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Light and Colour(光與顏色)

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Presentation on theme: "Light and Colour(光與顏色)"— Presentation transcript:

1 Light and Colour(光與顏色)
IJSO 2007 M22 (Light and Colour) Light and Colour(光與顏色) CHENG Kai Ming Department of Physics CUHK Time allocation: 6 hours

2 IJSO 2007 M22 (Light and Colour)
Content Reflection of Light(光的反射) Geometrical Optics(幾何光學 ) Law of Reflection(反射定律 ) Images(像) Plane Mirrors(平面鏡) Spherical Mirrors(球面鏡) Concave Mirrors(凹面鏡) Convex Mirrors(凸面鏡) Parabolic Mirror(拋物面鏡)

3 IJSO 2007 M22 (Light and Colour)
Refraction of Light(光的折射) Law of Refraction(折射定律 ) Refractive index(折射率) Total Internal Reflection(全內反射) Critical Angle(臨界角 ) Thin Lenses(薄透鏡) Convex Lenses(凸透鏡) Concave Mirrors(凹透鏡) Normal Lenses Short-sighted(近視) Long-sighted(遠視)

4 IJSO 2007 M22 (Light and Colour)
Magnification Equation & Mirror/lens Equation Telescope(望遠鏡)and Microscope(顯微鏡) Fermat’s Principle of Least Time(費爾馬最短時間原理) Wave Properties of Light(光的波動特性) Electromagnetic Waves(電磁波) Electromagnetic Spectrum(電磁波譜) Blackbody Radiation(黑體輻射)

5 IJSO 2007 M22 (Light and Colour)
Dispersion(色散) Primary Colours(原色) Complementary Colours(互補色) Selective Reflection(選擇反射) Pigments(顏料) Selective Transmission(選擇透射) Selective Scattering(選擇散射) Rainbow(彩虹) Laser(激光) Colour Deficiency(色弱)

6 IJSO 2007 M22 (Light and Colour) Reflection of Light
Part 1 Reflection of Light

7 IJSO 2007 M22 (Light and Colour)
Geometrical Optics Light travels in straight paths called rays.

8 IJSO 2007 M22 (Light and Colour)
Law of Reflection Incident ray, reflected ray and normal all lie on the same plane. Normal Incident ray Reflected ray qi qr

9 IJSO 2007 M22 (Light and Colour)
Law of Reflection Regular (specular) /diffuse reflection Regular (specular) reflection Diffuse reflection

10 IJSO 2007 M22 (Light and Colour)
Image The reflected ray appears to come from a point behind the mirror. This point is called the image. Real image  can be captured by a screen as a sharp image. Virtual image  rays of light seems to emanate from the image. Real image Virtual image Produced by converging beams Produced by diverging beams

11 IJSO 2007 M22 (Light and Colour)
Plane Mirrors mirror Image of a real object virtual, upright, laterally inverted, the same size as the object, and as far behind the mirror as the object is in front of it.

12 IJSO 2007 M22 (Light and Colour)
Plane Mirrors B A C D

13 IJSO 2007 M22 (Light and Colour)
Example A person is sitting in front of two mirrors that intersect at an angle of 90. How many images can he see? 3 images M1 M2 90 I1 O I12 or I21 I2

14 IJSO 2007 M22 (Light and Colour)
60 I1 I21 O I212 or I121 I2 I12

15 IJSO 2007 M22 (Light and Colour)
Spherical Mirrors A spherical mirror: a part of a spherical surface Concave Mirror Convex Mirror

16 IJSO 2007 M22 (Light and Colour)
Spherical Mirrors centre of curvature C = centre of the sphere radius of curvature R = radius of the sphere focal point (principal focus) F = midpoint between C and the mirror focal length f = R/2

17 IJSO 2007 M22 (Light and Colour)
Spherical Mirrors f C F

18 IJSO 2007 M22 (Light and Colour)
Ray Tracing The law of reflection applies just as it does for a plane mirror. The normal for the reflection is drawn between the point of incidence and C. Principal axis = straight line drawn through C and the midpoint of the mirror Paraxial rays = rays that lie close to the principal axis Object/image at infinity = parallel rays

