Chapter 22 The reflection and refraction of light 22 1 The nature of light Rays of particles Newton 1642 1727 Rays of waves Huygens 1629 1695 Mathematical description of waves Maxwell 1865 a beautiful end to the story of light But Planck suggested that light should have its energy as E nhf where f is the light frequency and h the Planck constant h 6 626 x 10 34J s n the number of quanta He had to apologize because he didn t understand why it worked for his calculations Einstein suggested 1905 that light is a ray of particles photons each having E hf How to reconcile with Maxwell the wave equations Light is both particles and waves Everything is a particle and a wave quantum physics Dual nature of matter 22 2 Reflection and refraction of light Absorption Angle of incidence Angle of reflection qi qr Reflection bounces Mirrors Refraction bends qi qr Lenses Often some of each Angles between light beam and normal 1 Which one is more reflecting If there is an online course for PHY101 and 102 would you want to take it assuming you are not taking it now Scattered Directional Total amount of reflected light depends on the material not how flat the surface is 1 Yes 2 No 3 Hell no 22 3 The Law of Refraction 186 000 miles second it s not just a good idea it s the law c v n Speed of light in medium v c Speed of light in vacuum Frequencies f1 and f2 in two media are the same Because v f or f v v1 1 v2 2 Using v c n 1n1 2 n2 Index of refraction so n 1 always 2 Refracted Bends q1 q2 v1 v2 Example with v c n Usually there is both reflection and refraction A ray of light traveling through the air n 1 is incident on water n 1 33 Part of the beam is reflected at an angle qr 60 The other part of the beam is refracted What is q2 q1 qr 60 q1 qr q2 40 6 degrees n1 n2 normal n1 sin q1 n2 sin q2 Snell s Law sin 60 1 33 sin q2 n1 sin q1 n2 sin q2 q 2 3 For HW when seeing several Example interfaces don t even have to be parallel deal with one interface at a time Move to the next interface with some geometry Be careful that the angle is always measured from the normal Example If q1 30o what is q2 22 4 Dispersion The index of refraction n depends on color In glass nblue 1 53 nred 1 52 nblue nred also true for water and many other materials prism White light Light bends when it goes from one material to another because its changes 1 2 3 4 intensity Speed Frequency None above Blue light gets deflected more 4 22 5 The rainbow First rainbow In second rainbow pattern is reversed Which is red Which is blue Skier sees blue coming up from the bottom 1 and red coming down from the top 2 of the rainbow In other words red is more vertical 5 For HW when asked to calculate angles between two colors calculate one color at a time and then find the difference Example A ray of blue and red light traveling through the air n 1 is incident on water nblue 1 33 nred 1 32 with an incident angle of 60o What is the angle between the refracted blue and red light Blue light sin 60 1 33 sin q2 q2 blue 40 6 degrees Red light sin 60 1 32 sin q2 q2 red 41 0 degrees Difference q2 red q2 blue 41 0o 40 6o 0 4o q1 qr n2 22 7 Total Internal Reflection When q2 90 q1 n1 sin q1 n2 sin q2 q 2 Fiber Optics Recall Snell s Law n1 sin q1 n2 sin q2 Example n1 1 6 n2 1 q1 60o sin 1 n normal n1 At each contact w the glass air interface if the light hits at greater than the critical angle it undergoes total internal reflection and stays in the fiber 2 n1 critical angle Light incident at a larger angle will only have reflection qi qr Total internal reflection can only happen going from a larger n typically a denser material to a smaller n noutside q2 normal qr qi qc n2 n1 ninside Telecommunications Laser surgery Total Internal Reflection only works if noutside ninside q1 6 1 n1 n2 and n2 n3 2 n1 n2 and n2 n3 3 n1 n2 and n2 n3 Example The total internal reflection is a result of What is the smallest value of q1 when it is total internal reflection at the bottom surface 1 Wavelength changing going into another medium 2 Snell s law 3 Reflected beam having the same angle as the incident angle 7