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Property 5: Refraction

Property 5: Refraction. experiment ? particle (photon)? wave (E&M) ?. Property 5: Refraction. experiment: objects in water seem closer than they really are when viewed from air. eye. air. water. apparent location. real object. Property 5: Refraction. particle (photon) ?.

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Property 5: Refraction

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  1. Property 5: Refraction experiment ? particle (photon)? wave (E&M) ?

  2. Property 5: Refraction • experiment: objects in water seem closer than they really are when viewed from air eye air water apparent location real object

  3. Property 5: Refraction • particle (photon) ? incident ray air surface water refracted ray

  4. Property 5: Refraction • particle (photon) ? incident ray vxair = vxwater vxair air vyair < vywater vyair surface therefore vi < vr water vxwater vywater refracted ray

  5. Property 5: Refraction normal line • wave (E&M) ? incident wave air surface surface water refracted wave normal line

  6. Property 5: Refraction crest of following wave • wave (E&M) ? crest of wave incident wave crest of preceding wave air air air x surface water water refracted wave normal line

  7. Property 5: Refraction • particle (photon) theory: vwater > vair • wave (E&M) theory: vwater < vair • experiment ?

  8. Property 5: Refraction • particle (photon) theory:vwater > vair • wave (E&M) theory: vwater < vair • experiment: vwater < vair wave theory works! particle theory fails!

  9. Properties 1, 2 & 5 Speed, Color and Refraction • Speed of light changes in different materials • Speed is related to frequency and wavelength: v = f • If speed changes, does wavelength change, frequency change, or BOTH?

  10. Properties 1, 2 & 5 • Speed, Color and Refraction • Speed of light changes in different materials • Speed is related to frequency and wavelength: v = f • What changes with speed? • Frequency remains constant regardless of speed • Wavelength changes with speed

  11. Refraction and Thin Lenses Can use refraction to try to control rays of light to go where we want them to go. Let’s see if we can FOCUS light.

  12. Refraction and Thin Lenses What kind of shape do we need to focus light from a point source to a point? lens with some shape for front & back point source of light screen s’ = image distance s = object distance

  13. Refraction and Thin Lenses Let’s try a simple (easy to make) shape: SPHERICAL. Play with the lens that is handed out Does it act like a magnifying glass?

  14. Refraction and Thin Lenses Let’s try a simple (easy to make) shape: SPHERICAL. Play with the lens that is handed out Does it act like a magnifying glass? Does it focus light from the night light?

  15. Refraction and Thin Lenses Let’s try a simple (easy to make) shape: SPHERICAL Play with the lens that is handed out Does it act like a magnifying glass? Does it focus light from the night light? Does the image distance depend on the shape of the lens? (trade with your neighbor to get a different shaped lens)

  16. Refraction and Thin Lenses Spherical shape is specified by a radius. The smaller the sphere (smaller the radius), the more curved is the surface! R R R1 R2

  17. Refraction and the Lens-users Eq. f > 0 s > 0 AND s > f s’> 0 AND s’> f f f s s’ Example: f = 10 cm; s = 20 cm; s’ = 20 cm: 1/20 + 1/20 = 1/10

  18. Refraction and the Lens-users Eq. as s gets bigger, s’gets smaller f f s s’ Example: f = 10 cm; s = 40 cm; s’ = 13.3 cm: 1/40 + 1/13.3 = 1/10

  19. Refraction and the Lens-users Eq. as s approaches infinity s’approaches f f f s s’ Example: f = 10 cm; s = 100 cm; s’ = 11.1 cm: 1/100 + 1/11.1 = 1/10

  20. Refraction and the Lens-users Eq. f > 0 s > 0 AND s > f s’> 0 AND s’> f f f s s’ Example: f = 10 cm; s = 20 cm; s’ = 20 cm: 1/20 + 1/20 = 1/10

  21. Refraction and the Lens-users Eq. as s gets smaller, s’gets larger f f s s’ Example: f = 10 cm; s = 13.3 cm; s’ = 40 cm: 1/13.3 + 1/40 = 1/10

  22. Refraction and the Lens-users Eq. as s approaches f, s’approaches infinity f f s s’ Example: f = 10 cm; s = 11.1 cm; s’ = 100 cm: 1/11.1 + 1/100 = 1/10

  23. Refraction and the Lens-users Eq. Before we see what happens when s gets smaller than f, let’s use what we already know to see how the lens will work.

