forms of EMR are essentially the same, differing only in their frequency and, therefore, their wavelength. The electromagnetic spectrum is roughly divided into seven categories depending on how the radiation is produced and the frequency. The energy carried by the electromagnetic radiation is proportional to the frequency. High-­‐frequency short-­‐wavelength gamma rays are at the high-­‐energy end of the spectrum. Low-­‐frequency long-­‐wavelength radio waves carry the least energy. Humans have cells in their eyes which can respond to EMR of frequencies between approximately 400 THz and 800 THz; these frequencies make up the visible light section of the electromagnetic spectrum. 2 3 Coloured light, different wavelengths Our eyes are responsive to many different colours of light from the deepest red through to the brightest violet, the visible spectrum (Figure 8.37). Each variation in colour or shade is caused by light of a different wavelength. Traditionally the colours quoted as making up the visible spectrum are red, orange, yellow, green, blue and violet. However, as shown in Figure 8.37, the actual allocation of separate names for the colours is difficult since they merge into one another. The wavelengths associated with visible light are very small: they range from approximately 390 nm (or 390x10-­‐9 m) for violet light to around 780 nm for red light. Colour addition or mixing light sources Red, green and blue (RGB) are called the primary colours of light. None of the primary colours can be produced by a combination of the other primary colours. Figure 8.39 shows the three primary colours of light overlapping to produce other colours. The particular colours formed by the overlapping of pairs of primary colours are called cyan, magenta and yellow. Any group of colours which combine to form white light are called complementary colours. All three primary colours when combined form white light. Combining any two primary colours forms the complementary colour of the remaining primary colour. So, for example, when red and green are combined they form the complement of blue, which is yellow. Yellow is the complement of blue. Cyan is the complement of red, and magenta is the complement of green. 4 8.4 Dispersion and Polarisation of light waves •
White light is made up of many different frequencies (colours) of light. •
For some materials the speed at which light is transmitted is actually slightly different for different frequencies (colours) of light. •
This means that on refraction different colours of light will take slightly different paths. This results in the spreading out of the white light into its component colours. •
This is called the dispersion of white light. As light enters a prism, it refracts due to a change in speed. Why does light slow down when it enters a more optically dense medium? The light energy is being momentarily absorbed and then re-­‐radiated by the atoms that make up the medium. Different colours of light interact differently with these atoms. As a result they travel at different speeds within the medium and so are refracted through different angles. Of the colours in the visible spectrum: •
Violet light is slowed down the most and so is refracted through the greatest angle. •
Red light is slowed least and so is refracted the least. Polarisation Further evidence for the wave nature of light is the finding that light can be polarised. Techniques for polarising light The most familiar way in which unpolarised (non-­‐
aligned) light can be converted to polarised (aligned) light is by using polarising filters. 5 The fact that light can be polarised provides strong evidence that light is actually a transverse wave since longitudinal waves cannot be polarised. How Polaroid sunglasses work When outdoors on a bright, sunny day, the smooth, highly reflective, horizontal surfaces around you are a significant contributor to the amount of light entering your eyes. Bring to mind the glare that can occur from the surface of water or snow. Fortunately light that is reflected from smooth, horizontal surfaces tends to be polarised (aligned) in a horizontal direction. An appropriately orientated polarising filter can be used. Lenses in a pair of Polaroid sunglasses are polarising filters orientated to block the horizontal wave components, allowing only vertical components through. Hence the intensity of light—that is, the glare—is markedly reduced. 6