Conceptual Physics

1. Conceptual Physics Chapter Twenty Seven Notes: LIGHT .

2. Introduction To understand light you have to know that what we call light is what is visible to us. Visible light is the light that humans can see. Other animals can see different types of light. Dogs can see only shades of gray and some insects can see light from the ultraviolet part of the spectrum. The key thing to remember is that our light is what scientists call visible light. Scientists also call light electromagnetic radiation. Visible light is only one small portion of a family of waves called electromagnetic (EM) radiation. The entire spectrum of these EM waves includes radio waves, which have very long wavelengths and both gamma rays and cosmic rays, which are at the other end of the spectrum and have very small wavelengths. Visible light is near the middle of the spectrum. The key thing to remember is that light and EM radiation carry energy. The quantum theory suggests that light consists of very small bundles of energy/particles; it's just that simple. Scientists call those small particles photons, and the wavelength determines the energy.

3. 27.1 Early Concepts of Light • For as long as the human imagination has sought to make meaning of the world, we have recognized light as essential to our existence. Whether to a prehistoric child warming herself by the light of a fire in a cave, or to a modern child afraid to go to sleep without the lights on, light has always given comfort and reassurance. • The earliest documented theories of light came from the ancient Greeks. Aristotle believed that light was some kind of disturbance in the air, one of his four "elements" that composed matter. Centuries later, Lucretius, who, like Democritus before him, believed that matter consisted of indivisible "atoms," thought that light must be a particle given off by the sun. In the tenth century A.D., the Persian mathematician Alhazen developed a theory that all objects radiate their own light. Alhazen’s theory was contrary to earlier theories proposing that we could see because our eyes emitted light to illuminate the objects around us. • In the seventeenth century, two distinct models emerged from France to explain the phenomenon of light. The French philosopher and mathematician Rene Descartes believed that an invisible substance,

4. which he called the plenum, permeated the universe. Much like Aristotle, he believed that light was a disturbance that traveled through the plenum, like a wave that travels through water. Pierre Gassendi, a contemporary of Descartes, challenged this theory, asserting that light was made up of discrete particles. Particles versus Waves • While this controversy developed between rival French philosophers, two of the leading English scientists of the seventeenth century took up the particles-versus-waves battle. Isaac Newton, after seriously considering both models, ultimately decided that light was made up of particles (though he called them corpuscles). Robert Hooke, already a rival of Newton’s and the scientist who would identify and name the cell in 1655, was a proponent of the wave theory. Unlike many before them, these two scientists based their theories on observations of light’s behaviors: reflection and refraction. Reflection, as from a mirror, was a well-known occurrence, but refraction, the now familiar phenomenon by which an object partially submerged in water appears to be “broken,” was not well understood at the time.

5. Proponents of the particle theory of light pointed to reflection as evidence that light consists of individual particles that bounce off of objects, much like billiard balls. Newton believed that refraction could be explained by his laws of motion, with particles of light as the objects in motion. As light particles approached the boundary between two materials of different densities, such as air and water, the increased gravitational force of the denser material would cause the particles to change direction, Newton believed (see our Density module). • Newton’s particle theory was also based partly on his observations of how the wave phenomenon diffraction related to sound. He understood that sound traveled through the air in waves, meaning sound could travel around corners and obstacles, thus a person in another room can be heard through a doorway. Since light was unable to bend around corners or obstacles, Newton believed that light could not diffract. He therefore supposed light was not a wave. • Hooke and others – most notably the Dutch scientist Christian Huygens – believed that refraction occurred because light waves slowed down as they entered a denser medium such as water and changed their direction as a result. These wave theorists believed, like Descartes, that light must travel through some material that permeates space. Huygens dubbed this medium the aether.

6. Speed of Light • The early Greek philosophers generally followed Aristotle's belief that the speed of light was infinite. 2 As late as 1600 A.D., Johannes Kepler, one of the fathers of modern astronomy, maintained the majority view that light was instantaneous in its travels. Rene Descartes, the highly influential scientist, mathematician and philosopher (who died in 1650), also strongly held to the belief in the instantaneous propagation of light. He strongly influenced the scientists of that period and those who followed. • In 1677 Olaf Roemer, the Danish astronomer, noted that the time elapsed between eclipses of Jupiter with its moons became shorter as the Earth moved closer to Jupiter and became longer as the Earth and Jupiter drew farther apart. This anomalous behavior could be accounted for by a finite speed of light. • Initially, Roemer's suggestion was hooted at. It took another half century for the notion to be accepted. In 1729 the British astronomer James Bradley's independent confirmation of Roemer's measurements finally ended the opposition to a finite value for the speed of light. Roemer's work, which had split the scientific community for 53 years, was finally vindicated.

