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Refractive index to measure temperature

  1. May 24, 2006 #1
    Here is the question:
    A factory uses a beam of light to allow workers to visually check the temperature of a liquid. A semi-circular crown glass (refractive index (n) =1.75) block is placed in a liquid X whose refractive index n changes with temperature T (in °C) according to the formula:
    n = 2.25 – 0.025T
    A light ray may be directed to the centre of the glass block makes and angle Ө = 60° with the normal

    If the ray is totally reflected at O, find the refractive index and the corresponding temperature of liquid X.

    ___________________________________________​

    My working:
    [tex]\theta_{critical}=\frac{n_{1}}{n_{2}}[/tex]
    from this point onwards I am stuck, any post regarding hints/working/solution will be greatly appreciated
    Thank you,
    Pavadrin
     
  2. jcsd
  3. May 24, 2006 #2
    well, it's sin(theta_c)=n2/n1 , ( n1>n2 )

    try working this out, with givens you have.
     
  4. May 25, 2006 #3
    thank you kindly

    thanks for this bit of imformation, i have now solved the problem
     
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