Chapter 21 / 22

1. Chapter 21 / 22 Electromagnetic Waves / Reflection and Refraction

2. Electromagnetic Waves Ch 21, Secs 8–12

3. James Clerk Maxwell • 1831 – 1879 • Electricity and magnetism were originally thought to be unrelated • In 1865, James Clerk Maxwell provided a mathematical theory that showed a close relationship between all electric and magnetic phenomena • Electromagnetic theory of light

4. Maxwell’s Starting Points • Electric field lines originate on positive charges and terminate on negative charges • Magnetic field lines always form closed loops – they do not begin or end anywhere

5. Maxwell’s Starting Points • A varying magnetic field induces an emf and hence an electric field (Faraday’s Law) • Magnetic fields are generated by moving charges or currents (Ampère’s Law)

6. Maxwell’s Hypothesis • Turning Faraday’s Law upside down, Maxwell hypothesized that a changing electric field would produce a magnetic field (Maxwell-Ampère’s Law)

7. Maxwell’s Predictions • Maxwell concluded that visible light and all other electromagnetic (EM) waves consist of fluctuating electric and magnetic fields, with each varying field inducing the other • Accelerating charges generate these time varying E and B fields • Maxwell calculated the speed at which these electromagnetic waves travel in a vacuum – speed of light c = 3.00 x 108 m/s

8. Hertz’s Confirmation of Maxwell’s Predictions • 1857 – 1894 • First to generate and detect electromagnetic waves in a laboratory setting • Showed radio waves could be reflected, refracted and diffracted • The unit Hz is named for him

9. Hertz’s Experimental Apparatus • An induction coil is connected to two large spheres forming a capacitor • Oscillations are initiated by short voltage pulses • The oscillating current (accelerating charges) generates EM waves

10. Hertz’s Experiment • Several meters away from the transmitter is the receiver • This consisted of a single loop of wire connected to two spheres • When the oscillation frequency of the transmitter and receiver matched, energy transfer occurred between them

11. Hertz’s Conclusions • Hertz hypothesized the energy transfer was in the form of waves • These are now known to be electromagnetic waves • Hertz confirmed Maxwell’s theory by showing the waves existed and had all the properties of light waves (e.g., reflection, refraction, diffraction) • They had different frequencies and wavelengths which obeyed the relationship v = f λ for waves • v was very close to 3 x 108 m/s, the known speed of light

12. EM Waves by an Antenna • Two rods are connected to an oscillating source, charges oscillate between the rods (a) • As oscillations continue, the rods become less charged, the field near the charges decreases and the field produced at t = 0 moves away from the rod (b) • The charges and field reverse (c) – the oscillations continue (d)

13. EM Waves by an Antenna, final • Because the oscillating charges in the rod produce a current, there is also a magnetic field generated • As the current changes, the magnetic field spreads out from the antenna • The magnetic field is perpendicular to the electric field

14. Electromagnetic Waves, Summary • A changing magnetic field produces an electric field • A changing electric field produces a magnetic field • These fields are in phase • At any point, both fields reach their maximum value at the same time

15. Electromagnetic Waves are Transverse Waves • The and fields are perpendicular to each other • Both fields are perpendicular to the direction of motion • Therefore, EM waves are transverse waves Active Figure: A Transverse Electromagnetic Wave

16. Properties of EM Waves • Electromagnetic waves are transverse waves • Electromagnetic waves travel at the speed of light • Because EM waves travel at a speed that is precisely the speed of light, light is an electromagnetic wave

17. Properties of EM Waves, 2 • The ratio of the electric field to the magnetic field is equal to the speed of light • Electromagnetic waves carry energy as they travel through space, and this energy can be transferred to objects placed in their path

18. Properties of EM Waves, 3 • Energy carried by EM waves is shared equally by the electric and magnetic fields • Average power per unit area

19. Properties of EM Waves, final • Electromagnetic waves transport linear momentum as well as energy • For complete absorption of energy U p = U/c  F = Pave/c • For complete reflection of energy U p = (2U)/c  F = 2Pave/c • Radiation pressures (forces) can be determined experimentally

20. Determining Radiation Pressure • This is an apparatus for measuring radiation pressure • In practice, the system is contained in a vacuum • The pressure is determined by the angle at which equilibrium occurs

