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Light Ray, Light Ray

No Light, No Sight. Light Ray, Light Ray. A Cruise Through the Wonderful World of Reflection and Refraction (aka Geometric optics). What is Light?. Electromagnetic Radiation with wavelength (visible) 400 – 700 nm (nanometers) Travels in straight lines

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Light Ray, Light Ray

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  1. No Light, No Sight Light Ray, Light Ray A Cruise Through the Wonderful World of Reflection and Refraction (aka Geometric optics)

  2. What is Light? • Electromagnetic Radiation with wavelength (visible) 400 – 700 nm (nanometers) • Travels in straight lines • Bounces (reflects) off certain materials • Refracts (bends) in transparent materials • Travels at c = 3 x 108 m/sec in vacuum

  3. Index of Refraction n = c/v • Light slows down in transparent materials other than vacuum(like car slows in sand) • v = c/n velocity of light in medium • n is called index of refraction • n = about 1.5 for glass • n = 1.33 for water

  4. Reflection • Light bounces off objects • Consider “rays” – light moving in straight line • Law of reflection: angle of incidence = angle of reflection

  5. Law of Reflection

  6. Law of Reflection Qi = Qr • I - incident ray • R - reflected ray • N – normal • Theta-I is angle of incidence • Theta –R is angle of reflection

  7. Types of Reflection

  8. How Plane Mirror Forms Image

  9. Real vs. Virtual Image • Real image – light is present at the image position • Virtual image – no light is present at the image position

  10. Image From Plane Mirror • Virtual • Behind mirror • Right side up(upright) • Left-right reversed • Located equal Distance behind mirror • Same size as object

  11. Distance RelationshipImage is as far behind mirror as object is in front

  12. How Curved Mirror Forms Real Images

  13. How Law of Reflection Leads to Images from Spherical Mirror • C is center of curvature • F is focal point • Real image will be located on same side of mirror as object • C = 2f

  14. Rules of Reflection – Two “Special” Rays • An incident ray parallel to principal axis will pass through the focal point after reflection. • An incident ray passing through the focal point will leave mirror parallel to principal axis

  15. What’s So “Special?” About Special Rays? • Its easy to predict where they will go • Use Law of Reflection

  16. Ray Diagram – Object Beyond C = 2f • Real image • Inverted • Smaller than object • Note use of two “special” rays • What is another?

  17. Third Special Ray – to P P

  18. Image inverted Located at 2f Same size as object Image inverted Further than 2f Larger than object Ray Diagram – Object at C = 2f or between f and 2f

  19. Object at 2f

  20. Object Between f and 2f

  21. Object Closer to Mirror Than f“Shaving Mirror” Case • Image virtual • Behind mirror • Upright • Larger than object

  22. Object Closer to Mirror Than F

  23. Object at f • Must use different ray(goes to intersection of principal axis and mirror) • No image formed

  24. Mirror Equation Derivation diagram • f is positive for concave mirror Question: Where will image formed by a lens with 20 cm focal length be if object is placed 60 cm from mirror? di = 30 cm

  25. How Big is The Image? • M is magnification • - sign means image is inverted Question: If the object in the question on previous slide is 2 cm high, how high is image? 1 cm

  26. Convex (Diverging) Mirrors • f is negative • Light rays spread, not focused; images virtual • 7-11 mirror foils thieves

  27. Ray Diagram for Convex Mirror • One ray parallel to p.a. • Second ray heads for focus behind mirror • Diverging rays must be extended behind mirror (dotted lines) • Image virtual, upright, smaller

  28. Ray Diagram for Convex Mirror • One ray parallel to p.a. • Second ray heads for focus behind mirror • Diverging rays must be extended behind mirror (dotted lines) • Image virtual, upright, smaller

  29. Why Are Some Rearview Mirrors Convex?

  30. Problem • A 1.6 m tall thief stands 10m away from a 7-11 mirror with 2m (negative) focal length. Where is the image and how tall is it? • Use • Note: negative di means image behind mirror di = -1.67 m hi = 0.267m

  31. solution • 1/di = -5/10 – 1/10 = -6/10 • di = -10/6 = -5/3 = -1.67 m • hi/ho = -di/d0 = 1.67/10 • hi =.167 x 1.6 = 0.267m

  32. Index of Refraction • Ratio of speed of light in vacuum to speed of light in material • n = c/v = 3.0 x 108 m/s/v • n always greater than one

  33. Refraction: How Much Does It Bend • Angle of incidence Qi • Angle of refraction Qr • Snell’s Law: ni sin Qi = nr sin Qr

  34. Helpful Analogy:The Band of Sand • What happens when a car drives into the sand? sand highway Which way does the car turn?

  35. Toward and Away from Normal • When light enters a more dense (greater n) medium, it bends toward the normal • When light enters a less dense (smaller n) medium, it bends away from the normal

  36. Mysteries? • Why do a person’s legs appear shorter when they are standing in water? • Why Does A Glass Rod Disappear in Mineral Oil?

  37. Mysteries? • Why do a person’s legs appear shorter when they are standing in water? • Why Does A Glass Rod Disappear in Mineral Oil?

  38. Mysteries? • Why do a person’s legs appear shorter when they are standing in water? • Why Does A Glass Rod Disappear in Mineral Oil? • Both have same index of refraction

  39. Practical Application • Fluorocarbon (semi invisible under water) fishing line

  40. Problem • Light strikes a flat piece of glass(n = 1.5) at 60 degrees to the normal. What is the angle of the light in the glass? Qr Qi = 60o

  41. Solution • ni sin Qi = nr sin Qr • ni = 1 nr = 1.5 sinQr =1.00x sinQi /1.5= 0.577 Qr = 35.2o

  42. Total Internal Reflection

  43. Total Internal Reflection • Light ray leaves more dense medium • Angle of refraction approaches 900 • Past critical angle there is no refracted ray

  44. Critical AngleThe angle of incidence past which there is no refracted ray • ni sin Qi = nr sin Qr • sin Qc = nr/ni sin900 =nr/ni • If ray emerges into air • sin Qc = 1/ni Qc

  45. Example • What is the critical angle for light rays leaving a swimming pool? What does the world look like to a swimmer at the bottom of the pool? Sin Qc = 1.00/1.33 = 0.750 Qc = 490 Swimmer sees outside world compressed into a circle whose edge makes a 49 degree angle to the vertical

  46. Applications of TIR • Prisms in Binoculars

  47. Applications of TIR • Prisms in Binoculars

  48. Fiber Optics • Fiber Optic Amplifier Module Spy under door optics Photos courtesy JDS Uniphase Inc. endoscope

  49. Lenses • Lenses can focus or diverge light • Act like tiny prisms

  50. Thin Lens • Convex lenses have two focal points

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