19 Ray Tracing (Concave Mirrors)
IJSO 2007 M22 (Light and Colour) Ray Tracing (Concave Mirrors) For paraxial rays: Rays parallel to the principal axis will be reflected passing through the focal point. Rays passing through the focal point F will be reflected parallel to the principal axis. Rays passing through C will be reflected back along its own path. C F

20 IJSO 2007 M22 (Light and Colour)
Concave Mirrors Real Object Image Properties of image Beyond C Between C and F Real Inverted Diminished / Reduced At C Same Size Magnified / Enlarged At F At  - Between F and mirror Behind mirror Virtual Upright / Erect

21 IJSO 2007 M22 (Light and Colour)
Concave Mirrors

22 Ray Tracing (Convex Mirrors)
IJSO 2007 M22 (Light and Colour) Ray Tracing (Convex Mirrors) For paraxial rays: Rays parallel to the principal axis will be reflected in a way that it appears to be originated from the focal point. Rays directing towards the focal point F will be reflected parallel to the principal axis. Rays directing towards C will be reflected back along its own path. C F

23 IJSO 2007 M22 (Light and Colour)
Convex Mirrors The image of a real object is always Virtual Erect Diminished

24 Concave and Convex Mirrors
IJSO 2007 M22 (Light and Colour) Concave and Convex Mirrors F Converging Diverging F

25 IJSO 2007 M22 (Light and Colour)
Think 1 Tom is observing a concave mirror and claimed that he found an image between the focus and the mirror. What would you say about his finding?

26 IJSO 2007 M22 (Light and Colour)
Think 1 Tom must be either lying or performing the experiment perfunctorily. The image of a real object for a concave mirror can be anywhere (including anywhere behind the mirror) except between F and the mirror.

27 Principle of Reversibility
IJSO 2007 M22 (Light and Colour) Principle of Reversibility If the direction of a light ray is reversed, the light retraces its original path. f O I I O

28 IJSO 2007 M22 (Light and Colour)
Parabolic Mirror principal axis For a parabolic mirror, all rays parallel to the principal axis (not necessarily paraxial) will be reflected passing through the focal point F as shown.

29 Reflector (telescope)
IJSO 2007 M22 (Light and Colour) Reflector (telescope) (Primary mirror) (Focal length of primary mirror) (Eyepiece) (Mount) (Aperture) (Incident light)

30 IJSO 2007 M22 (Light and Colour) Refraction of Light
Part 2 Refraction of Light

31 IJSO 2007 M22 (Light and Colour)
Law of Refraction Incident ray, refracted ray and normal all lie on the same plane. Snell’s law refractive index c = speed of light in vacuum, defined to be exactly 299,792,458 m/s (~3108 m/s) q1 Medium 1 Medium 2 q2

32 IJSO 2007 M22 (Light and Colour)
Substance Refractive index / Index of refraction n Solids at 20C Diamond 2.419 Glass, crown 1.523 Ice (0C) 1.309 Sodium chloride 1.544 Quartz - Crystalline Quartz – Fused 1.458 Liquids at 20C Benzene 1.501 Carbon disulfide 1.632 Carbon tetrachloride 1.461 Ethyl alcohol 1.362 Water 1.333 Gases at 0C and 1 atm Air Carbon dioxide Oxygen Hydrogen

33 IJSO 2007 M22 (Light and Colour)
Example A light ray strikes an air/water surface at an angle of 46 with respect to the normal. The index of refraction for water is Find the angle of refraction when the direction of the ray is from air to water. Medium 1 = medium of incidence, i.e. air Medium 2 = medium of refraction, i.e. water

34 IJSO 2007 M22 (Light and Colour)
Use the same example Find the angle of refraction when the direction of the ray is from water to air. Medium 1 = medium of incidence, i.e. water Medium 2 = medium of refraction, i.e. air

35 IJSO 2007 M22 (Light and Colour)
Refraction by a Slab q1 q2 q3 Medium 1 Medium 2 The emergent and incident rays are parallel. Yet is displaced laterally relative to the incident ray.

