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Given small samples of three liquids, you are asked to determine their refractive indexes. However, you do not have enough of each liquid to measure the angle of refraction for light retracting from air into the liquid. Instead, for each liquid, you take a rectangular block of glass (n= 1.52) and Place a drop of the liquid on the top surface f the block. you shine a laser beam with wavelength 638 nm in vacuum at one Side of the block and measure the largest angle of incidence for which there is total internal reflection at the interface between the glass and the liquid. Your results are given in the table.

Liquid A B C
θ 52.0 44.3 36.3

Required:
a. What is the refractive index of liquid A at this wavelength?
b. What is the refractive index of liquid B at this wavelength?
c. What is the refractive index of liquid C at this wavelength?

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sqdancefan

Answer:

  • A — 1.198
  • B — 1.062
  • C — 0.900

Explanation:

The index of refraction of the liquid can be computed from ...

  [tex]n_i\sin{(\theta_t)}=n_t[/tex]

where ni is the index of refraction of the glass block (1.52) and θt is the angle at which there is total internal refraction. nt is the index of refraction of the liquid.

For the given incidence angles, the computed indices of refraction are ...

  A: n = 1.52sin(52.0°) = 1.198

  B: n = 1.52sin(44.3°) = 1.062

  C: n = 1.52sin(36.3°) = 0.900

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