1 Light Chapters 36 – 39

2 Wave or Particle? Newton -- particles. In the early 19 th century, Young, Fresnel, and others -- wave. In 1860 Maxwell -- electromagnetic wave.

3 Photoelectric effect 19 th century -- Hertz -- shining light on a metal plate would make it emit electrons – producing an electric current. Kinetic energy of the emitted electrons was independent of the intensity of the light. Not wave theory

4 Photons In 1905 Einstein proposed that light is quantized in small bundles called photons. The energy of a photon depends on the frequency of the light, not the intensity.

5 Wave Particle Duality In some situations, light behaves like a wave. In other situations, it behaves like a particle. This unit will only deal with light as a wave.

6 Light Basics Light is an electromagnetic wave. Doesn’t need a medium to travel Travels at the speed of light

7 Speed of light

8 Speed of Light Defined as m/s We use 3.00 x 10 8 m/s Denoted as the letter c

9 Electromagnetic Spectrum We detect a very small part of the electromagnetic spectrum as visible light.

10 Visible Spectrum We can see wavelengths from about 400 to 700 nm. Different wavelengths correspond to different colors.

11 Wave Front Leading edge of a wave Shows the crests of the wave

12 Ray Model A ray is an imaginary line along the direction of travel of a wave.

13 Reflection

14 Law of Reflection The angle of reflection equals the angle of incidence. Angles are measured from the normal, not the surface.

15 Example A ray reflects off 2 perpendicular mirrors. How does its final direction relate to its initial direction? 30° 60° 30° anti-parallel

16 You try Repeat example for 2 mirrors at a 60° angle. 90° 60° 30° 60° anti-parallel

17 Speed of Light in Matter The speed of light in a transparent material such as air, water, or glass is less than the speed of light in a vacuum. Each material has an index of refraction, n, where Can n be greater than 1? Less than 1? Equal to 1?

18 Refraction When light travels from one material into another, its path is bent. If the second material has a higher index of refraction, it is bent towards the normal.

19 Color The index of refraction of a material has a slight dependence on wavelength. Red (longer wavelength) is refracted less than violet (shorter wavelength).

20 Prisms

21 Rainbows Rainbows are reflected light from water droplets in the air. Different colors are refracted at different angles by the water, so they are separated.

22 Snell’s Law

23 You try Light traveling in glass with n = 1.5 enters air with an angle of incidence of 30°. What is the angle of refraction? Did the light bend toward the normal or away from it?

24 Wavelength in new material For any wave, the wavelength and the frequency f are related by the equation During refraction, the frequency does not change.

25 Wavelength in new material

26 Wavelength in new material

27 Mirages

28 Mirages

29 Total Internal Reflection

30 Total Internal Reflection What if n 2 is greater than n 1 ?

31 Total Internal Reflection

32 Fiber Optics

33   Plane Mirrors Image is same distance from mirror. Image is the same size. Image is upright. mirror object image

34 Real Images An image is real if the light rays actually converge at that location. A real image can be shown on a card or screen. A real image is located in front of the mirror.

35 Virtual Images An image is virtual if the light rays only appear to converge at that location. A virtual image cannot be shown on a card or screen. A virtual image is located behind the mirror.

36 Depth Inversion The front and back of an object are reversed in a plane mirror. This causes right and left to be reversed between the object and the image.

37 Spherical Mirrors In spherical mirrors, the mirror is on the inner or outer surface of part of a hollow sphere.

38 Concave Mirrors Reflect light from inner surface of sphere. Are “caved in”. Also called converging.

39 Mirrors C is the center of the sphere. r is the radius of curvature. F is the focal point. f is the focal length. Principal axis CF r f

40 Finding the image 1 Image is inverted. Image is real. Principal axis F

41 Concave Mirrors To find the image Draw a ray parallel to the principal axis. – It will reflect through the focal point. Draw a ray through the focal point. – It will reflect parallel to the principal axis. The image is located at the intersection of the two reflected rays. You can draw a ray to the center of the mirror. It will reflect according to the law of reflection for flat surfaces.

42 Convex Mirrors Reflect light from outer surface of sphere. Also called diverging.

43 Finding the image 2 Image is upright. Image is virtual. FF

44 Convex Mirrors To find the image Draw a ray parallel to the principal axis. – It will reflect as if it had come from the focal point. Draw a ray through the focal point. – It will reflect parallel to the principal axis. – Extend the parallel reflected ray behind the mirror. The image is located at the intersection of the two reflected rays (or their extensions).

45 Mirror Practice 1 Image is upright or inverted. Image is real or virtual. F

46 Mirror Practice 2 Image is upright or inverted. Image is real or virtual. F No Image!

47 Mirror Practice 3 Image is upright or inverted. Image is real or virtual. FF

48 Mirror Practice 4 Image is upright or inverted. Image is real or virtual. FF

49 The Mirror Equation Used to locate the image mathematically. d o = object distance d i = image distance f = focal length r = radius of curvature

50 Mirror Conventions d o is always positive. d i is positive for real images. – Same side of mirror as object. d i is negative for virtual images. – Opposite side of mirror as the object.