7. 27.2 The Speed of Light • Over the past 300 years, the velocity of light has been measured 163 times by 16 different methods. (As a Naval Academy graduate, I must point out that Albert Michelson, Class of 1873, measured the speed of light at the Academy. In 1881 he measured it as 299,853 km/sec. In 1907 he was the first American to receive the Nobel Prize in the sciences. In 1923 he measured it as 299,798 km/sec. In 1933, at Irvine, CA, as 299,774 km/sec.) • The first quantitative estimate of the speed of light was made in 1676 by Ole Christensen Rømer, who was studying the motions of Jupiter's moon, Io, with a telescope. It is possible to time the orbital revolution of Io because it enters and exits Jupiter's shadow at regular intervals (at C or D). Rømer observed that Io revolved around Jupiter once every 42.5 hours when Earth was closest to Jupiter (at H). He also observed that, as Earth and Jupiter moved apart (as from L to K), Io's exit from the shadow would begin progressively later than predicted. It was clear that these exit "signals" took longer to reach Earth, as Earth and Jupiter moved further apart. This was as a

8. result of the extra time it took for light to cross the extra distance between the planets, time which had accumulated in the interval between one signal and the next. The opposite is the case when they are approaching (as from F to G). On the basis of his observations, Rømer estimated that it would take light 22 minutes to cross the diameter of the orbit of the Earth (that is, twice the astronomical unit); the modern estimate is about 16 minutes and 40 seconds. • Around the same time, the astronomical unit was estimated to be about 140 million kilometres. The astronomical unit and Rømer's time estimate were combined by Christiaan Huygens, who estimated the speed of light to be 1,000 Earth diameters per minute. This is about 220,000 kilometres per second (136,000 miles per second), 26% lower than the currently accepted value, but still very much faster than any physical phenomenon then known. Rømer's observations of the occultations of Io from Earth.

9. In 1926, Michelson used a rotating prism to measure the time it took light to make a round trip from Mount Wilson to Mount San Antonio in California, a distance of about 22 miles (36 km). The precise measurements yielded a speed of 186,285 miles per second (299,796 kilometres per second). Michelson’s Method for Measuring the Speed of Light The diagram below is not to scale. Light from the source passes through a narrow slit. It is reflected by face A of the octagonal metal prism. It then travels a distance, s, (a few kilometres) and returns to be reflected by face B. The prism now rotates. If it rotates fast enough, when light returns to the prism, face B is no longer in the right position to reflect it into the observer’s

10. eye. The image of the slit disappears. • The speed of rotation is increased. At a certain speed of rotation, the image of the slit reappears. This is because the time taken for light to go from face A to face B was the same as the time taken by the prism to rotate 1/8th of a revolution. • If the prism completes n rotations per second then the time for one revolution is 1/n. • Therefore, the time taken for the light to cover the distance, s is given by • So, the speed of light, c is given by In 1931, Michelson found c = 2·99774×108ms-1. The modern value is c = 2·997925×108ms-1 c = 8ns

11. 27.3 Electromagnetic Waves • Electromagnetic waves exist with an enormous range of frequencies. This continuous range of frequencies is known as the electromagnetic spectrum. The entire range of the spectrum is often broken into specific regions. The subdividing of the entire spectrum into smaller spectra is done mostly on the basis of how each region of electromagnetic waves interacts with matter. The diagram below depicts the electromagnetic spectrum and its various regions. The longer wavelength, lower frequency regions are located on the far left of the spectrum and the shorter wavelength, higher frequency regions are on the far right. Two very narrow regions within the spectrum are the visible light region and the X-ray region. You are undoubtedly familiar with some of the other regions of the electromagnetic spectrum. • ROYGBIV

12. 27.4 Light and Transparent Materials • Transparent:  material transmitting light without distorting directions of waves. • Translucent: material transmitting light without but distorting its path. • Opaque:  material that does not transmit light. • These are the three terms that refer to a materials ability to transmit light through the material and to what degree. We will cover the third one in the next section. • Light passes through materials whose atoms absorb the energy and immediately reemit it as light. • Materials that transmit light are transparent. Glass and water are transparent. Visualize the electrons in an atom as connected by imaginary springs, as shown in Figure 27.6 in your books. When light hits the electrons, they vibrate. • Electrons in glass have a natural vibrational frequency in the ultraviolet range. The vibration in glass becomes so large that the energy is given up in the form of heat, and the ultraviolet light is blocked!

