Physics 1230: Light and Color Ivan I. Smalyukh, Instructor

1. Office: Gamow Tower, F-521 • Email: • ivan.smalyukh@colorado.edu • Phone: 303-492-7277 • Lectures: • Tuesdays & Thursdays, • 3:30 PM - 4:45 PM • Office hours: • Mondays & Fridays, • 3:30 PM – 4:30 PM • TA: Jhih-An Yang • jhihan.yang@colorado.edu Physics 1230: LightandColorIvan I. Smalyukh, Instructor Class # 6

2. Physics 1230: Light and Color Lecture 6: Reading: Finish Chapter 2 HW due today; New HW assigned (due in 2 weeks);

3. Chapter 2 – Geometrical Optics Geometrical optics is the theory of RAYS (straight lines) and how they reflect and refract (bend). Lots of similarity to GEOMETRY of lines and triangles. • Shadows • Reflection • Refraction • Dispersion Main Topics We are here

4. Chapter 2 – Geometrical Optics • Shadows • Reflection • Specular or diffuse • Equal angle rule • Mirror images, ray tracing • Refraction • Dispersion • Point source or diffuse source • Umbra and penumbra • How tall is my shadow? • Pinhole camera We are here

5. What can happen to incoming light Transmitted Glass Silver, water Reflected (including scattering) Black pavement absorbed Or any partial combination of these things

6. Specular or diffuse? Diffuse reflection (paper) Specular reflection (mirror) Diffuse transmission(wax paper)

7. qi qr Normal Mirror Equal angle rule (specular reflection) qi = angle of incidence qr = angle of reflection qi = qr is specular reflection A normal is a line perpendicular to the surface. Reflected Ray Incident Ray

8. Metals reflect all waves below a certain frequency This plasma frequency varies from metal to metal Silver reflects light waves at all visible frequencies Gold and copper have a yellow-brownish color because they reflect greens, yellows and reds but not blues or violets Plasma frequency of silver Plasma frequency of gold Plasma frequency of copper Metals with mobile electrons can cancel out the light field in forward direction - only reflection

9. Since silver is such a good reflector a coating of silver on glass - 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 A half-silvered mirror used with proper lighting can show objects on one side or the other of the mirror What is a mirror?

10. The ray from the light bulb is diffusely reflected off chin. We show one of the many rays coming off his chin hitting a mirror. Normal This angle = this angle • The incident ray undergoes specular reflectionoff the mirror • Note the reflected ray The normal to the mirror is an imaginaryline drawn perpendicular to it from where the incident ray hits the mirror Law of specular reflection of a ray from a mirror Mirror • Draw the normal to the mirror • The angle of incidence = the angle of reflection

11. To find out how Bob "sees" Alex by looking in the mirror we trace rayswhich obey the law of reflection Mirror How is an imageproduced in a mirror?Part 1: Ray-tracing Bob looks atAlex's image Alex

12. We interpret all rays coming into our eye as traveling from a fictitiousimage in a straight line to our eye even if they are reflected rays! Mirror The psychology of image interpretation Bob looks atAlex's image Alex • Example: To find the location of his hair in the virtual image we extend any reflected ray from hair backwards

13. 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. Bob looks atAlex's image Mirror Bob sees Alex's imagein the same placewhen he moves his head Virtual image of Alexis behind mirror The meaning of a virtual image Alex • Alex's virtual image is the same size as the real Alex

14. Let’s look at specular reflection

15. Ray reflection practice retroreflector

16. Retroreflectors • Bike reflectors • Roadside reflectors • Measuring distance to moon?

17. Half-silvered 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 • A half-silvered mirror used with proper lighting can show objects on one side or the other of the mirror Glass is like a 4% silvered mirror

18. Image in a mirror • If a point on the object is distance X in front of the mirror, the same point in the image appears to be distance X in back of the mirror, or Xobject = Ximage. • The image point is on the normal (extended) from the object to the mirror. Mirror normal extended Xobject Ximage

19. Ray tracing: Draw the image, then the rays First: draw rays from image to eyes Viewed from the side. Mirror Xobject Ximage

20. Ray tracing: Draw the image, then the rays First: draw rays from image to eyes Second: draw rays from mirror to object Mirror Xobject Ximage qi = qr happens automatically using this method. Demo on board

21. Right side up image? The top ray goes to the top of the bottle. It is right side up. Mirror Xobject Ximage qi = qr happens automatically using this method.

22. Right side up image? The top ray goes to the bottom of the bottle. It is upside down. Xobject Extension Mirror (to do this drawing, the mirror must be extended) Ximage qi = qr happens automatically using this method.

23. Bottle on its side Viewed from the side. Mirror (to do this drawing, the mirror must be extended) qi = qr happens automatically using this method.

24. Mirror Mirror Mirror Mirror For simple (flat) mirrors the image location is therefore predictable without knowing where the observer's eye is and without ray-tracing

25. Periscope • The image of the bottle in the lower mirror is: • Inverted • Not inverted • Something else mirror Original OBJECT mirror

26. Periscope? extension The first IMAGE Original OBJECT

27. Periscope? extension The second IMAGE

28. Periscope? • The image of the bottle in the lower mirror is: • Inverted • Not inverted • Something else

29. Question: Where are the images of Alex in the 2 mirrors? At A only At B only At A and B only At C only At A, B and C B A C Multiple mirrors - a virtual image can act as a real object and have its own virtual image Mirror Alex Mirror The virtual image at A acts as an object to produce the virtual image of C. It acts as an intermediate image. More precisely it is the red rays which reflect as green rays.

30. Is the writing reversed? (Two mirrors, viewed from above) AR • YES • NO

31. Is the writing reversed? AR ЯA

32. Is the writing reversed? AR AR extension ЯA

33. Is the writing reversed? AR AR • YES • NO ЯA

34. Lec. 6: Ch. 2 - Geometrical Optics Shadows Reflection Refraction Dispersion We are here 34

35. Refraction • Index of refraction: n = c / v • Ray in water is closer to the normal • Total internal reflection • Mirages

36. Part of the wave can be transmitted into the second medium while part is reflected back You can hear someone from outside the pool when you are underwater because sound waves are transmitted from the air through the water (withdifferent speed in each). When light waves are incident on a glass slab they are mostly transmitted but partly reflected (about 4%)! Reflection of waves occurs where the medium of propagation changes abruptly Glass slab • Is the speed of light in the glass slab the same as in the free space??? • No.

37. The speed of an electromagnetic (EM) wave is constant (for every wavelength) in empty space! The speed of light is slower than c in glass, water and other transparent media (Einstein showed that light can never travel faster than c) The speed of light in a medium is v = c/n, where n is a number larger than one called the index of refraction n = 1.5 for glass n = 1.3 for water n = 1.5 for vegetable oil Light is reflected and transmitted at a boundary because When a light wave travels in a medium the electric field of the light jiggles the electrons in the medium. This produces new electric fields which can cancel or addto the original light wave both in the forward and backward directions These are the transmitted and reflected light waves How can reflection require that the speed of the wave changes? We thought the speed of light was alwaysc = 3 x 108 m/s!

38. Refractive indices of different materials • Can we see a glass rod immersed into the oil with the same refractive index? • A. Yes • B. No Demo

39. Got to here on Thursday 6/10/2010

40. A ray going from a fast medium to a slow medium bends towards the normal to the surface of the medium A ray going from a slow medium to a fast medium bends away from the normal to the surface of the medium The speed of light in a medium is v = c/n, where n is a number larger than one called the index of refraction andc = 3 x 108 m/s n = 1.3 for glass n = 1.5 for water Hence, a ray going into a medium with a higher index of refraction bends towards the normal and a ray going into a medium with a lower index of refraction bends away from the normal Refraction is the bending of a ray after it enters a medium where its speed is different Air (fast medium) Normal Glass or water(slow) nair< nwater 1.0008 < 1.33 Air (fast medium) Normal Glass or water(slow) How about light going into a medium with exactly the same index of refraction?

41. Ray-bending together with our psychological straight-ray interpretation determine the location of images underwater normal • The precise amount of bending is determined by the law of refraction (sometimes called Snell's law): • ni sinqi = nt sinqt • Here, qi = angle between incident ray and normal, • and qt = angle between transmitted ray and normal • ni and nt are the indices of refraction in the medium containing the incident ray and in the medium containing the transmitted ray • Fig 2.49 Fisherman and fish transmitted ray image of fish for someone out of water incident ray fish • In order to observe the fish from outside the water a transmitted ray must enter your eye. • You will think it comes from a point obtained by tracing it backwards, • Extend any 2 of the many many transmitted rays from the fish backwards to find the image of the fish (where they intersect). • The location of that image will be the same for any observer outside of the water.

42. What we see and how different it can be from what it seems to be • The woman will see the underwater part of body being • Smaller than it really is; • Much larger than it really is; • Of natural size;

43. What we see and how different it can be from what it seems to be • The woman will see the underwater part of body being • Smaller than it really is; • Much larger than it really is; • Of natural size;

44. What we see and how different it can be from what it seems to be • The boy will see the underwater part of body being • Smaller than it really is; • Much larger than it really is; • Of natural size;

45. Criticalangle Total internal reflection is an extreme case of a ray bending away from the normal as it goes from a higher to a lower index of refraction medium (from a slower to a faster medium) Just below the critical angle for total internal reflection there is a reflected and a transmitted (refracted) ray Normal Air (fast medium) Glass or water(slow) Just above the critical angle for total internal reflection there is a reflected ray but no transmitted (refracted) ray Normal Glass or water(slow) For the glass-air interface

46. Total internal reflection • The precise amount of bending is determined by the law of refraction (sometimes called Snell's law): • ni sinqi = nt sinqt • Here, qi = angle between incident ray and normal, • and qt = angle between transmitted ray and normal • ni and nt are the indices of refraction in the medium containing the incident ray and in the medium containing the transmitted ray • Show that the internal reflection is a consequence of the Snell’s law

47. What we see and how different it can be from what it seems to be • If the critical angle condition is satisfied, will the boy see the part of body above water: • yes; • No. • Extra Credit: Refractive index of water is 1.33; What is the critical angle for the case of air-water interface?