  24. Refraction and the Lens-users Eq. • Any ray that goes through the focal point on its way to the lens, will come out parallel to the optical axis. (ray 1) f f ray 1

  25. Refraction and the Lens-users Eq. • Any ray that goes through the focal point on its way from the lens, must go into the lens parallel to the optical axis. (ray 2) f f ray 1 ray 2

  26. Refraction and the Lens-users Eq. • Any ray that goes through the center of the lens must go essentially undeflected. (ray 3) object image ray 1 f f ray 3 ray 2

  27. Refraction and the Lens-users Eq. • Note that a real image is formed. • Note that the image is up-side-down. object image ray 1 f f ray 3 ray 2

  28. Refraction and the Lens-users Eq. • By looking at ray 3 alone, we can see by similar triangles that M = h’/h = -s’/s. object h s’ image h’<0 f s f ray 3 note h’ is up-side-down and so is <0 Example: f = 10 cm; s = 40 cm; s’ = 13.3 cm: M = -13.3/40 = -0.33 X

  29. Refraction and the Lens-users Eq. This is the situation when the lens is used in a camera or a projector. Image is REAL. object image ray 1 f f ray 3 ray 2

  30. Refraction and the Lens-users Eq. What happens when the object distance, s, changes? object image ray 1 f f ray 3 ray 2

  31. Refraction and the Lens-users Eq. Notice that as s gets bigger, s’ gets closer to f and |h’| gets smaller. object image ray 1 f f ray 3 Example: f = 10 cm; s = 100 cm; s’ = 11.1 cm: M = -11.1/100 = -0.11 X ray 2

  32. Focusing To focus a camera, we need to change s’ as s changes. To focus a projector, we need to change s as s’ changes. We do this by screwing the lens closer or further from the film or slide. But what about the eye? How do we focus on objects that are close and then further away with our eyes? Do we screw our eyes in and out like the lens on a camera or projector?

  33. Focusing But what about the eye? How do we focus on objects that are close and then further away with our eyes? Do we screw our eyes in and out like the lens on a camera or projector? - NO, instead our eyes CHANGE SHAPE and hence change f as s changes, keeping s’ the same!

  34. Refraction and the Lens-users Eq. Let’s now look at the situation where s < f (but s is still positive): s f f

  35. Refraction and the Lens-users Eq. We can still use our three rays. Ray one goes through the focal point on the left side. ray 1 s f f

  36. Refraction and the Lens-users Eq. Ray two goes through the focal point on the right side (and parallel to the axis on the left). ray 1 s f f ray 2

  37. Refraction and the Lens-users Eq. Ray three goes through the center of the lens essentially undeflected. ray 1 h’ s f f ray 2 s’ ray 3

  38. Refraction and the Lens-users Eq. Notice that: s’ is on the “wrong” side, which means that s’ < 0 , and that |s’| > |s| so f > 0. ray 1 h’ s f f ray 2 s’ ray 3 Example: f = 10 cm; s = 7.14 cm; s’ = -25 cm: 1/7.14 + 1/(-25) = 1/10

  39. Refraction and the Lens-users Eq. Notice that: h’ right-side-up and so h’ > 0., M = h’/h = -s’/s . M > 0 (s’ < 0 but -s’ > 0). h’ s f f s’ ray 3 Example: f = 10 cm; s = 7.14 cm; s’ = -25 cm: M = - (-25)/ 7.14 = 3.5 X

  40. Refraction and the Lens-users Eq. This is the situation when the lens is used as a magnifying glass! Image is VIRTUAL. ray 1 h’ s f f ray 2 s’ ray 3

  41. Refraction and the Lens-users Eq. The same lens can be used as: • a camera lens: s >> f, s > s’, M < 0, |M| < 1 • a projector lens: s > f, s’ > s, M < 0, |M| > 1 • a magnifying glass: s < f, s’ < 0, M > 0, M > 1

  42. Refraction and the Lens-users Eq. Notes on using a lens as a magnifying glass: • hold lens very near your eye • want IMAGE at best viewing distance which has the nominal value of 25 cm so that s’ = -25 cm.

  43. Refraction and the Lens-users Eq. Are there any limits to the magnifying power we can get from a magnifying glass?

  44. Refraction and the Lens-users Eq. • Magnifying glass has limits due to size • As we will see in a little bit, magnifying glass has limits due to resolving ability • NEED MICROSCOPE (two lens system) for near and small things; need TELESCOPE (two lens system) for far away things.

  45. Telescope Basics Light from far away is almost parallel. objective lens eyepiece fe fo

  46. Telescope Basics:Get More Light The telescope collects and concentrates light. objective lens eyepiece fe fo

  47. Telescope Basics Light coming in at an angle, in is magnified to out . objective lens eyepiece x fe fo

  48. Magnification in = x/fo, out = x/fe; M = out/in = fo/fe objective lens eyepiece x fe fo

  49. Limits on Resolution telescopes • magnification: M =out/in = fo /fe • light gathering: Amt D2 • resolution: 1.22  = D sin(limit) so in = limit and out = 5 arc minutes so limit 1/D implies Museful = 60/in * D where D is in inches • surface must be smooth on order of 

  50. Limits on Resolution:calculation Mmax useful = out/in = eye/limit = 5 arc min / (1.22 *  / D) radians = (5/60)*(/180) / (1.22 * 5.5 x 10-7 m / D) = (2167 / m) * D * (1 m / 100 cm) * (2.54 cm / 1 in) = (55 / in) * D

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