14. 27.5 Opaque Materials • Materials such as paper, paint, and biological tissue are opaque because the light that passes through them is scattered in complicated and seemingly random ways. A new experiment conducted by researchers at the City of Paris Industrial Physics and Chemistry Higher Educational Institution (ESPCI) has shown that it's possible to focus light through opaque materials and detect objects hidden behind them, provided you know enough about the material. The experiment is reported in the current issue of Physical Review Letters, and is the subject of Viewpoint in APS Physics (physics.aps.org) by Elbert van Putten and Allard Moskof the University of Twente. Knowing enough about the way light is scattered through materials would allow physicists to see through opaque substances, such as the sugar cube on the right. In addition, physicists could use information characterizing an opaque material to put it to work as a high quality optical component, comparable to the glass lens show on the left. - American Physical Society

15. 27.6 Shadows Shadows • A shadow is formed where light is 'missing'. A dark shadow (umbra) is formed where no light falls and a light shadow (penumbra) is formed where some light falls, but some is blocked. • If the light source is very tiny and concentrated in one place (a point source) only a sharp shadow is formed.

16. If the source is broader light from the top of the source causes a lower shadow than that from the top. You therefore get partial shadow or penumbra as well as umbra. • If we use coloured lights at different points we can see the effect of these multiple shadows:

17. The size of a shadow changes as you move the source closer or further from the screen • These terms are used to express ideas in astronomy So, why are some shadows lighter than others?

18. How dark a shadow is depends on the lighting conditions that create it. If there is only once point source of light, then when it is blocked, no light will reach the shadowed area and the shadow will be dark. If there is a lot of reflection, diffuse light, or multiple light sources, however, the shadow will be lighter. Shadows Outside • On a sunny day, most of the light is coming directly from the sun, but some of it is coming as blue scattered light coming from the sky. This hits you at all angles as it comes from all directions. Therefore, if you stand in front of the sun, the sun's light is blocked, but your shadow still receives light from the rest of the sky, and you can still see the shadowed ground. On a cloudy day, the light is completely diffuse, not coming from anywhere in particular, and you don't cast much of a shadow at all.

19. 27.7 Polarization Polarization • A light wave is an electromagnetic wave which travels through the vacuum of outer space. Light waves are produced by vibrating electric charges. The nature of such electromagnetic waves is beyond the scope of The Physics Classroom Tutorial. For our purposes, it is sufficient to merely say that an electromagnetic wave is a transverse wave which has both an electric and a magnetic component. • The transverse nature of an electromagnetic wave is quite different from any other type of wave which has been discussed in The Physics Classroom Tutorial. Let's suppose that we use the customary slinky to model the behavior of an electromagnetic wave. As an electromagnetic wave traveled towards you, then you would observe the vibrations of the slinky occurring in more than one plane of vibration. This is quite different than what you might notice if you were to look along a slinky and observe a slinky wave traveling towards you. Indeed, the coils of the slinky would be

20. vibrating back and forth as the slinky approached; yet these vibrations would occur in a single plane of space. That is, the coils of the slinky might vibrate up and down or left and right. Yet regardless of their direction of vibration, they would be moving along the same linear direction as you sighted along the slinky. If a slinky wave were an electromagnetic wave, then the vibrations of the slinky would occur in multiple planes. Unlike a usual slinky wave, the electric and magnetic vibrations of an electromagnetic wave occur in numerous planes. A light wave which is vibrating in more than one plane is referred to as unpolarized light. Light emitted by the sun, by a lamp in the classroom, or by a candle flame is unpolarized light. Such light waves are created by electric charges which vibrate in a variety of directions, thus creating an electromagnetic wave which vibrates in a variety of directions. This concept of unpolarized light is rather difficult to visualize. In general, it is helpful to picture unpolarized light as a wave which has an average of half its vibrations in a horizontal plane and half of its vibrations in a vertical plane.

