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 # 7

2. Physics 1230: Light and Color Lecture 7: Reading: Finish reading Chapter 2 Demos

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

4. Part of the wave can be transmitted into the second medium while part is reflected back When light waves are incident on a glass slab they are mostly transmitted but partly reflected (about 4%)! Reflection at transparent material interfaces Glass slab • Is the speed of light in the glass slab the same as in the free space??? • No.

5. 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 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 How can reflection require that the speed of the wave changes? c = 3 x 108 m/s! Glass slab

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

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

8. Air Water Air Water What is refraction? • Refraction is bending of a ray at a boundary due to a different speed of light in the substance. Demo: tank, laser pointer

9. The incident ray has peaks and troughs in the wave. The wave that hits the material first slows down. Causes the wave to bend. Just like waves hitting the shoreline. Analogy with car driving (twee wheels on a slippery part of the road) … Why does the ray bend? Higher index Higher index High index Incident ray

10. Air Water Air Water Why does the ray bend? • Refraction is bending of a ray at a boundary due to a different speed of light in the substance. Demo: tank, laser pointer Towards or away from the interface

11. Indices of refraction v = c / n

12. Clicker Question A material with a larger index of refraction, n, has a: • Faster speed of light • Slower speed of light • Depends upon the particular material. Recall: v = c / n

13. Air Water Snell’s law n1 sin q1 = n2 sin q2 n1 = 1.0003 q1 q2 n2 = 1.33

14. A ray going from a fast medium to a slow medium bends towards the normal A ray going from a slow to a fast medium bends away from the normal Hence, a ray going into a medium with a higher n bends towards the normal & a ray going into a medium with a lower n bends away from the normal Refraction - 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 n?

15. Light coming out of water: 2 possibilities Refraction out OR Total internal reflection! Refracted Air Water Reflected internally Case 2, far from normal incidence(internal reflection) Case 1near normal incidence (light comes out) The critical angle is about 42 degrees. Demo: tank, laser pointer

16. Total internal reflection • The amount of bending is determined by the law of refraction (sometimes called Snell's law): • ni sinqi = nt sinqt • Show that the internal reflection is a consequence of the Snell’s law

17. Criticalangle Total internal reflection - extreme case of a ray bending away from the normal as it goes from higher to lower n Just below the critical angle for total internal reflection there is a reflected & a transmitted ray Normal Air (fast medium) Glass or water(slow) Above the critical angle for total internal reflection there is reflected ray but no transmitted ray Normal Glass or water(slow) For the glass-air interface

18. Ray-bending & our psychological straight-ray interpretation normal • 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. transmitted ray image of fish for someone out of water incident ray fish

19. What we see and how different it can be from what it seems to be Two observers, one above the water and one under the water, view an object (fellow to the left)… • The woman will see the underwater part of body being • Smaller than it really is; • Much larger than it really is; • Of natural size;

20. 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;

21. What we see and how different it can be from what it seems to be Two observers, one above the water and one under the water, view an object (fellow to the left)… • The boy will see the underwater part of body being • Smaller than it really is; • Much larger than it really is; • Of natural size; • Something else.

22. 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 upper part of the man’s body? • Yes; • No.

23. 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; • Something else. Legs up and down!

24. Lec. 6: Ch. 2 - Geometrical Optics Shadows Reflection Refraction Dispersion We are here 24

25. Spectrum Prism Light bulb Dispersion Dispersion: refraction (bending) of different colors by different amounts.

26. Index n varies with color Quartz glass

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

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

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

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

32. How we see two rainbows three total internal reflections sun two total internal reflections

33. Waterfall droplets create rainbows

35. Fogbow(sun behind you) (sun if front of you) 22 degrees, center to edge

36. 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.

37. 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.

38. Superior mirage (image above the object)

40. Sun pillar and sun dogs How do these work?

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

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

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

44. Lec. 6: Ch. 2 - Geometrical Optics Shadows Reflection Refraction DispersionMove to Chap. 3 We are here 44