1. Physics 1700 Geometric Optics (rough draft) W. Pezzaglia Updated: 2012Aug21

2. Geometric Optics A.Focal Length B.Lens Law, object & image C.Optical Instruments 2

3. A. Focal Length 1.Converging Lens (or Mirror) 2.Diverging Lens (or Mirror) 3.Lens Maker Equation 3

4. 1. Converging Systems Converging: o Concave mirror o Convex lens Light parallel to principle axis converges at the “focal point”. 4

5. 2. Diverging Systems Diverging: o Convex mirror o Concave lens Focal length is “negative” 5

6. 3. Lens Maker Equation Focal length “f” of a mirror with radius of curvature “R”: Focal length “f” of a lens of index “n” with radius of curvature “R” (in air) For Lens “f” of index n 2 submerged in medium of index n 1 : 6

7. 3. Lens Maker Equation The more curved a lens or mirror, the shorter the focal length. A bigger index of refraction makes a shorter focal length lens. A lens underwater will have a longer focal length than above water. Hence you become “farsighted” underwater. 7

8. B. Lens Law 1.Lens Equation 2.Virtual images 3.Lens combination 8

9. 1. Lens Equation (Gauss) Distance to object “p” Distance to image “q” If p>f then image will be “real” and inverted. 9

10. 2. Virtual Image For converging lens if p<f then image will be “virtual” and erect. [Magnifying glass] [Diverging systems only can make virtual images.] 10

11. 3. Lens Combination Two lenses (close together) act as one lens with focal length given by: Example: eyeglasses. Farsighted eye’s lens focal length is too long. Adding an extra lens shortens it. 11

12. C. Optical Instruments 1.The Eye 2.Telescopes 3.Microscopes 12

13. 1a Structure of eye Fovea of eye has best resolution (this is what you are using to read), which only has cones (color vision) Optic nerve creates a blind spot Lens is flexible Peripheral part of retina is mostly “rods” which are black & white but can see much fainter light (more than 10x) 13

14. 1b Color Perception Eye has 3 types of color receptors (blue green red). Hence using just these three colors can “trick” eye into seeing nearly all colors (can’t do violet) Your computer screen has only these 3 colors! 14

15. 1c Eye: Farsighted Hyperopia, also known as farsightedness Cannot see clearly closer than “near point” Correct with a converging lens 15

16. 1c Eye: Nearsighted Myopia or nearsighted Cannot see clearly past “far point” Correct with diverging lens (focal length equal to negative of far point) 16

17. 1c Astigmatism Focal length horizontal is not same as vertical 17

18. 1c Astigmatism 18 Generically, means you can focus on one axis, but the other is out of focus.

19. 1c Astigmatism 19

20. 1d Binocular Vision 20 Two eyes see slightly different images (due to parallax). Brain puts it together to “see” 3D. Can “trick” brain into seeing 3D by giving each eye a different picture (stereographs). Modern 3D movies do it using polarization glasses. Columbian Exposition 1893, stereograph, viewer

21. 1d. 3D Vision 21

22. 1d. 3D Vision 22

23. 1e. Magnitudes and Brightness 43 1.Magnitude Scale: Hipparchus of Rhodes (160-127 B.C) assigns “magnitudes” to stars to represent brightness. The eye can see down to 6 th magnitude

24. 1e Herschel Extends the Table 44 William Herschel (1738-1822) extended the scale in both directions

25. 1e Herschel-Pogson Relation 45 Herschel’s measurements suggested a 1 st magnitude star is 100x more luminous that a 6 th magnitude one. Norman Pogson (1854) showed that this is because the eye’s response to light is logarithmic rather than linear. 22.5

26. C.3b Gemini 26 Ma g 2 Ma g 3 Mag 4 Mag 6

27. Our new telescope! Meade 14" LX200-ACF (f/10) Advanced Coma-Free w/UHTC #1410-60-03 USD$ 6,999.00 Schmidt-Cassegrain Focus Aperture 14 inch (356 mm) Focal Length 3556 mm (f/10) Resolution 0.321” 2. Telescopes 27

28. 2a Light Gathering Power Light Gathering Power (aka Light Amplification) is proportional to area of mirror More light, can see fainter (more distant) objects. Aperture=diameter of objective mirror (for our telescope its 14 inches=356 mm) 28

29. 2b Limiting Magnitude Consulting table, a LGP of 3520 translates to more than 8.5 magnitudes. Exact calculation: Limiting magnitude of naked eye is +6, can see over 8000 stars. hence looking through scope we can see up to +14.8 or over 100,000,000 stars in our galaxy, and over 1000 galaxies! 29

30. 2c. Basic Telescope Design Refractor Telescope (objective is a lens) Focal Length of Objective is big Focal Length of eyepiece is small 30

31. 2d Chromatic Aberration 4 Different colors are bent (refracted) at slightly different angles, with red light focusing the furthest away. Difficult to get a sharp color picture. Problem with refracting telescopes

32. 2e Newtonian Reflecting Telescope Objective is a mirror, no chromatic problems! Focal length is approximately the length of tube Light is directed out the side for the eyepiece 32

33. 2f Schmidt Cassegrain Reflecting Telescope Cassegrain focus uses “folded optics” so the focal length is more than twice the length of tube Light path goes through hole in primary mirror Schmidt design has corrector plate in front 33

34. 2. Magnification Power The overall magnification of the angular size is given by the ratio of the focal lengths For our scope (F=3556 mm), with a 26 mm eyepiece, the power would be: 34

35. 2g. Too Much Magnification? Extended objects (planets, nebulae, galaxies) when magnified more will appear fainter 35 Low Power High Power

36. 2h. Too Much Magnification? Too much magnification and you won’t see it at all! Its about surface brightness! Your eye can’t see below a certain amount. 36 Low Power High Power

37. Creates a BIG virtual image 25 cm away from the eye. 3. Microscopes (briefly) 37

38. D. References Lick Observatory Video: http://www.youtube.com/watch?v=g63lk_0kngk http://www.youtube.com/watch?v=g63lk_0kngk Video: Mechanical Universe #40, Optics#40, Optics Stereographs: http://www.library.hbs.edu/hc/pc/stereograph.htmlhttp://www.library.hbs.edu/hc/pc/stereograph.html Stereograph: http://www.sun.travel.pl/stereoscope&page=6 38