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Angle of refraction of light in water

  1. Jun 21, 2010 #1
    1. The problem statement, all variables and given/known data
    A ray of pure yellow light reaches the surface of a pond at an angle of incidence of 60°. What angle does it make with the normal inside the water?

    Speed of light in air = 300,000,000 m/s
    Speed of light in water = 225,000,000 m/s
    So the Refractive index μ = 1.33

    2. Relevant equations
    μ = angle of incidence / angle of refraction


    3. The attempt at a solution
    μ = sin i / sin r
    1.33 = 60° / sin r
    sin r = 60° / 1.33

    So the angle of refraction equals 45.11°. Is this correct? I believe this is the correct way to work it out, yet when I check the answer online using various calculators the answer comes up as 40.62°. Am I doing something wrong?
     
  2. jcsd
  3. Jun 21, 2010 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    yes, you are. And the problem is shown in your writing "μ = angle of incidence / angle of refraction" when it should be "μ = sin(angle of incidence) / sin(angle of refraction)"

    You write that below but then you write "1.33= 60°/ sin r" and "sin r= 60°/1.33= 45.11°"

    sin r= sin(60°)/1.33. Use a calculator to determine sin(60°) and once you have sin r, use a calculator again to determine r itself.
     
  4. Jun 21, 2010 #3
    Ah, I see now. Sin r = 0.6511469, so r = 40.62°

    Thank you sir!
     
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