Lecture 17 - Light and Optics (2/21/96)

Seeds: Chapter 5

1. More on the Nature of Light
   • The electric and magnetic forces from an electromagnetic wave, such as visible light or radio waves, can be measured.
   • A radio wave, with a wavelength of 1 meter for example, can cause electrons in a wire of about that same length to move back and forth due to the oscillating electric force in the wave. These moving electrons are measureable as an electric current in the wire - this is how a radio or TV antenna works to receive signals!
   • The electrons in the metal of the antenna (which is basically just a long wire) are free to move a little in response to the radio wave electric field. The current alternates like a sine wave.
   • The reverse is also true! If you oscillate the current like a sine wave in a long wire, an electromagnetic wave of the same frequency is generated. This is how radio and TV transmitters work.
   • The 19th century scientist who played an analogous role for electricity and magnetism to what Isaac Newton did for gravity was the Scottish physicist James Clerk Maxwell (1831-1879). His four equations described the electic and magnetic forces just like Newton's equation described the gravitational force.
   • In fact, they are very similar. The electric force between two point charges is proportional to the product of the charges times the inverse square of the distances - just take Newton's gravitational force equation and replace the masses with charges, and change the constant! Note that because electric charge can be both positive and negative, the force can both attract and repel (like charges repel, opposites attract).
   • Maxwell found that there was a special solution to his 4 equations that corresponded to an oscillating electric and magnetic field which moves through space at the speed of light. He realised that this was exactly the description of light waves that was needed! In one fell swoop, he unified electromagnetism and light!
2. The Nature of Forces
   • Once again, I will diverge from our discussion of astronomy to talk a little of the nature of modern physics and our view of the universe.
   • You have seen and heard me use the term field, as in electric field, magnetic field, gravitational field, or just plain force field. Technically speaking, a field is any quantity that has a specific value at any point in space.
   • If we place a mass such as the Sun somewhere in space, then take a second mass such as the Earth and move it about, I would measure a force on the Earth that depended on the distance from the Sun to the point in space that I happened to place the Earth. Thus, we can think of a gravitational field generated by the Sun's mass such that at every point in space one would compute the correct gravitational force on a mass at that position.
   • The same thing can be said for an electric charge - it would generate an electric field at each point in space whose size was proportional to the charge times the inverse square of the distance from the charge.
   • If I can measure a force from a mass at every point in space, and represent it as a gravitational or electric or magnetic field, what does that really mean? How do forces get transmitted through space from one mass or charge to another? If I change the mass of the Sun, for example, does the force on the Earth instantly change?
   • We belive that the fundamental forces of nature are transmitted from one place to another through the intermediation of special particles which travel at the speed of light.
   • If you think about Maxwell's discovery for a bit, which says that light waves are just electromagnetic waves, it seems logical that electric and magnetic forces are transmitted by photons of light! Basically, this is true, though of course it is more complicated than just photons travelling between electric charges. It is beyond the scope of this course to explain this in more detail.
   • There are four fundamental forces in physics, each with their intermediary particle:
     1. Electromagnetic Force - photon (electric and magnetic forces on charged particles such as electrons and protons)
     2. Gravitational Force - graviton (gravitational force between masses, this particle is as yet undiscovered)
     3. Strong Nuclear Force - gluon ("glues" together the quarks that make up protons and neutrons, and hold the nucleus together)
     4. Weak Nuclear Force - W, Z particles (causes some kinds of radioactive decays, and governs creation of particles called neutrinos)
   • All the particles and forces make up our theory of physics called the "standard model". This is our paradigm for the way the universe works.
   • It is a very complicated theory now, with four forces and 12 (or more) elementary particles. Many physicists are searching for a simpler and more elegant theory, as it seems that the standard model looks like a theory with too many "epicycles", just like the incorrect Ptolemaic model.
3. Elementary Optics
   • We will use the term "ray" to represent the "path" of a light wave or photon as it moves through space. It is not really the path of a photon, since a single photon is also a wave that fills space, but in some senses it is. It is also a line connecting the light source to the point in question that is always perpendicular to the wavefront of the light. This seems confusing, but it is a useful conceptual tool as we will see.
   • There are three processes in elementary optics: reflection, refraction, and dispersion.
   • Reflection is just light bouncing off a shiny surface like a mirror or glass. Stand in front of a mirror and move around and look at different angles to it, and you will discover the law of reflection: the angle that an incident light ray makes to the normal of the reflecting surface is just the same as the angle the reflected ray makes, and in the same plane.
   • The normal is just a line perpendicular to the surface at the point where the ray intersects the mirror.
   • Summary: a light ray bounces off a mirror at the same angle that it hits it, staying in the same plane.
   • Refraction is what happens when light rays move from one transparent material to another. It is a bending of light.
   • A transparent material, like air, water, or glass, has an index of refraction, which is the ratio of the speed of light in a vacuum (3 x 10^8 m/s) to the speed of light in the material, which is less. (Note: a vacuum is the absence of all matter, or at least nearly all matter, like in outer space.)
   • Clarification: the speed of light in a vacuum is the constant c = 2.998 x 10^8 m/s. It is actually true that the electromagnetic waves of light move at slower speeds in the presence of matter. In general, the denser the material, the slower the speed.
   • The index of refraction is usually denoted by the symbol n. The index of refraction in a vacuum, like space, is of course n = 1. In some common materials: air (n = 1.0003), water (n = 1.3), glass (n = 1.5), and diamond (n = 2.4). When you look at a diamond, you should realise that light moves less than half its normal speed when passing through it!
   • The law of refraction states that the angle that the ray in the material with the higher index of refraction makes to the normal at the interface is less than the angle to the normal in the material with the lower index of refraction.
   • Thus, a ray is bent toward the normal when it passes from air into glass, for instance, but then is bent farther from the normal when it passes from glass into air.
   • Note that if you take a slab of glass with parallel faces, the refraction from air into glass is undone exactly by the refraction from glass into air! That is why smooth window panes give no distortion while wavy glass would give a really bent and distorted view of the outside.
   • Also note that if we take a wedge of glass, where the faces are not parallel, then the refractions at the interfaces do not cancel, and we can see the bending of the rays.
   • A lens is just a piece of refractive material, like glass, that is shaped so that parallel rays in from one side are bent in such a way that they cross at a focus on the other side. It turns out that two spherically curved surfaces can make such a lens. This is how a magnifying glass lens works.
   • However, it turns out that the amount of the bending in a refractive material usually depends upon the wavelength of the light. The exact value of the index of refraction in a material such as glass and water depends upon the wavelength of the light, such that that shorter wavelengths see a higher index, and are bent more.
   • This effect is called dispersion, since when passing through a refractive interface between media the blue and red light rays are bent differently and spread out in a "dispersed" fan on the other side. This is why a wedge of glass makes a prism that will spread out the different colors of light. This is also the effect that makes colorful rainbows when sunlight is refracted through many tiny droplets of water in rain!
   • A dispersive optical element like a prism spreads light into its composite colors, or spectrum (think of the "electromagnetic spectrum"). A spectroscope is the technical name for such a device.
   • Note that a curved mirror can also focus rays of light through reflection - like a shaving mirror. Next time we will see how to use lenses and mirrors to make useful telescopes.

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