21. Polarization by Use of a Polaroid Filter • The most common method of polarization involves the use of a Polaroid filter. Polaroid filters are made of a special material which is capable of blocking one of the two planes of vibration of an electromagnetic wave. (Remember, the notion of two planes or directions of vibration is merely a simplification which helps us to visualize the wavelike nature of the electromagnetic wave.) In this sense, a Polaroid serves as a device which filters out one-half of the vibrations upon transmission of the light through the filter. When unpolarized light is transmitted through a Polaroid filter, it emerges with one-half the intensity and with vibrations in a single plane; it emerges as polarized light. • Polarization of light by use of a Polaroid filter was is often demonstrated in a Physics class through a variety of demonstrations. Filters are used to look through an view objects. The filter does not distort the shape or dimensions of the object; it merely serves to

22. produce a dimmer image of the object since one-half of the light is blocked as it passed through the filter. A pair of filters are often placed back to back in order to view objects looking through two filters. By slowly rotating the second filter, an orientation can be found in which all the light from an object is blocked and the object can no longer be seen when viewed through two filters. What happened? In this demonstration, the light was polarized upon passage through the first filter; perhaps only vertical vibrations were able to pass through. These vertical vibrations were then blocked by the second filter since its polarization filter is aligned in a horizontal direction. While you are unable to see the axes on the filter, you will know when the axes are aligned perpendicular to each other because with this orientation, all light is blocked. So by use of two filters, one can completely block all of the light which is incident upon the set; this will only occur if the polarization axes are rotated such that they are perpendicular to each other.

23. A picket-fence analogy is often used to explain how this dual-filter demonstration works. A picket fence can act as a polarizer by transforming an unpolarized wave in a rope into a wave which vibrates in a single plane. The spaces between the pickets of the fence will allow vibrations which are parallel to the spacings to pass through while blocking any vibrations which are perpendicular to the spacings. Obviously, a vertical vibration would not have the room to make it through a horizontal spacing. If two picket fences are oriented such that the pickets are both aligned vertically, then vertical vibrations will pass through both fences. On the other hand, if the pickets of the second fence are aligned horizontally, then the vertical vibrations which pass through the first fence will be blocked by the second fence. This is depicted in the diagram to the right. In the same manner, two Polaroid filters oriented with their polarization axes perpendicular to each other will block all the light. Now that's a pretty cool observation which could never be explained by a particle view of light.

24. Polarization by Reflection • Unpolarized light can also undergo polarization by reflection off of nonmetallic surfaces. The extent to which polarization occurs is dependent upon the angle at which the light approaches the surface and upon the material which the surface is made of. Metallic surfaces reflect light with a variety of vibrational directions; such reflected light is unpolarized. However, nonmetallic surfaces such as asphalt roadways, snow fields and water reflect light such that there is a large concentration of vibrations in a plane parallel to the reflecting surface. A person viewing objects by means of light reflected off of nonmetallic surfaces will often perceive a glare if the extent of polarization is large. Fisherman are familiar with this glare since it prevents them from seeing fish which lie below the water. Light reflected off a lake is partially polarized in a direction parallel to the water's surface. Fisherman know that the use of glare-reducing sunglasses with the proper polarization axis allows for the blocking of this partially polarized light. By blocking the plane-polarized light, the glare is reduced and the fisherman can more easily see fish located under the water.

25. 27.8 Polarized Light and 3-D Viewing Applications of Polarization • Polarization has a wealth of other applications besides their use in glare-reducing sunglasses. In industry, Polaroid filters are used to perform stress analysis tests on transparent plastics. As light passes through a plastic, each color of visible light is polarized with its own orientation. If such a plastic is placed between two polarizing plates, a colorful pattern is revealed. As the top plate is turned, the color pattern changes as new colors become blocked and the formerly blocked colors are transmitted. A common Physics demonstration involves placing a plastic protractor between two Polaroid plates and placing them on top of an overhead projector. It is known that structural stress in plastic is signified at locations where there is a large concentration of colored bands. This location of stress is usually the location where structural failure will most likely occur. Perhaps you wish that a more careful stress analysis was performed on the plastic case of the CD which you recently purchased.

26. Polarization is also used in the entertainment industry to produce and show 3-D movies. Three-dimensional movies are actually two movies being shown at the same time through two projectors. The two movies are filmed from two slightly different camera locations. Each individual movie is then projected from different sides of the audience onto a metal screen. The movies are projected through a polarizing filter. The polarizing filter used for the projector on the left may have its polarization axis aligned horizontally while the polarizing filter used for the projector on the right would have its polarization axis aligned vertically. Consequently, there are two slightly different movies being projected onto a screen. Each movie is cast by light which is polarized with an orientation perpendicular to the other movie. The audience then wears glasses which have two Polaroid filters. Each filter has a different polarization axis - one is horizontal and the other is vertical. The result of this arrangement of projectors and filters is that the left eye sees the movie which is projected from the right projector while the right eye sees the movie which is projected from the left projector. This gives the viewer a perception of depth.

27. How do 3D movies use polaroid filters?

28. A different approach: • Use color filters to make the left and right eyes perceiving slightly different images • http://www.3dmovies.com/