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 # 11

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

3. 3 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

4. 4 Note light-dispersing property of convex lens The “backwards” light collector: create a collimated light beam

5. 5 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

6. 6 Ray Tracing foci (focuses?) Where will this ray go?

7. 7 Ray Tracing Where will this ray go? Suppose it’s emitted from this object foci (focuses?)

8. 8 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

9. 9 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

10. 10 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

11. 11 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)?

12. 12 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.

13. 13 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.

14. A Question 14 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

15. A Question 15 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.

16. 16 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:

17. 17 F’F’ F For diverging lens focal length defined to be negative Thin concave (diverging) lens

18. 18 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

19. 19 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)

20. 20 Ray tracing a convex lens: object inside focus

21. 21 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?

22. 22 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?

23. 23 Ch. 3 – Spherical mirrors and lenses 1.Virtual images (review) 2.Spherical mirrors 3.Spherical lenses Thin lens approximation Formulas Magnification Adding lenses Image distance 4.Aberrations of lenses We are here 23

24. Object distance, image distance, focal length 24 XiXi XoXo F

25. Magnification formula S 0 = object height S i = image height Note the similar triangles. 25 Distances below the horizontal axis are defined as negative. Demo: big mama lens and bulb

26. Image distance equation F = focal length X O = object distance X I = image distance Usually, F is given. 26 Distant objects: Let X o be very large, say 1,000,000 meters. Then 1/X o = 0.000001, which is very small. You can ignore it. Then For distant objects, the image is at the focal point (ask a burnt ant) Demo: find focal length of lenses

27. What is lens power (or diopters)? Lens power: D = 1/F Units of D are 1/meters, also called diopters Eyeglass lenses are measured in diopters. Example: D = 2/m = what focal length? F = 1/D = 1/(2/m) = (1/2) m = 0.5 m

28. How thin lenses add F tot = final focal length F 1 = focal length lens 1 F 2 = focal length lens 2 Diverging lenses (concave) have negative focal lengths This is the same as adding powers: D tot = D 1 + D 2 28 Demo: put together some lenses

29. Compound Lenses Can have less aberration. A modern lens can have 16 elements and can “zoom”. 29 “stop” Reduces aberration Image plane

30. 30 Ch. 3 – Spherical mirrors and lenses 1.Virtual images (review) 2.Spherical mirrors 3.Spherical lenses 3 formulas 4.Aberrations of lenses We are here 30

31. Aberrations Field curvature Off-axis aberration Spherical aberration Distortion Chromatic aberration 31

32. Aberration: field curvature 32 Image does not lie in one plane

33. Off axis aberration Edges of images are less clear. 33 Demo with lens and bulb

34. Spherical aberration Rays at the edge focus closer to the mirror 34 Demo with lens, not mirror

35. Aberrations: Distortion 35 Demo with overhead and small lenses

36. Chromatic Aberration 36 Demo with lens and bulb

37. Web tutorials with Java Applets Useful web links on curved mirrors http://micro.magnet.fsu.edu/primer/java/mirrors/concavemirrors/index.html http://micro.magnet.fsu.edu/primer/java/mirrors/convexmirrors/index.html http://micro.magnet.fsu.edu/primer/java/mirrors/concave.html Useful web links on lenses http://micro.magnet.fsu.edu/primer/lightandcolor/lenseshome.html http://micro.magnet.fsu.edu/primer/java/lenses/simplethinlens/index.html http://micro.magnet.fsu.edu/primer/java/lenses/converginglenses/index.html http://micro.magnet.fsu.edu/primer/java/lenses/diverginglenses/index.html http://micro.magnet.fsu.edu/primer/java/components/perfectlens/index.html http://micro.magnet.fsu.edu/primer/java/mirrors/convex.html 37

38. Fresnel Lens Used in lighthouses 38 Fresnel stage light Lighthouse lens

39. 39 http://sandiartfullyyours.com/NewFiles/lighthouse3/images/Ponce%20Fresnell.jpg