51 Mirror Conventions f is positive for a converging (concave) mirror. f is negative for a diverging (convex) mirror.

52 Magnification Ratio of the image size to the object size. Same as the negative of the ratio of the image distance to the object distance.

53 Magnification Negative magnification means the image is inverted. Magnification between 1 and –1 means the image is smaller than the object.

54 Example Scenario from mirror practice 4. d o is always positive. f is negative for a diverging (convex) mirror.

55 Example Negative sign means virtual image

56 Example Find the magnification of the image Positive means upright image. Image is half as big as object.

57 Thin Lenses Lenses are considered thin if their thickness is considerably smaller than their focal length. Can be concave or convex, like mirrors. Form images by refraction.

58 Convex Lenses Convex lenses are converging. – Opposite of mirrors.

59 Finding the image 3 Image is inverted. Image is real. FF

60 Convex lenses To Find the image Draw a ray parallel to the axis. – It will refract through the far focal point. Draw a ray through the near focal point. – It will refract parallel to the axis. You can also draw a ray through the center of the lens. It will continue straight through the lens without being bent. The image is located at the intersection of the two refracted rays.

61 Concave Lenses Concave lenses are diverging. – Opposite of mirrors.

62 Finding the image 4 Image is upright. Image is virtual. F

63 Concave Lenses To find the image Draw a ray parallel to the principal axis. – It will be refracted as if it came from the focal point. – Extend this ray behind the lens. Draw a ray through the center of the lens. – It will go straight through the lens. The image forms at the intersection of the refracted rays (or their extensions).

64 Lens practice 1 FF Image is upright or inverted. Image is real or virtual.

65 Lens practice 2 FF Image is upright or inverted. Image is real or virtual. No Image!

66 Lens practice 3 Image is upright or inverted. Image is real or virtual. F

67 Lens practice 4 Image is upright or inverted. Image is real or virtual. F

68 The Lens Equation The same as the mirror equation. Magnification is also the same as for mirrors.

69 Lens Conventions d o is always positive. d i is positive for real images. – Opposite side of lens as the object. d i is negative for virtual images. – Same side of lens as object. f is positive for a converging lens. f is negative for a diverging lens.

70 The eye Diagram on page 872 Light is refracted at the cornea and the lens. A real image is formed on the retina at the back of the eye. The optic nerve sends the data to the brain. Vision is best in a small central region.

71 The eye For a clear vision, the image must be formed exactly at the retina. This distance, d i does not change. In order to focus objects at varying d o distances, the focal length of the lens must change. The eye does this by bending the lens.

72 Near point The shortest object distance you can see clearly. Depends on the ability of your muscles to bend your lens. Muscle flexibility decreases with age, so the near point increases. – Reading glasses needed

73 Myopic eyes Near-sighted. The eye is too long, so the image forms in front of the retina. Too much convergence – needs a diverging lens to correct.

74 Hyperopic eye Far-sighted The eye is too short, so the image forms behind the retina. Not enough convergence – needs a converging lens to correct.

75 astigmatism The cornea is not spherical. Cannot focus on horizontal and vertical lines at the same time. Corrected with a cylindrical lens – curved in one direction.

76 diopters The power of a lens is measured in diopters. The power is the reciprocal of the focal length in meters. How glasses are prescribed. The numbers on your contacts.

77 LASIK Laser reshapes cornea to refract light differently. Cornea must be sufficiently thick. Works best for near-sightedness and astigmatism. Will not increase lens flexibility – Reading glasses may still be needed.

78 cameras The film is like the retina in your eye. The area of the lens is adjusted by the aperture. Aperture size is described by the “f- number”, which is the focal length divided by the diameter.

79 Interference Principle of linear superposition: – When two or more waves overlap, the resultant displacement at any point and at any instant may be found by adding the instantaneous displacements that would be produced at the point by the individual waves – You just add them

80

81 Two source interference Thomas Young

82 Two Source Interference From the diagram we can see that If we use the fact that for very small angles, tan  is about sin , we can say

83 Approximation If we assume that the distance L from the slits to the screen is much larger than the spacing, d, between the slits, then we can say that the path length between the two rays r 1 and r 2 is

84 Two Source interference In order to have constructive interference from the light from two adjacent slits, the path difference between their light rays must be a complete wavelength.

85 Diffraction Gratings Consist of a large number of equally spaced lines or slits on a flat surface. N is the number of slits per unit length (such as mm or cm) d is the distance between two adjacent slits.

86 Diffraction gratings Use the same equations as two source interference. However, the patterns produced are sharper and narrower