Chapter 18 Wave Properties of Light

2. Chapter 18 Wave Properties of Light 18.1 The Electromagnetic Spectrum 18.2 Interference, Diffraction, and Polarization 18.3 Special Relativity

3. Chapter 18 Objectives Calculate the frequency or wavelength of light when given one of the two. Describe the relationship between frequency, energy, color, and wavelength. Identify at least three different waves of the electromagnetic spectrum and an application of each. Interpret the interference pattern from a diffraction grating. Use the concept of polarization to explain what happens as light passes through two polarizers. Describe at least two implications of special relativity with regards to energy, time, mass, or distance.

4. Chapter 18 Vocabulary Terms • diffraction grating • electromagnetic • spectrum • electromagnetic wave • gamma ray • inference pattern • microwave • polarization • polarizer • radio wave • rest energy • special relativity • spectrometer • spectrum • time dilation • transmission axis • visible light • x-ray

5. Inv 18.1 The Electromagnetic Spectrum Investigation Key Question: What is the electromagnetic spectrum?

6. The energy field created by electricity and magnetism can oscillateand it supports waves that move. These waves are called electromagnetic waves. 18.1 The Electromagnetic Spectrum

7. Electromagnetic waves have both an electric part and a magnetic part and the two parts exchange energy back and forth. A 3-D view of an electromagnetic wave shows the electric and magnetic portions. 18.1 The Electromagnetic Spectrum • The wavelength and amplitude of the waves are labeled λ and A, respectively.

8. The higher the frequency of the light, the higher the energy of the wave. Since color is related to energy, there is also a direct relation between color, frequency, and wavelength. 18.1 The Electromagnetic Spectrum

9. The speed of light waves • The speed of light is incredibly fast (3 × 108 m/s) and is represented by its own symbol, c. • The index of refraction (n), is actually the ratio of the speed of light in a material to the speed of light in a vacuum. • The passage of light through matter takes more time because the light is absorbed and re-emitted to pass through neighboring atoms.

10. 18.1 Speed of Light Wavelength (m) c = f l Speed of light 3 x 108 m/sec Frequency (Hz)

11. Calculating wavelength Calculate the wavelength in air of blue-green light that has a frequency of 600 × 1012 Hz. • You are asked for wavelength. • You are given frequency. • Use speed of light, c =ƒl • Solve l= c ÷ƒ • l= (3 x 108 m/s) ÷ ( 600 x 1012 Hz) • l= 5 x 10 -7 m

12. 18.1 Waves of the electromagnetic spectrum Visible light is a small part of the energy range of electromagnetic waves. The whole range is called the electromagnetic spectrum and visible light is in the middle of it.

14. 18.1 Waves of the electromagnetic spectrum • Radio waves are on the low-frequency end of the spectrum. • Microwaves range in length from approximately 30 cm (about 12 inches) to about 1 mm. • The infraredregion (IR) of the electromagnetic spectrum lies between microwaves and visible light.

16. 18.1 Medium to high-energy waves • Ultraviolet radiation has a range of wavelengths from 400 down to about 10 nm. • X-rays are high-frequency waves that have great penetrating power and are used extensively in medical and manufacturing applications. • Gamma rays are generated in nuclear reactions.

17. Chapter 18 Wave Properties of Light 18.1 The Electromagnetic Spectrum 18.2 Interference, Diffraction, and Polarization 18.3 Special Relativity

18. Inv 18.2 Interference, Diffraction, and Polarization Investigation Key Question: What are some ways light behaves like a wave?

19. 18.2 Interference, Diffraction, and Polarization In 1807, Thomas Young (1773-1829) did the most convincing experiment demonstrating that light is a wave. A beam of light fell on a pair of parallel, very thin slits in a piece of metal. After passing through the slits, the light fell on a screen. A pattern of alternating bright and dark bands formed is called an interference pattern.

20. 18.2 Interference • An interference pattern is created by the addition of two waves.

21. 18.2 Diffraction gratings A diffraction grating is a precise array of tiny engraved lines, each of which allows light through. The spectrum produced is a mixture of many different wavelengths of light.

22. 18.2 How a Diffraction Grating Works When you look at a diffracted light you see: the light straight ahead as if the grating were transparent. a "central bright spot". the interference of all other light waves from many different grooves produces a scattered pattern called a spectrum.

23. 18.2 Spectrometer A spectrometer is a device that measures the wavelength of light. A diffraction grating can be used to make a spectrometer because the wavelength of the light at the first-order bright spot can be expressed in a mathematical relationship.

24. 18.2 Grating Formula Distance between grating lines (m) Wavelength of light (nm) l = d sinq Angle 

25. 18.2 Polarization Polarization is another wave property of light. The fact that light shows polarization tells us that light is a transverse wave.

26. 18.2 Polarization The direction of polarization is a vector and can be resolved into components in two directions. A wave that has 45-degree polarization is the addition of two smaller-amplitude component waves with horizontal and vertical polarizations.

27. 18.2 Polarization A wave with polarization at 45 degrees can be represented as the sum of two waves. Each of the component waves has smaller amplitude.

28. 18.2 Polarization A polarizer is a material that selectively absorbs light depending on polarization. A polarizer re-emits a fraction of incident light polarized at an angle to the transmission axis.

30. 18.2 Applications of polarization Polarizing sunglasses are used to reduce the glare of reflected light The LCD (liquid crystal diode) screen on a laptop computer uses polarized light to make pictures.

31. Chapter 18 Wave Properties of Light 18.1 The Electromagnetic Spectrum 18.2 Interference, Diffraction, and Polarization 18.3 Special Relativity

32. Inv 18.3 Special Relativity Investigation Key Question: What are some of the implications of special relativity?

33. 18.3 Special Relativity The theory of special relativity describes what happens to matter, energy, time, and space at speeds close to the speed of light.

34. 18.3 Special Relativity These effects are observed in physics labs: Time moves more slowly for an object in motion than it does for objects that are not in motion. This is called time dilation. As objects move faster, their mass increases. The definition of the word “simultaneous” changes. Space itself gets smaller for an observer moving near the speed of light.

35. 18.3 Speed of light paradox The theory of special relativity comes from thinking about light. A ball thrown from a moving train approaches you at the speed of the ball relative to the train plus the speed of the train relative to you. The speed of light appears the same to all observers independent of their relative motion.

36. 18.3 Speed of light paradox If the person on the train were to shine a flashlight toward you, you would expect the light to approach you faster. The light should come toward you at 3 × 108 m/sec plus the speed of the train. Michelson and Morley found experimentally that the light comes toward you at a speed of 3 × 108 m/sec no matter how fast the train approaches you!

37. 18.3 Consequences of time dilation In the early 1970s an experiment was performed by synchronizing two precise atomic clocks. One was put on a plane and flown around the world, the other was left on the ground. When the flying clock returned home, the clocks were compared. The clock on the plane measured less time than the clock on the ground. The difference agreed precisely with special relativity.

38. 18.3 Einstein's formula This equation tells us that matter and energy are really two forms of the same thing. E = mc2 Speed of light 3.0 x108 m/sec Energy (J) Mass (kg)

39. 18.3 The equivalence of energy and mass If a particle of matter is as rest, it has a total amount of energy equal to its rest energy. If work is done to a particle by applying force, the energy of the particle increases. At speeds that are far from the speed of light, all the work done increases the kinetic energy of the particle. It would take an infinite amount of work to accelerate a particle to the speed of light, because at the speed of light the mass of a particle also becomes infinite.

40. 18.3 The equivalence of energy and mass Einstein’s was able to deduce the equivalent of mass and energy by thinking about the momentum of two particles moving near the speed of light. Since the speed of light must be the same for all observers regardless of their relative motion and energy and momentum must be conserved, as the speed of an object gets near the speed of light, the increase in mass must come from energy.

41. Calculating equivalence A nuclear reactor converts 0.7% of the mass of uranium to energy. If the reactor used 100 kg of uranium in a year, how much energy is released? One gallon of gasoline releases 1.3 × 108 joules. How many gallons of gasoline does it take to release the same energy as the uranium? • You are asked for energy and no. of gallons. • You are given mass of uranium, % converted to energy, rate • Use Einstein’s formula: E = mc2 • Solve for mass converted to energy: m = (.007) ( 100 kg)= 0.7 kg • Solve for energy released: E = (0.7 kg)( 3 x 108 m/s)2 • E = 6.3 x 1016 J • Calculate equivalent using rate: 6.3 x 1016 J ÷ 1.3 x 108 J/gal = 4.8 108 J • 1 kg of U releases same energy as 480 million gallons of gas.

42. 18.3 Simultaneity When we say that two events are simultaneous, we mean they happen at the same time. Since time is not constant for all observers, whether two events are simultaneous depends on the relative motion of the observers.

43. 18.3 Simultaneity The two lightning strikes are simultaneous to the observer at rest, but the observer moving with the train sees the lightning strike the front of the train first.

44. Holography • A well-made hologram appears to have depth and perspective as if the actual three-dimensional scene was embedded in the picture. • A true 3D scene looks different when seen from different angles. • A hologram duplicates the three-dimensional shape of the wave front that is coming from the real object.