7 Geometrical Optics Light travels in straight paths called rays.
8 Law of Reflection Incident ray, reflected ray and normal all lie on the same plane. ii rr Incident ray Normal Reflected ray
9 Law of Reflection Regular (specular) /diffuse reflection Regular (specular) reflection Diffuse reflection
10 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 beamsProduced by diverging beams
11 Plane Mirrors Image of a real object 1. virtual, 2. upright, 3. laterally inverted, 4. the same size as the object, and 5. as far behind the mirror as the object is in front of it. mirror
13 Example Q. A person is sitting in front of two mirrors that intersect at an angle of 90 . How many images can he see? A. 3 images I 12 or I 21 M1M1 M2M2 90 I2I2 I1I1 O
14 I 12 I 21 I 212 or I 121 M1M1 M2M2 60 I2I2 I1I1 O
15 Spherical Mirrors A spherical mirror: a part of a spherical surface Concave Mirror Convex Mirror
16 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
18 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) For paraxial rays: 1. Rays parallel to the principal axis will be reflected passing through the focal point. 2. Rays passing through the focal point F will be reflected parallel to the principal axis. 3. Rays passing through C will be reflected back along its own path. C F
20 Concave Mirrors Real Object Image Properties of image Beyond C Between C and F RealInverted Diminished / Reduced At C RealInverted Same Size Between C and F Beyond C RealInverted Magnified / Enlarged At F At --- Between F and mirror Behind mirror Virtual Upright / Erect Magnified / Enlarged
22 Ray Tracing (Convex Mirrors) C F For paraxial rays: 1. Rays parallel to the principal axis will be reflected in a way that it appears to be originated from the focal point. 2. Rays directing towards the focal point F will be reflected parallel to the principal axis. 3. Rays directing towards C will be reflected back along its own path.
23 Convex Mirrors The image of a real object is always 1. Virtual 2. Erect 3. Diminished
24 Concave and Convex Mirrors Diverging FF Converging
25 Think 1 Q. 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 Think 1 A. 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 If the direction of a light ray is reversed, the light retraces its original path. f O I I O
28 Parabolic Mirror 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. principal axis
31 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 10 8 m/s) 11 22 Medium 1 Medium 2
Substance Refractive index / Index of refraction n Solids at 20 C Diamond2.419 Glass, crown 1.523 Ice (0 C) 1.309 Sodium chloride 1.544 Quartz - Crystalline 1.544 Quartz – Fused 1.458 Liquids at 20 C Benzene1.501 Carbon disulfide 1.632 Carbon tetrachloride 1.461 Ethyl alcohol 1.362 Water1.333 Gases at 0 C and 1 atm Air1.000293 Carbon dioxide 1.00045 Oxygen1.000271 Hydrogen1.000139
33 Example Q. 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 1.33. 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 A.
34 Use the same example Q. 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 A.
35 Refraction by a Slab The emergent and incident rays are parallel. Yet is displaced laterally relative to the incident ray. 11 22 33 22 Medium 1 Medium 2
36 Total Internal Reflection Occurs only when n 1 > n 2 Normal incidence means 1 = 0 When 1 , it reaches a certain value, called the critical angle c, such that 2 = 90 . When 1 further, there is no more refraction. cc
38 Example Q. A beam of light is propagating through diamond ( n 1 = 2.42) and strikes a diamond-air interface at an angle of incidence of 28 . Will part of the beam enter the air ( n 2 = 1) or will the beam be totally reflected at the interface? A.
39 Example Since 28 > c, 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 1 > c, they are totally reflected back into the diamond, eventually exiting the top surface to give the diamond its sparkle.
40 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. Convex lens Concave lens
41 Convex Lenses For paraxial rays: 1. Rays parallel to the principal axis will be refracted passing through the focal point. 2. Rays passing through the focal point will be refracted parallel to the principal axis. 3. Rays passing through the centre of the lens will be passing through straightly without bending. FF O I
ObjectImage Properties of image Beyond 2F Between 2F and F RealInverted Diminished / Reduced At 2F RealInverted Same Size Between 2F and F Beyond 2F RealInverted Magnified / Enlarged At F At --- Between F and lens Same side as Object Virtual Upright / erect Magnified / Enlarged
43 Concave Lenses For paraxial rays: 1. Rays parallel to the principal axis will be refracted in a way that it appears to be originated from the focal point. 2. Rays directing towards the focal point will be refracted parallel to the principal axis. 3. Rays passing through the centre of the lens will be passing through straightly without bending. FF
44 Concave Lenses The image of a real object is always 1. Virtual 2. Erect 3. Diminished
45 Example Q. 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. A. Image distance = 10 cm, image size = 2 cm. I 10 cm 5 cm O
46 Normal Eyes Far point at Near point at about 25 cm
47 Short-sighted Image of distant object formed in front of retina Far point not at Eyeball too long Focal length too short
48 Short-sighted Corrective lens: Concave lens Object at , image at far point of eye
49 Long-sighted Image of close object formed behind retina Near point too far away Eyeball too short Focal length too long
50 Corrective lens: Convex lens Close objects form images at near point of eye
51 Example Q. 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 ( n water = 1.33 and n air = 1)? 2004 IJSO
A. 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: Where h o is the object height and is always +ve. h i 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). d o is the object distance from the lens/mirror and is always +ve. d i 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: 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 I O F dodo didi hoho hihi f A B C D
56 AOD ~ CID => Proof of Magnification Equation Note: The Magnification Equations for concave lens and mirrors can be proved similarly by considering appropriate ray diagrams.
57 BDF ~ CIF => Proof of lens Equation Note: The Lens/Mirror Equations for concave lens and mirrors can be proved similarly by considering appropriate ray diagrams.
58 Example Q. A 2.0-cm diameter coin is placed a distance of 20.0 cm from a convex mirror which has a focal length of -12.0 cm. Determine the image distance and the diameter of the image. A. By Mirror Equation, we have
59 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. Example Check the answers by drawing an appropriate ray diagram
60 Telescope and Microscope F1F1 d o1 -d i2 L 1 (Objective) d i1 F2F2 d o2 To eye L 2 (Eyepiece)
61 Telescope and Microscope Always converging mirrors or lenses since diverging mirrors or lenses always give smaller images The focal length, F 1, of the objective lens is always longer (shorter) than the focal length,F 2, 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 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!
68 Sodium Lamps, Florescent Tubes, Laser Electrons inside atoms jump from outer orbits to inner orbits and release energy http://hal.physast.uga.edu/~rls/1020/ch6/emission.swf
69 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 Dispersion Due to the difference in refractive index for different colours Angle of deviation Violet deflected most 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 Crown glass
71 Light in diamond White light Violet Red Dispersion + Total internal reflection
72 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 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 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 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 ___. What do you see? red black
76 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.
78 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 ” ?
80 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? 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? 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? Different sizes of water molecule clusters scatter different wavelengths. The overall result is a white cloud. Why are the rain clouds dark?
87 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 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 two different kinds of red-green deficiency and one blue-yellow deficiency red-green deficiencies are by far the most common
90 Think 2 Q. 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 Think 2 A. 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.