1. 2 nd & 3 th N.U.T.S. Workshops Gulu University Naples FEDERICO II University 2 – Reflection, Refraction

2. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 2 Four ways of interaction of light with matter Light interacts with matter by: a)reflection b)refraction c)scattering d)absorption Medium 1Medium 2 Reflection a) b) Refraction c)Scattering d) Absorption All four types of interaction depends on properties of the two media. These properties can be described macroscopically by parameters that summarize the microscopic features of a medium

3. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 3 Reflection of Light A beam of light, (represented as a ray, the incident ray) travels in a medium When it encounters a boundary with a second medium, part of the incident beam is reflected back into the first medium Angle of incidence = Angle of reflection  i =  r Normal Angle of Incidence Angle of Reflection

4. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 4 b)in specular reflection, a smooth surface reflects a light beam undistorted Angles of Reflection and Incidence are Equal c)a rough surface results in diffuse reflection (law of reflection still hold for each individual ray but the normal changes direction point by point)

5. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 5 Specular Reflection: Diffuse Reflection: A parallel beam is reflected as bunch of diverging rays An incident parallel beam is reflected as a parallel beam Reflection is a way to bend light beams!

6. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 6 Well, it depends, what you actually want to get… What type of reflection is more useful?

7. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 7 Which of the below figures shows specular reflection of light from the roadway? With diffuse reflection you see the road; With specular reflection you see the lights of the car reflected off the road. Specular and Diffuse Reflection

8. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 8 Therefore the mirror surface is invisible by itself. There are no point sources of light on mirror surface. Therefore, looking into a mirror you see reflections of objects, not the mirror itself. Mirrors are designed to give specular reflection

9. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 9 (Metallic) Mirrors Materials like metals (with many mobile electrons) can completely reflect light of some colors. Silver is particularly interesting because it reflects light of all colors Gold and copper have a yellowish-brownish color because they reflect greens, yellows and reds light but not blues or violets light Since silver is such a good reflector a coating of silver on glass makes a good (common) mirror. If the silver coating is thin enough the mirror can be made to transmit 50% of the light and to reflect the other 50%. This is called a half-silvered mirror

10. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 10 The Colour of the Light The colour of the light has to do with the wavelength of the light. Visible light is only a very thin wavelength interval of the electromagnetic waves

11. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 11 Electromagnetic Waves

12. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 12 The Numbers of Colours of Visible Light Incorrectly, many text books say that the spectrum of the white light has seven colour. The same for the colours of the rainbow. Avoid the trap of teaching that there is sharp transition from one colour to the following, as the 7 colours schema proposes.

13. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 13 The Infinite Numbers of Colours The number of colours is much more than seven, ideally one could say that there is an infinite number of colours since there are infinite values of wavelength. Practically some intervals of wave length are perceived as common colours (e.g. yellow is the colour perceived for the region around 580 nm) but the number of colours a person can perceive depends on many factors; a painter usually perceive many more colours that a layman.

14. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 14 Law of specular reflection of a ray from a mirror Mirror This angle = this angle The normal to the mirror is an imaginary line drawn perpendicular to it from where the incident beam hits the mirror Normal One of many beams from a light bulb hits Alex's chin. The beam from the light bulb is diffusely reflected off his chin. We show one of the many beams coming off his chin hitting a mirror. –In rays model this is called an incident ray The incident beam undergoes specular reflection off the mirror Draw the normal to the mirror –The angle of incidence = the angle of reflection

15. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 15 To find out how Bob "sees" Alex by looking in the mirror we trace rays which obey the law of reflection Mirror Alex Bob looks at Alex's image How is an image produced in a mirror? Part 1: Ray-tracing Consider an incident ray from Alex's chin which reflects according to the law of reflection at a specific point on the mirror and goes into Bob's eye. A ray from Alex's hair will reflect at one point on the mirror into Bob's eye (and satisfies the law of reflection).

16. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 16 Mirror Alex Bob looks at Alex's image To find the location of his hair in the virtual image we extend any reflected ray from his hair backwards How is an image produced in a mirror? Part 2: The psychology of ray interpretation To find the image of Alex we must learn how Bob’s eye (and our eyes) interpret rays Bob cannot directly know whether the rays entering his eyes have been reflected or not! We interpret all rays coming into our eye as traveling from a fictitious image in a straight line to our eye even if they are reflected rays! To find the virtual (fictitious) image of Alex’s chin we extend each reflected ray backwards in a straight line to where there are no real rays

17. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 17 Virtual image of Alex is behind mirror Mirror Alex When all of the reflected rays from Alex's chin are traced backwards they all appear to come from the virtual image of Alex’s chin –Hence Alex's image is always in the same place regardless of where Bob looks Bob looks at Alex's image Bob sees Alex's image in the same place when he moves his head How is an image produced in a mirror? Part 3: The meaning of a virtual image If we trace rays for every ray from every part of Alex which reflects in the mirror we get a virtual image of the real Alex behind the mirror. It is virtual because there is no light energy there, no real rays reach it, and it cannot be seen by putting a screen at its position!!

18. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 18 For simple (flat) mirrors the image location is therefore predictable without knowing where the observer's eye is and without ray-tracing Mirror Flat Mirrors Image Location

19. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 19 Plane Mirror Exercise 1  Plane Mirror In the overhead view of the figure, the image of the stone seen by observer 1 is at C. Where does observer 2 see the image – at A, at B, at C, at D, at E, or not at all? Position of an image is defined just as well as position of the object!

20. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 20 Looking into a Mirror Looking into a mirror at yourself: for an unobstructed, complete view you only need a mirror, which is a half of your height. Question: What is going to happen to your image in the mirror if you walk away from it? Answer: Nothing other than it will appear to be further away, twice the distance of that from you to the mirror.

21. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 21 An incident light ray reflects in an anti-parallel direction independent of the incident direction! Adding a third mirror at right angles forms a corner cube which returns any beam from which it came Reflecting cubes left on the Moon allows for laser-based measurements of the Moon’s distance to within 15 cm! Corner Reflector From the geometry of the corner Reflector and the law of reflection

22. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 22 Question: Where are the images of Alex in the 2 mirrors? a) At A only b) At B only c) At A and B only d) At C only e) At A, B and C A virtual image can act as a real object and have its own virtual image Mirror Alex Mirror AC B Multiple Mirrors & Virtual Image

23. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 23 “a Mirror Image” Mirrors are known to turn left into right, that is to make the image of your left hand look as your right hand. It is this effect that gives rise to the expression “ A Mirror Image ” (or “ A Specular Image ” )

24. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 24 Chirality The mirrors actually do a very special transformation, known as inversion, which cannot be reduced to translations and rotations… Maybe to turning inside out?... Chiral objects and chiral molecules…

25. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 25 When a ray of light traveling through a transparent medium encounters a boundary leading into another medium, part of the ray is reflected and part of the ray enters the second medium The ray that enters the second medium is bent at the boundary This bending of the ray is called refraction Refraction of Light - 1

26. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 26 Ray  is the incident ray Ray  is the reflected ray Ray is refracted into the lucite Ray  is internally reflected in the lucite Ray is refracted as it enters the air from the lucite Following the Reflected and Refracted Rays Refraction is a way to bend light beams!

27. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 27 The incident ray, the reflected ray, the refracted ray, and the normal all lie in the same plane The angle of refraction, θ 2, depends on the properties of the two media (the refractive index of media n 1, n 2 related to speed of light in the media) Refraction of Light - 2

28. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 28 The angle of refraction depends upon the two materials and the angle of incidence The path of the light through the refracting surface is reversible Refraction occurs because the speeds of light, v 1 and v 2, are different in the two media The index of refraction n, of a medium is defined as Refraction Law (Snell’s Law)

29. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 29 In terms of speeds the law of refraction becomes: Refraction Law and Speeds (of light) Snell’s law of refraction is written in a form symmetric to the incident and refracted beams:

30. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 30 Table of Refraction Index For a vacuum, n = 1

31. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 31 What is the maximum θ 1 for which the beam will emerge through the bottom of the glass cylinder? Example of Snell’s Law

32. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 32 Refraction of Light - 3

33. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 33 Refraction of Light - 4 When light refracts into a material, where the index of refraction is lower, the angle of refraction is greater than the angle of incidence The ray bends away from the normal When light refracts into a material, where the index of refraction is higher, the angle of refraction is less than the angle of incidence The ray bends toward the normal

34. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 34 Example of Refraction Law

35. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 35 A material has an index of refraction that increases continuously from top to bottom. Of the three paths shown in the figure below, which path will be the path of a light ray as it goes through the material? (b). When light goes from one material into one having a higher index of refraction, it refracts toward the normal line of the boundary between the two materials. If, as the light travels through the new material, the index of refraction continues to increase, the light ray will refract more and more toward the normal line. Another Example of Refraction Law

36. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 36 When light refracts into a material, where the index of refraction is lower, the angle of refraction is greater than the angle of incidence The ray bends away from the normal Snell’s law of refraction : We have What if  1 is so large that also That we always have ? Strange Refraction

37. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 37 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 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 A particular angle of incidence will result in an angle of refraction of 90° This angle of incidence is called the critical angle Critical Angle

38. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 38 And what does the fish see beyond the cone?? Reflections back into the water, other creatures of the deep. Fish Watch The fish sees the entire world above surface in a cone of half angle θ c. Looking beyond this cone, it sees ??

39. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 39 Water and air: Air and vacuum: Critical Angles Glass and air:

40. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 40 Critical angle - an angle of incidence which result in an angle of refraction of 90° Cold air and hot air with 10% lower index of refraction It is still 0.4° from the surface! Hot and Cold Air

41. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 41 Optical Illusions

42. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 42 Prisms as excellent reflectors

43. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 43 Total internal reflection at the boundaries between the core and cladding. Optical Fibers At high angles on incidence (grazing angles) only small differences of indices of refraction between the core and cladding are needed. They are made of two different kinds of glass.

44. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 44 The index of refraction in anything except a vacuum depends on the color (wavelength) of the light This dependence of n on λ is called dispersion The index of refraction for a material usually decreases going from violet to re (with increasing wavelength) The angle of refraction when light enters a material depends on the color (wavelength) of the light Violet light refracts more than red light when passing from air into a material Dispersion

45. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 45 Prism Dispersion

46. 2- Reflection, Refraction 2nd & 3th NUTS Workshop ( Jan 2010) 46 Prism Spectrometer A prism spectrometer uses a prism to cause the wavelengths to separate The instrument is commonly used to study wavelengths emitted by a light source