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 # 10

2. Announcements HW #2 due today HW #3 assigned – Due Sept 29; Exam #1 - October 11 Overview of Exam #1 material – Sept 29;

3. 3 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 from the image (rather than appearing to come from there). You may need a screen to see it. a real image: Light appears to come from behind mirror

4. 4 1.All rays incident parallel to the C- F axis are reflected so that they appear to be coming from the focal point F 2.All rays that (when extended) pass through the center C are reflected back on themselves. 3.All rays that (when extended) pass through the focal point F are reflected back parallel to the axis 2 C F 1 3 Three easy rules for convex, spherical mirrors

5. 5 1.All rays incident parallel to the C-F axis are reflected through the focal point F 2.All rays that pass through the center C are reflected back on themselves. 3.All rays that pass through the focal point F are reflected back parallel to the axis 2 1 3 C F Three easy rules for concave, spherical mirrors

6. 6 Ray tracing: concave mirror object outside center CF

7. 7 CF Questions: (A) OR (B) Is the image real or virtual? Is the image larger or smaller than the object? Is the image right-side-up or upside-down? How could a mirror be useful when used like this?

8. 8 Ray tracing: concave mirror object between center and focus CF Questions: Is the image real or virtual? Is the image larger or smaller than the object? Is the image right-side-up or upside-down? How could a mirror be useful when used like this?

9. 9 Ray tracing: concave mirror object between focus and mirror CF

10. 10 Ray tracing: concave mirror object between focus and mirror CF Questions: Is the image real or virtual? Is the image larger or smaller than the object? Is the image right-side-up or upside-down? How could a mirror be useful when used like this?

11. 11 Convex spherical mirror Concave spherical mirror, object outside center Concave spherical mirror, object between center and focus Concave spherical mirror, object between focus and mirror For each case, you can now answer: Image larger/smaller? Virtual? Where? AND you can answer these question by ray tracing with three simple rules We now have many distinct cases

12. 12 On to lenses: first, review refraction air n=1 (nearly) v = c (nearly) glass, e.g. n=1.5 v = c/n < c Rays bend toward normal when entering slower medium (larger n), away from normal when entering faster medium (smaller n).

13. 13 Soldiers in mud analogy pavement (soldiers go fast) deep mud (soldiers march slower through deep mud) “fronts” “rays” (perpendicular to fronts) As soldiers slow down, space between them narrows A trick to remember which way rays bend

14. 14 Review: Dispersion Dispersion: refraction (bending) of different colors by different amounts. Light bulbSpectrumPrism

15. 15 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

16. 16 Ray tracing with lenses n>1 Rays entering “slower” material bend toward normal Rays entering “faster” material bend away from normal n=1 Brute force ray tracing: 1.As long as ray stays in same medium, it goes straight. 2.At each interface to a different medium, use Snell’s law to calculate how it will bend. Go back to 1. This gets tedious! Notice: This lens shape seems to focus the rays!

17. 17 F F Thin convex (converging) lens foci } focal length If the glass surface is nearly a section of a sphere, it will FOCUS parallel rays. A THIN LENS is very thin compared to the focal length. Then we can simplify the treatment with THREE NEW RULES.

18. 18 1)A ray parallel to the axis is deflected through the focus on the other side 2)A ray through the center of the lens continues undeviated 3)A ray coming from the focus on one side goes out parallel to the axis on the other F’F’ F Ray might have to be extended 1 2 3 3 Thin convex lens: three easy rules for ray tracing foci } focal length

19. 19 Note light-focusing property of convex (converging) lens a good light collector or solar oven; can also fry ants with sunlight, but please don’t do that unless you’re going to eat them

20. 20 Note light-dispersing property of convex lens The “backwards” light collector: create a collimated light beam

21. 21 Ray Tracing foci (focuses?) Where will this ray go?

22. 22 Ray Tracing Where will this ray go? Suppose it’s emitted from this object foci (focuses?)

23. 23 Ray Tracing Where will this ray go? Suppose it’s emitted from this object foci (focuses?) We know where these 3 rays go, using the simple ray rules

24. 24 Ray Tracing Where will this ray go? Suppose it’s emitted from this object foci (focuses?) We know where these 3 rays go, using the simple ray rules Amazing property of this lens: all rays from the object will converge to the same point

25. 25 Ray Tracing Where will this ray go? Suppose it’s emitted from this object foci (focuses?) We know where these 3 rays go, using the simple ray rules Amazing property of this lens: all rays from the object will converge to the same point

26. 26 Ray Tracing: thin lens, object outside focus Amazing property of this lens: all rays from the object will converge to the same point (the image) See how the rays emerge from this point (the image)?

27. 27 Ray Tracing: thin lens, object outside focus Amazing property of this lens: all rays from the object will converge to the same point (the image) Eye sees an image here. The Lens acts as our “Magic Ray Machine”, creating the rays to produce an image.

28. 28 A Question In this case, the image is: Eye sees an image here. A)Virtual B)Real Real because the light rays really go through the image. You can put a screen there to see it.

29. A Question 29 Two point sources of light are imaged onto a screen by a converging lens. The images are labeled 1 and 2. You slide a mask over the left half of the lens. What happens to the images? A)Image 1 vanishes B)Image 2 vanishes C)Something else happens

30. A Question 30 Two point sources of light are imaged onto a screen by a converging lens. The images are labeled 1 and 2. You slide a mask over the left half of the lens. What happens to the images? A)Image 1 vanishes B)Image 2 vanishes C)Something else happens The image gets dimmer, but half the lens is still a lens, and it produces a pair of images.

31. 31 F’F’ F For diverging lens focal length defined to be negative (of the distance between focus and lens) Thin concave (diverging) lens Guess how this ray will be bent:

32. 32 F’F’ F For diverging lens focal length defined to be negative Thin concave (diverging) lens

33. 33 1)A ray parallel to the axis is deflected as if it came from the focus 2)A ray through the center of the lens continues undeviated 3)A ray aimed at the focus on the other side comes out parallel F’F’ F Ray might have to be extended 1 2 3 For diverging lens focal length defined to be negative Thin concave (diverging) lens: three easy ray rules

34. 34 F’F’ F 1 Difference between convex (converging) & concave (diverging) lenses F’F’ F 1 (Rule 3, the backwards version of rule 1, also differs)

35. 35 Ray tracing a convex lens: object inside focus

36. 36 Ray tracing a convex lens: object inside focus The image appears larger (and farther away) than the object. This is a magnifying glass. (Remember: a magnifying glass is a convex lens.) Aside: near-sighted people need concave/diverging lenses; can a marooned myopic start a fire with his eye-glasses?

37. 37 Convex lens ray tracing: 3 cases Like concave mirrors, convex lenses have 3 kinds of cases for ray tracing: 1. object inside focal length 2. object outside focal length, inside twice focal length 3. object outside twice focal length You can do the ray tracing and answer the following questions: Is the image real/virtual? Is the image larger/smaller than the object? Is the image erect/inverted? How can the lens be used?