Presentation is loading. Please wait.

Presentation is loading. Please wait.

Chapter 22, 23 Ray Optics, Mirrors, Lenses, Image and Optical Instruments.

Similar presentations


Presentation on theme: "Chapter 22, 23 Ray Optics, Mirrors, Lenses, Image and Optical Instruments."— Presentation transcript:

1 Chapter 22, 23 Ray Optics, Mirrors, Lenses, Image and Optical Instruments

2 A Brief History of Light 1000 AD 1000 AD It was proposed that light consisted of tiny particlesIt was proposed that light consisted of tiny particles Newton Newton Used this particle model to explain reflection and refractionUsed this particle model to explain reflection and refraction Huygens Huygens Explained many properties of light by proposing light was wave-likeExplained many properties of light by proposing light was wave-like

3 A Brief History of Light, cont Young Young Strong support for wave theory by showing interferenceStrong support for wave theory by showing interference Maxwell Maxwell Electromagnetic waves travel at the speed of lightElectromagnetic waves travel at the speed of light

4 A Brief History of Light, final Planck Planck EM radiation is quantizedEM radiation is quantized Implies particles Implies particles Explained light spectrum emitted by hot objectsExplained light spectrum emitted by hot objects Einstein Einstein Particle nature of lightParticle nature of light Explained the photoelectric effectExplained the photoelectric effect

5 C = f  C: speed of light C = 3 x 10 8 m/s in vacuum In other medium, the speed of light is smaller than in vacuum. EM wave can travel in the absence of medium.

6 nano = x 10 8 = f

7 How do we see an object? Detection of light directly emitted by object Detection of light directly emitted by object Detection of light reflected by object (most common) Detection of light reflected by object (most common)

8 Ray Optics – Using a Ray Approximation Light travels in a straight-line path in a homogeneous medium until it encounters a boundary between two different media Light travels in a straight-line path in a homogeneous medium until it encounters a boundary between two different media The ray approximation is used to represent beams of light The ray approximation is used to represent beams of light A ray of light is an imaginary line drawn along the direction of travel of the light beams A ray of light is an imaginary line drawn along the direction of travel of the light beams

9 The Index of Refraction Speed of light c= 3x 10 8 m/s in vacuum. Speed of light c= 3x 10 8 m/s in vacuum. Speed of light is different (smaller) in other media Speed of light is different (smaller) in other media The index of refraction, n, of a medium can be defined The index of refraction, n, of a medium can be defined

10 Index of Refraction, cont For a vacuum, n = 1 For a vacuum, n = 1 For other media, n > 1 For other media, n > 1 n is a unitless ratio n is a unitless ratio Normal air: Water: 1.33 Flint glass: 1.66 Diamond 2.42

11 Reflection of Light A ray of light, the incident ray, travels in a medium 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 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 mediumThis means it is directed backward into the first medium

12 Specular Reflection Specular reflection is reflection from a smooth surface Specular reflection is reflection from a smooth surface The reflected rays are parallel to each other The reflected rays are parallel to each other All reflection in this text is assumed to be specular All reflection in this text is assumed to be specular

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

14 Law of Reflection The normal is a line perpendicular to the surface The normal is a line perpendicular to the surface It is at the point where the incident ray strikes the surfaceIt is at the point where the incident ray strikes the surface The incident ray makes an angle of θ 1 with the normal The incident ray makes an angle of θ 1 with the normal The reflected ray makes an angle of θ 1 ’ with the normal The reflected ray makes an angle of θ 1 ’ with the normal

15 Law of Reflection, cont The angle of reflection is equal to the angle of incidence The angle of reflection is equal to the angle of incidence θ 1 = θ 1 ’ θ 1 = θ 1 ’

16 Reflection and Mirrors 11  1  1 =  1 Law of reflection Specular ReflectionDiffuse Reflection

17 When we talk about an image, start from an ideal point light source. Every object can be constructed as a collection of point light sources. p |q| IMAGE Image forms at the point where the light rays converge. When real light rays converge  Real Image When imaginary extension of L.R. converge  Virtual Image VIRTUAL Only real image can be viewed on screen placed at the spot.

