Chapter 31 Maxwell’s Equations and Electromagnetic Waves

1. Chapter 31Maxwell’s Equations and Electromagnetic Waves

2. 32-4 Index of Refraction In general, light slows somewhat when traveling through a medium. The index of refraction of the medium is the ratio of the speed of light in vacuum to the speed of light in the medium:

3. 32-5 Refraction: Snell’s Law Light changes direction when crossing a boundary from one medium to another. This is called refraction, and the angle the outgoing ray makes with the normal is called the angle of refraction.

4. 32-5 Refraction: Snell’s Law Refraction is what makes objects half-submerged in water look odd.

5. 32-5 Refraction: Snell’s Law The angle of refraction depends on the indices of refraction, and is given by Snell’s law:

6. 32-5 Refraction: Snell’s Law Example 32-9: Apparent depth of a pool. A swimmer has dropped her goggles to the bottom of a pool at the shallow end, marked as 1.0 m deep. But the goggles don’t look that deep. Why? How deep do the goggles appear to be when you look straight down into the water?

7. air air 1 ConcepTest 32.4aRefraction I Parallel light rays cross interfaces from air into two different media, 1 and 2, as shown in the figures below. In which of the media is the light traveling faster? 1) medium 1 2) medium 2 3) both the same 2

8. air air 1 ConcepTest 32.4aRefraction I Parallel light rays cross interfaces from air into two different media, 1 and 2, as shown in the figures below. In which of the media is the light traveling faster? 1) medium 1 2) medium 2 3) both the same The greater the difference in the speed of light between the two media, the greater the bending of the light rays. 2 Follow-up:How does the speed in air compare to that in #1 or #2?

9. ConcepTest 32.5a Gone Fishin’ I 1) aim directly at the image 2) aim slightly above 3) aim slightly below To shoot a fish with a gun, should you aim directly at the image, slightly above, or slightly below?

10. ConcepTest 32.5a Gone Fishin’ I 1) aim directly at the image 2) aim slightly above 3) aim slightly below To shoot a fish with a gun, should you aim directly at the image, slightly above, or slightly below? Due to refraction, the image will appear higher than the actual fish, so you have to aimlower to compensate.

11. 32-6 Visible Spectrum and Dispersion The visible spectrum contains the full range of wavelengths of light that are visible to the human eye.

12. 32-6 Visible Spectrum and Dispersion The index of refraction of many transparent materials, such as glass and water, varies slightly with wavelength. This is how prisms and water droplets create rainbows from sunlight.

13. 32-6 Visible Spectrum and Dispersion This spreading of light into the full spectrum is called dispersion.

14. 32-7 Total Internal Reflection; Fiber Optics If light passes into a medium with a smaller index of refraction, the angle of refraction is larger. There is an angle of incidence for which the angle of refraction will be 90°; this is called the critical angle:

15. 32-7 Total Internal Reflection; Fiber Optics If the angle of incidence is larger than this, no transmission occurs. This is called total internal reflection.

16. 32-7 Total Internal Reflection; Fiber Optics Conceptual Example 32-11: View up from under water. Describe what a person would see who looked up at the world from beneath the perfectly smooth surface of a lake or swimming pool.

17. 32-7 Total Internal Reflection; Fiber Optics Optical fibers also depend on total internal reflection; they are therefore able to transmit light signals with very small losses.

18. 32-8 Refraction at a Spherical Surface Rays from a single point will be focused by a convex spherical interface with a medium of larger index of refraction to a single point, as long as the angles are not too large.

19. 32-8 Refraction at a Spherical Surface Geometry gives the relationship between the indices of refraction, the object distance, the image distance, and the radius of curvature:

20. 32-8 Refraction at a Spherical Surface For a concave spherical interface, the rays will diverge from a virtual image.

21. 32-8 Refraction at a Spherical Surface Example: Apparent depth II. A person looks vertically down into a 1.0-m-deep pool. How deep does the water appear to be?

22. 32-8 Refraction at a Spherical Surface Example: A spherical “lens.” A point source of light is placed at a distance of 25.0 cm from the center of a glass sphere of radius 10.0 cm. Find the image of the source.

23. Summary of Chapter 32 • Light paths are called rays. • Index of refraction: • Angle of reflection equals angle of incidence. • Plane mirror: image is virtual, upright, and the same size as the object. • Spherical mirror can be concave or convex. • Focal length of the mirror:

24. Summary of Chapter 32 • Mirror equation: • Magnification: • Real image: light passes through it. • Virtual image: light does not pass through.