36 Total Internal Reflection
IJSO 2007 M22 (Light and Colour) Total Internal Reflection Occurs only when n1>n2 Normal incidence means q1 = 0 When q1 , it reaches a certain value, called the critical angle qc, such that q2 = 90. When q1  further, there is no more refraction. qc

37 IJSO 2007 M22 (Light and Colour)
Critical Angle qc

38 IJSO 2007 M22 (Light and Colour)
Example A beam of light is propagating through diamond (n1 = 2.42) and strikes a diamond-air interface at an angle of incidence of 28. Will part of the beam enter the air (n2 = 1) or will the beam be totally reflected at the interface?

39 IJSO 2007 M22 (Light and Colour)
Example Since 28 > qc, there is no refraction, and the light is totally reflected back into the diamond. Similarly, many of the rays of light are striking the bottom facet of the diamond at q1 > qc, they are totally reflected back into the diamond, eventually exiting the top surface to give the diamond its sparkle.

40 IJSO 2007 M22 (Light and Colour)
Thin Lenses A convex lens is known as a converging lens because paraxial incident rays will be converged to the principal axis. A concave lens is known as a diverging lens because paraxial incident rays will be diverged away from the principal axis. Concave lens Convex lens

41 IJSO 2007 M22 (Light and Colour)
Convex Lenses For paraxial rays: Rays parallel to the principal axis will be refracted passing through the focal point. Rays passing through the focal point will be refracted parallel to the principal axis. Rays passing through the centre of the lens will be passing through straightly without bending. F O I

42 IJSO 2007 M22 (Light and Colour)
Object Image Properties of image Beyond 2F Between 2F and F Real Inverted Diminished / Reduced At 2F Same Size Magnified / Enlarged At F At  - Between F and lens Same side as Object Virtual Upright / erect

43 IJSO 2007 M22 (Light and Colour)
Concave Lenses For paraxial rays: Rays parallel to the principal axis will be refracted in a way that it appears to be originated from the focal point. Rays directing towards the focal point will be refracted parallel to the principal axis. Rays passing through the centre of the lens will be passing through straightly without bending. F

44 IJSO 2007 M22 (Light and Colour)
Concave Lenses The image of a real object is always Virtual Erect Diminished

45 IJSO 2007 M22 (Light and Colour)
Example An object 2 cm tall is placed 10 cm away from a convex lens with a focal length of 5 cm. Find the image position and its size. Image distance = 10 cm, image size = 2 cm. 10 cm 5 cm O I

46 IJSO 2007 M22 (Light and Colour)
Normal Eyes Far point at  Near point at about 25 cm

47 IJSO 2007 M22 (Light and Colour)
Short-sighted Image of distant object formed in front of retina Far point not at  Eyeball too long Focal length too short

48 IJSO 2007 M22 (Light and Colour)
Short-sighted Corrective lens: Concave lens Object at , image at far point of eye

49 IJSO 2007 M22 (Light and Colour)
Long-sighted Image of close object formed behind retina Near point too far away Eyeball too short Focal length too long

50 IJSO 2007 M22 (Light and Colour)
Corrective lens: Convex lens Close objects form images at near point of eye

51 IJSO 2007 M22 (Light and Colour)
Example A student sees the top and the bottom edges of a pool simultaneously at an angle of 14 above the horizontal as shown in the Figure. What is the new view angle, if he wants to see the top edge and the bottom center of the pool (nwater = 1.33 and nair = 1)? 2004 IJSO

52 IJSO 2007 M22 (Light and Colour)
In order to see the bottom edge of the pool, In order to see the bottom centre of the pool, The new view angle is

53 Magnification Equation:
IJSO 2007 M22 (Light and Colour) Magnification Equation: Where ho is the object height and is always +ve. hi is the image height and is +ve if the image is an upright image (and therefore, also virtual) and is -ve if the image is an inverted image (and therefore, also real). do is the object distance from the lens/mirror and is always +ve. di is the image distance from the lens/mirror. It is +ve if the image is a real image and located on the opposite(same) side of the lens(mirror) and is -ve if the image is a virtual image and located on the same(opposite) side of the lens(mirror).

54 Mirror/lens Equation:
IJSO 2007 M22 (Light and Colour) Mirror/lens Equation: where f is the focal length and is +ve if the lens(mirror) is convex(concave) and is -ve if the lens(mirror) is concave(convex).