18 p |q| IMAGE VIRTUAL For plane mirror: p = |q| How about left-right? Let’s check? p: object distance q: image distance

19 Spherical Mirror concaveconvex Optical axis R: radius of curvature Parallel light rays: your point light source is very far away. f: focal length = R/2 focal Point Focal point: (i) Parallel incident rays converge after reflection (ii) image of a far away point light source forms (iii) On the optical axis

20 Reflected rays do not converge:  Not well-defined focal point  not clear image Spherical Aberration f = R/2 holds strictly for a very narrow beam. Parabolic mirror can fix this problem.

21 f p q Real Image P > q Case 1: p > R

22 p = q Real Image Case 2: p = R

23 p < q Real Image Case 3: f < p < R

24 q = infinite Case 4: p = f

25 q < 0 Virtual Image Case 5: p < f

26 Mirror Equation 1/p + 1/q = 1/f For a small object, f = R/2 (spherical mirror) 1/p + 1/q = 2/R Alert!! Be careful with the sign!! Negative means that it is inside the mirror!! p can never be negative (why?) negative q means the image is formed inside the mirror How about f?

27 For a concave mirror: f > 0 Focal point inside the mirror f < 0 1/p + 1/q = 1/f < 0 : q should be negative.

28 1/p + 1/q = 1/f < 0 : q should be negative. All images formed by a convex mirror are VIRTUAL. Magnification, M = -q/p Negative M means that the image is upside-down. For real images, q > 0 and M < 0 (upside-down).

29 Example: An object is 25 cm in front of a concave spherical mirror of radius 80 cm. Determine the position and characteristics of the image. 1/p + 1/q = 1/ff = R/2 = 40 cm Object is at the center: p = 25 cm 1/q = 1/40 – 1/25 = q = cm < 0 (Virtual Image, 66.7 cm behind mirror) M = -q/p = -(-66.7)/25 = 2.7 Erect, 2.7 times the size of the object

30 Example: What kind of spherical mirror must be used, and what must be its radius, in order to give an erect image 1/5 as Large as an object placed 15 cm in front of it? M = -q/p  -q/p=1/5 So q = -p/5 = -15/5 = -3 cm 1/p + 1/q = 1/f  1/15 - 1/3 = 1/f 1/f = (1-5)/15 f = -15/4 = cm R = 2 f = -7.5 cm Convex

31 Example: Where should an object be placed with reference to a concave spherical mirror of radius 180 cm in order to form a Real image having half its size? M = -q/p  -q/p=-1/2 So q = p/2 f = R/2 = 90 cm 1/p + 1/q = 1/f  1/p + 2/p = 1/f 3/p=1/90 p = 270 cm

32 Refraction Details, 1 Light may refract into a material where its speed is lower Light may refract into a material where its speed is lower The angle of refraction is less than the angle of incidence The angle of refraction is less than the angle of incidence The ray bends toward the normalThe ray bends toward the normal

33 Refraction Details, 2 Light may refract into a material where its speed is higher Light may refract into a material where its speed is higher The angle of refraction is greater than the angle of incidence The angle of refraction is greater than the angle of incidence The ray bends away from the normalThe ray bends away from the normal

34 Snell’s Law 11 11 22 n 1 sin  1 = n 2 sin  2 All three beams (incident, reflected, and refracted) are in one plane. n > 1

35 water 11 11 22  1 >  2

36

37 Total Internal Reflection Total internal reflection can occur when light attempts to move from a medium with a high index of refraction to one with a lower index of refraction Total internal reflection can occur when light attempts to move from a medium with a high index of refraction to one with a lower index of refraction Ray 5 shows internal reflectionRay 5 shows internal reflection

38 Critical Angle A particular angle of incidence will result in an angle of refraction of 90° A particular angle of incidence will result in an angle of refraction of 90° This angle of incidence is called the critical angleThis angle of incidence is called the critical angle

39 Critical Angle, cont For angles of incidence greater than the critical angle, the beam is entirely reflected at the boundary For angles of incidence greater than the critical angle, the beam is entirely reflected at the boundary This ray obeys the Law of Reflection at the boundaryThis ray obeys the Law of Reflection at the boundary Total internal reflection occurs only when light attempts to move from a medium of higher index of refraction to a medium of lower index of refraction Total internal reflection occurs only when light attempts to move from a medium of higher index of refraction to a medium of lower index of refraction

40 Examples of critical angles (relative to vacuum) SubstanceNCritical angle Vacuum  Air  Ice  Water  Ethyl Alcohol  Glycerine  Crown glass  Sodium chloride  Quartz  Heavy flint glass  Tooth enamel  Sapphire  Heaviest flint glass  Diamond 

41 How could fish survive from spear fishing? Fish vision  f = 2 c  c = sin -1 (1/1.33) = 49

42 n core n clad >

43

44 Lenses Converging lens Diverging lens

45 Thin Lenses A thin lens consists of a piece of glass or plastic, ground so that each of its two refracting surfaces is a segment of either a sphere or a plane A thin lens consists of a piece of glass or plastic, ground so that each of its two refracting surfaces is a segment of either a sphere or a plane Lenses are commonly used to form images by refraction in optical instruments Lenses are commonly used to form images by refraction in optical instruments

46 Thin Lens Shapes These are examples of converging lenses These are examples of converging lenses They have positive focal lengths They have positive focal lengths They are thickest in the middle They are thickest in the middle

47 More Thin Lens Shapes These are examples of diverging lenses These are examples of diverging lenses They have negative focal lengths They have negative focal lengths They are thickest at the edges They are thickest at the edges

48 Glass lens (n G = 1.52)

49 The focal length of a lens is determined by the shape and material of the lens. Same shape lenses: the higher n, the shorter f Lenses with same n: the shorter radius of curvature, the shorter f Typical glass, n = 1.52 Polycarbonate, n = 1.59 (high index lens) Higher density plastic, n ≈ 1.7 (ultra-high index lens)

50 Rules for Images Trace principle rays considering one end of an object off the optical axis as a point light source. A ray passing through the focal point runs parallel to the optical axis after a lens. A ray coming through a lens in parallel to the optical axis passes through the focal point. A ray running on the optical axis remains on the optical axis. A ray that pass through the geometrical center of a lens will not be bent. Find a point where the principle rays or their imaginary extensions converge. That’s where the image of the point source.

51 two focal points: f 1 and f 2 Parallel rays: image at infinite!!

52 Virtual image Magnifying glass

53 Lens equation and magnification 1/p + 1/q = 1/f M = -q/p This eq. is exactly the same as the mirror eq. Now let’s think about the sign. positivenegative p real object virtual object (multiple lenses) q real image (opposite side of object) virtual image (same side of object) f for converging lens for diverging lens M erect image inverted image

54 two focal points: f 1 and f 2 Parallel beams: image at infinite!! 1/p + 1/q = 1/f 1/2f + 1/q = 1/f 1/q = 1/2f M = -q/p = -1 1/p + 1/q = 1/f 1/f + 1/q = 1/f 1/q = 0  q = infinite

55 Virtual image Magnifying glass 1/p + 1/q = 1/f 2/f + 1/q = 1/f 1/q = -1/f M = -(-f)/(f/2) = 2

56 Example: A thin converging lens has a focal length of 20 cm. An object is placed 30 cm from the lens. Find the image Distance, the character of image, and magnification. positive f f = 20, p = 30 1/q = 1/f – 1/p = 1/20 – 1/30 = 1/60 q = 60 M = -q/p = -60/30 = -2 real image (opposite side) < 0 inverted

57 Magnifier Consider small object held in front of eye Consider small object held in front of eye Height yHeight y Makes an angle  at given distance from the eyeMakes an angle  at given distance from the eye Goal is to make object “appear bigger”: ' >  Goal is to make object “appear bigger”: ' >  y 

58 Magnifier Single converging lens Single converging lens Simple analysis: put eye right behind lensSimple analysis: put eye right behind lens Put object at focal point and image at infinityPut object at focal point and image at infinity Angular size of object is , bigger!Angular size of object is , bigger! Outgoing rays Rays seen coming from here  f f Image at Infinity  y

59 (angular) Magnification One can show One can show f must be in cm f must be in cm

60 Example Find angular magnification of lens with f = 5 cm Find angular magnification of lens with f = 5 cm

61 Combination of Thin Lenses, example

62 Telescope View Distant Objects View Distant Objects (Angular) Magnification M=f obj /f eye (Angular) Magnification M=f obj /f eye Increased Light Collection Increased Light Collection Large Telescopes use Mirrors Large Telescopes use Mirrors

63


Download ppt "Chapter 22, 23 Ray Optics, Mirrors, Lenses, Image and Optical Instruments."

Similar presentations


Ads by Google