25. Summary of Chapter 32 • Law of refraction (Snell’s law): • Total internal reflection occurs when angle of incidence is greater than critical angle:

26. Slight Digression

27. 35-11 Polarization Light is polarized when its electric fields oscillate in a single plane, rather than in any direction perpendicular to the direction of propagation.

28. 35-11 Polarization Polarized light will not be transmitted through a polarized film whose axis is perpendicular to the polarization direction.

29. 35-11 Polarization When light passes through a polarizer, only the component parallel to the polarization axis is transmitted. If the incoming light is plane-polarized, the outgoing intensity is:

30. 35-11 Polarization This means that if initially unpolarized light passes through crossed polarizers, no light will get through the second one.

31. 35-11 Polarization Example 35-13: Two Polaroids at 60°. Unpolarized light passes through two Polaroids; the axis of one is vertical and that of the other is at 60° to the vertical. Describe the orientation and intensity of the transmitted light.

32. 35-11 Polarization Conceptual Example 35-14: Three Polaroids. When unpolarized light falls on two crossed Polaroids (axes at 90°), no light passes through. What happens if a third Polaroid, with axis at 45° to each of the other two, is placed between them?

33. 35-11 Polarization Light is also partially polarized after reflecting from a nonmetallic surface. At a special angle, called the polarizing angle or Brewster’s angle, the polarization is 100%: .

34. 35-11 Polarization Example 35-15: Polarizing angle. (a) At what incident angle is sunlight reflected from a lake plane-polarized? (b) What is the refraction angle?

35. 35-12 Liquid Crystal Displays (LCD) Liquid crystals are unpolarized in the absence of an external voltage, and will easily transmit light. When an external voltage is applied, the crystals become polarized and no longer transmit; they appear dark. Liquid crystals can be found in many familiar applications, such as calculators and digital watches.

36. 35-12 Liquid Crystal Displays (LCD) This particular type of liquid crystal, called a twisted crystal, shows how the crystal passes light when the voltage is off but not when it is on.

37. 35-13 Scattering of Light by the Atmosphere Skylight is partially polarized due to scattering from molecules in the air. The amount of polarization depends on the angle that your line of sight makes with the Sun.

38. 1 2 3 ConcepTest 35.3Polarization 1) only case 1 2) only case 2 3) only case 3 4) cases 1 and 3 5) all three cases If unpolarized light is incident from the left, in which case will some light get through?Assume perfect polarizers.

39. 1 2 3 ConcepTest 35.3Polarization 1) only case 1 2) only case 2 3) only case 3 4) cases 1 and 3 5) all three cases If unpolarized light is incident from the left, in which case will some light get through?Assume perfect polarizers. In cases 1 and 3, light is blocked by the adjacent horizontal and vertical polarizers. However, in case 2, the intermediate 45° polarizer allows some light to get through the last vertical polarizer.

40. Chapter 33Lenses and Optical Instruments

41. Units of Chapter 33 • Thin Lenses; Ray Tracing • The Thin Lens Equation; Magnification • Combinations of Lenses • Lensmaker’s Equation • Cameras: Film and Digital • The Human Eye; Corrective Lenses • Magnifying Glass

42. Units of Chapter 33 • Telescopes • Compound Microscope • Aberrations of Lenses and Mirrors

43. 33-1 Thin Lenses; Ray Tracing Thin lenses are those whose thickness is small compared to their radius of curvature. They may be either converging (a) or diverging (b).

44. 33-1 Thin Lenses; Ray Tracing Parallel rays are brought to a focus by a converging lens (one that is thicker in the center than it is at the edge).

45. 33-1 Thin Lenses; Ray Tracing A diverging lens (thicker at the edge than in the center) makes parallel light diverge; the focal point is that point where the diverging rays would converge if projected back.

46. 33-1 Thin Lenses; Ray Tracing The power of a lens is the inverse of its focal length: Lens power is measured in diopters, D: 1 D = 1 m-1.

47. 33-1 Thin Lenses; Ray Tracing • Ray tracing for thin lenses is similar to that for mirrors. We have three key rays: • This ray comes in parallel to the axis and exits through the focal point. • This ray comes in through the focal point and exits parallel to the axis. • This ray goes through the center of the lens and is undeflected.

48. 33-1 Thin Lenses; Ray Tracing

49. 33-1 Thin Lenses; Ray Tracing For a diverging lens, we can use the same three rays; the image is upright and virtual.

50. 33-2 The Thin Lens Equation; Magnification The thin lens equation is similar to the mirror equation: