1. Physics 1230: Light and Color Ivan I. Smalyukh, Instructor 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 Class # 8

2. Which path takes the least time, from P to Q? (You throw a ball in the water, how will your dog run to get it quickest?) Water (have to do the doggy paddle) We’ll start out with a clicker question

3. refraction incident Which path takes the least time, from P to Q? (You throw a ball in the water, how will your dog run to get it quickest?) reflection Analogy with bending of rays at the interface of 2 media?

4. reflection refraction incident

5. I II

6. I

7. θ critical n 1 sin θ 1 = n 2 sin θ 2 Here, n 1 =1, sin θ 1 =1 so sin θ crit =1/n I II θ 1 =90 OPTIONAL MATH:

8. θ  θ critical I II Total Internal Reflection!

9. 99 Lec. 6: Ch. 2 - Geometrical Optics 1.Shadows 2.Reflection 3.Refraction 4.Dispersion We are here

10. 10 Dispersion Dispersion: refraction (bending) of different colors by different amounts. Light bulbSpectrumPrism

11. 11 Index n varies with color wavelengthn (index of refraction) 300 nm (UV)1.486 (bent more) 500 nm1.462 700 nm (deep red)1.455 (bent less) Quartz glass

12. Prisms demonstrate refraction and dispersion 12 Reflection at a transparent surface occurs because the n values are different. Only a few percent of the light is reflected this way.

13. 13 Rainbows: dispersion & by water raindrops 180 degree rainbow is possible. Double rainbow is possible. Both together is very rare.

14. 14 How we see a rainbow big raindrops Sun (behind you) this ray not seen these rays are seen

15. Raindrop Dispersion occurs here during refraction white light comes in Reflections Dispersion occurs here during refraction A spectrum of colors comes out The colors are spread inside the prism as well as outside. The colors start to spread inside the raindrop.

16. 16 How we see two rainbows sun total internal reflection two total internal reflections

17. 17

18. 18 Waterfall droplets create rainbows

19. 19 Rainbows: dispersion by water raindrops 180 degree rainbow is possible. Double rainbow is possible. Both together is very rare.

20. 20 Fogbow (sun behind you) (sun in front of you) 22 degrees, center to edge A fog bow is a similar phenomenon to a rainbow, however, as its name suggests, it appears as a bow in fog rather than rain

21. 21 What is a mirage? A mirage is an image (often upside down) caused by heated air refracting rays. n falls from 1.003 at room temperature to 1.002 when the temperature goes up 100 C.

22. 22 Inferior mirage (image below the object) sky appears to be on the ground The ray bends from the low n material toward the high n material.

23. 23 Superior mirage (image above the object)

24. Mirages occur if the index of refraction increases as the ray goes deeper into the slower medium? In our analogy with the marching soldiers this means they go slower and slower as they advance. Imagine the mud getting deeper and deeper as they advance. The ray keeps bending more and more towards the normal as the mud deepens In the limit as the muddier transitions become more gradual the refracted ray looks curved Incident ray Muddy Muddier Muddiest

25. "in the early morning sun the islands are inverted in mirage, and seem to hang there, suspended between sky and water." James Morris, in Heavens Command, describes a view from Grosse Isle, Gulf of St. Lawrence n decreases at higher altitudes: the ray coming from the island continuously bends away from the (vertical) normal. At the top of its trajectory critical reflection occurs and the reflected ray then refracts towards the normal on its way down until it reaches the eye. The brain then interprets this curved ray as a straight ray tangent to the curved one at the point of entry into the eye. Hence, the island appears to be in the sky. Hot air, low density, index of refraction closer to 1, FAST medium Grosse Isle Image of Grosse Isle Sky Water Grosse Isle Sky Cool air, higher density, index of refraction > 1, SLOW medium Cool air Hot air

26. A closer look at the curved ray from Grosse Isle to the eye of the beholder Slow Fast Muddy Muddiest At the top of its trajectory the ray undergoes total internal reflection Think of marching soldiers entering increasingly muddy terrain

27. 27

28. 28 Total internal reflection makes fiber optic communication possible The ray bends from the low n material toward the high n material. Demo: glass tube, laser pointer

29. Time for a demo! 29 If we pull the cork, and water starts to pour out of the tank, the laser light will… A)Shine across the room to the wall. B)Stay entirely inside the tank C)Stay entirely inside the water stream D)Something else happens.

30. 30 This illustration appears in "La Nature" magazine in 1884. Demo: tank

31. 31 Lec. 6: Ch. 2 - Geometrical Optics 1.Shadows 2.Reflection 3.Refraction 4.Dispersion Move to Chap. 3 1.Virtual images We are here

32. 32 Question Consider the rays and the observer as shown below. What does the observer perceive? A)A red arrow with many blue arrows. B)A confusing image of light from many directions C)A bright point of light D)A uniformly lit background

33. 33 What does the observer SEE??! How does the “eye” know the object is here? and not here? 1)Only the rays that enter the eye.

34. 34 What does the observer SEE??! How does the “eye” know the object is here? and not here? 1)Only the rays that enter the eye. 2)Several rays enter. The eye effectively traces nearby rays back toward their intersection; it “sees” an image at that intersection.

35. 35 A Question Consider the rays and the observer as shown below. What does the observer perceive? A)A red arrow with many blue arrows. B)A confusing image of light from many directions C)A bright point of light D)A uniformly lit background

36. 36 How does the eye make sense of all these light rays? You are not aware of all those rays, but rather of 3 points of light A)Uniform background B)Several points of light C)This is not an image D)No idea.

37. 37 What is an image? X object X image Extension In this context, an image is a point from which light rays emerge in a range of directions: (the image doesn’t necessarily emit or produce the light)

38. 38 object virtual image Virtual image: (p. 73) The light appears to come from the virtual image, but in fact does not come from there. Real image: (p. 84) The light comes to you from a real image. You may need a screen to see it. a real image:

39. 39 Lec. 6: Ch. 2 - Geometrical Optics 1.Shadows 2.Reflection 3.Refraction 4.Dispersion Move to Chap. 3 We are here