55 Let’s consider the ray diagram of a convex lens
IJSO 2007 M22 (Light and Colour) Let’s consider the ray diagram of a convex lens I O F do di ho hi f A B C D

56 Proof of Magnification Equation
IJSO 2007 M22 (Light and Colour) Proof of Magnification Equation  AOD ~  CID => => Note: The Magnification Equations for concave lens and mirrors can be proved similarly by considering appropriate ray diagrams.

57 IJSO 2007 M22 (Light and Colour)
Proof of lens Equation  BDF ~  CIF => => => Note: The Lens/Mirror Equations for concave lens and mirrors can be proved similarly by considering appropriate ray diagrams.

58 IJSO 2007 M22 (Light and Colour)
Example A 2.0-cm diameter coin is placed a distance of 20.0 cm from a convex mirror which has a focal length of cm. Determine the image distance and the diameter of the image. By Mirror Equation, we have

59 IJSO 2007 M22 (Light and Colour)
Example By Magnification Equation, we have Therefore, a virtual image forms 7.5 cm behind the mirror and the diameter of the coin is 0.75 cm. Check the answers by drawing an appropriate ray diagram

60 Telescope and Microscope
IJSO 2007 M22 (Light and Colour) Telescope and Microscope F1 do1 -di2 L1(Objective) di1 F2 do2 To eye L2(Eyepiece)

61 Telescope and Microscope
IJSO 2007 M22 (Light and Colour) Telescope and Microscope Always converging mirrors or lenses since diverging mirrors or lenses always give smaller images The focal length, F1, of the objective lens is always longer (shorter) than the focal length,F2, of the eyepiece in telescope (microscope) – Why? The magnification, M, is equal to the product of the magnifications of the individual lenses:

62 Fermat’s Principle of Least Time
IJSO 2007 M22 (Light and Colour) Fermat’s Principle of Least Time Out of all possible paths that light might take to get from one point to another, it takes the path that requires the shortest time. The Principle is true for both reflection and refraction!

63 IJSO 2007 M22 (Light and Colour) Wave Properties of Light and Colour
Part 3 Wave Properties of Light and Colour

64 IJSO 2007 M22 (Light and Colour)
Waves Amplitude Wavelength

65 Electromagnetic Waves
IJSO 2007 M22 (Light and Colour) Electromagnetic Waves E B v

66 Electromagnetic Spectrum
IJSO 2007 M22 (Light and Colour) Electromagnetic Spectrum Increase in frequency Image credit:

67 IJSO 2007 M22 (Light and Colour)
Blackbody Radiation T4 T2 T1 T3 T4>T3>T2>T1

68 Sodium Lamps, Florescent Tubes, Laser
IJSO 2007 M22 (Light and Colour) Sodium Lamps, Florescent Tubes, Laser Electrons inside atoms jump from outer orbits to inner orbits and release energy

69 IJSO 2007 M22 (Light and Colour)
From longest to shortest wavelength: red, orange, yellow, green, blue, indigo, violet Light of different wavelengths are perceived as different colours. All the colours combine to make white.

70 IJSO 2007 M22 (Light and Colour)
Dispersion Due to the difference in refractive index for different colours Angle of deviation d Violet deflected most d Crown glass Colour Wavelength in vacuum (nm) Refractive index n Red 660 1.520 Orange 610 1.522 Yellow 580 1.523 Green 550 1.526 Blue 470 1.531 Violet 410 1.538

71 IJSO 2007 M22 (Light and Colour)
Light in diamond Violet Red White light Dispersion + Total internal reflection

72 IJSO 2007 M22 (Light and Colour)
Primary Colours 3 types of cone-shaped receptors in our eyes perceive colour Light that stimulates the cones sensitive to longest wavelengths appears red. …middle…green …shortest…blue Red + Green + Blue = White

73 Complementary Colours
IJSO 2007 M22 (Light and Colour) Complementary Colours Red+Blue=Magenta Red+Green=Yellow Blue+Green=Cyan Magneta+Green=White Yellow+Blue=White Cyan+Red=White (Magneta,Green), (Yellow,Blue) and (Cyan, Red) are complementary colours

74 IJSO 2007 M22 (Light and Colour)
Selective Reflection Most objects reflect rather than emit light. Many of them reflect only part of the light that shines upon them. If a material absorbs all light except red, it appears red. If it reflects all, it appears white. If it reflects none, it appears black.