21. The Spectrum of EM Waves • Forms of electromagnetic waves exist that are distinguished by their frequencies and wavelengths • c = ƒλ • Wavelengths for visible light range from 400 nm to 700 nm – visible light is a small portion of the spectrum • There is no sharp division between one kind of EM wave and the next

22. Reflection and Refraction Ch 22, Secs 2–4, 7

23. Ray Approximation A ray of light is an imaginary line drawn along the direction of travel of the light beams A wave front is a surface passing through points of a wave that have the same phase and amplitude The rays, corresponding to the direction of the wave motion, are perpendicular to the wave fronts

24. Reflection of Light • A ray of light, the incident ray, travels in a medium • When it encounters a boundary with a second medium, part of the incident ray is reflected back into the first medium • This means it is directed backward into the first medium

25. Reflection of Light, cont • The angle of reflection is equal to the angle of incidence: θ1= θ1’ Active Figure: Reflection • The normal is a line perpendicular to the surface • It is at the point where the incident ray strikes the surface • The incident ray makes an angle of θ1 with the normal • The reflected ray makes an angle of θ1’with the normal

26. Specular Reflection Specular reflection is reflection from a smooth surface (for example, a glass window pane) The reflected rays are parallel to each other All reflection in this text is assumed to be specular

27. Diffuse Reflection Diffuse reflection is reflection from a rough surface The reflected rays travel in a variety of directions Diffuse reflection makes the dry road easy to see at night

28. Refraction of Light • When a ray of light traveling through a transparent medium encounters a boundary leading into another transparent medium, part of the ray is reflected and part of the ray enters the second medium • The ray that enters the second medium is bent at the boundary • This bending of the ray is called refraction

29. Refraction of Light, cont The incident ray, the reflected ray, the refracted ray, and the normal all lie on the same plane The angle of refraction, θ2, depends on the properties of the medium

30. The Index of Refraction • When light passes from one medium to another, it is refracted because the speed of light is different in the two media • The index of refraction, n, of a medium can be defined • For a vacuum, n = 1 (for air, n ≈ 1) • For other media, n > 1

31. Some Indices of Refraction

32. Frequency Between Media As light travels from one medium to another, its frequency does not change Both the wave speed and the wavelength do change The wavefronts do not pile up, nor are created or destroyed at the boundary, so ƒ must stay the same Since light waves obey v = ƒ λ in the media, we find

33. Snell’s Law • The angle of refraction depends upon the speed of light in the materials and the angle of incidence • n1 sin θ1 = n2 sin θ2 • θ1 is the angle of incidence • θ2 is the angle of refraction

34. Refraction Details, 1 Light refracts into a material where its speed is lower (index of refraction is higher) The angle of refraction is less than the angle of incidence The ray bends toward the normal n1 sin θ1 = n2 sin θ2 Active Figure: Refraction

35. Refraction Details, 2 Light refracts into a material where its speed is higher (index of refraction is lower) The angle of refraction is greater than the angle of incidence The ray bends away from the normal n1 sin θ1 = n2 sin θ2

36. Dispersion The index of refraction in anything except a vacuum depends on the wavelength of the light This dependence of n on λ is called dispersion n = n(λ) Snell’s Law indicates that the angle of refraction made when light enters a material depends on the wavelength of the light θ2 = θ2(λ)

37. Variation of Index of Refraction with Wavelength The index of refraction for a material usually decreases with increasing wavelength Violet light refracts more than red light when passing from air into a material

38. Refraction in a Prism The amount the ray is bent away from its original direction is called the angle of deviation, δ Since all the colors have different angles of deviation, they will spread out into a spectrum Violet (400 nm blue end) deviates the most Red (700 nm red end) deviates the least • The total dispersion for visible light is measured by Δδ = δB - δR

39. Prism Spectrometer A prism spectrometer uses a prism to cause the wavelengths to separate The instrument is commonly used to study wavelengths emitted by a light source

40. Total Internal Reflection Total internal reflection can occur when light attempts to move from a medium with a higher index of refraction to one with a lower index of refraction Ray 5 shows total internal reflection

41. Critical Angle A particular angle of incidence will result in an angle of refraction of 90° This angle of incidence is called the critical angle • For angles of incidence greater than the critical angle, the beam is entirely reflected at the boundary Active Figure: Total Internal Reflection

42. Fiber Optics An application of internal reflection Plastic or glass rods are used to “pipe” light from one place to another • Applications of fiber optics include • Medical use of fiber optic cables for diagnosis and treatment of medical problems • Telecommunications