75 IJSO 2007 M22 (Light and Colour)
What do you see? If white light shines on a red ball, the ball appears ___. If red light shines on a red ball, the ball appears ___. If green light shines on a red ball, the ball appears ___. red red black

76 IJSO 2007 M22 (Light and Colour)
Pigments Pigments are tiny particles that absorb specific colours. Magenta = white – green (absorb green) Yellow = white – blue (absorb blue) Cyan = white – red (absorb red) Red, green, blue are additive primaries. Magenta, yellow, cyan are subtractive primaries.

77 IJSO 2007 M22 (Light and Colour)
Pigments

78 Selective Transmission
IJSO 2007 M22 (Light and Colour) Selective Transmission Colour of a transparent object depends on the light it transmits. Pigments in a red glass absorb all colours except red. Energy of the absorbed light warms the glass. Can we have something “transparent white”?

79 Which disc is warmer in sunlight?
IJSO 2007 M22 (Light and Colour) Which disc is warmer in sunlight?

80 IJSO 2007 M22 (Light and Colour)
Selective Scattering Light that incidents on an atom sets the atom into vibration. The vibrating atom then re-emit light in all directions. Violet light is scattered the most by nitrogen and oxygen which make up most of our atmosphere. But why does the sky appears blue instead of violet?

81 Why do we have a whitish sky?
IJSO 2007 M22 (Light and Colour) Why do we have a whitish sky? When the atmosphere contains a lot of particles of dust and other particles larger than oxygen and nitrogen, light of the longer wavelengths is also scattered strongly. After a heavy rainstorm when the particles have been washed away, the sky becomes a deeper blue.

82 Why is the setting sun red?
IJSO 2007 M22 (Light and Colour) Why is the setting sun red? Light that is not scattered is light that is transmitted. Red, which is scattered the least, passes through more atmosphere than any other colour. So the thicker the atmosphere through which a beam of sunlight travels, the more time there is to scatter all the shorter wavelengths. Why is the rising sun less red?

83 Why are the clouds white?
IJSO 2007 M22 (Light and Colour) Why are the clouds white? Different sizes of water molecule clusters scatter different wavelengths. The overall result is a white cloud. Why are the rain clouds dark?

84 Rainbows (double rainbows)
IJSO 2007 M22 (Light and Colour) Rainbows (double rainbows) Secondary rainbow Primary rainbow

85 IJSO 2007 M22 (Light and Colour)
Primary rainbows refraction reflection red violet

86 IJSO 2007 M22 (Light and Colour)
Secondary rainbows sunlight red violet

87 IJSO 2007 M22 (Light and Colour)
Laser Monochromatic = single wavelength / colour Laser (Light Amplification by Stimulated Emission of Radiation) A laser is an instrument that produces a beam of coherent light.

88 IJSO 2007 M22 (Light and Colour)
Colour Deficiency ability to distinguish colours and shades is less than normal Though “colour blind” is often used, only a very small number of people are completely unable to identify any colours. more common in males than females usually inherited, but can also result from certain diseases, trauma or as a side effect of certain medications occurs when an individual partially or completely lacks one or more types of the three kinds of cones

89 Types of Colour Deficiencies
IJSO 2007 M22 (Light and Colour) Types of Colour Deficiencies two different kinds of red-green deficiency and one blue-yellow deficiency red-green deficiencies are by far the most common

90 IJSO 2007 M22 (Light and Colour)
Think 2 If you hold a small source of white light between you and a piece of red glass, you’ll see two reflections from the glass: one from the front surface and one from the back surface. What colour is each reflection?

91 IJSO 2007 M22 (Light and Colour)
Think 2 The reflection from the front surface is white because the light does not go far enough into the coloured glass to allow absorption of non-red light. Only red light reaches the back surface because the pigments in the glass absorb all the other colours, and so the back reflection is red.


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