We have used a "freshman physics" spectrometer to measure the index of refraction of two samples of mineral oil for six lines of the mercury spectrum. We have fit these measurements to a single resonance dense material model and find an indexo of refraction, n_D= 1.4627+/-.0008+/-.0004 with a dispersion (n_D-1)/(n_F-n_C) = 51.4 for the Witco oil and n_D= 1.4616+/-.0008+/-.0004 with a dispersion (n_D-1)/(n_F-n_C) = 51.3 for the Amoco oil. For the indices of refraction, the first error is the measurement error during measurement of the oil and the second is the calibration error for the angle of the prism.

We have used the above apparatus to measure the index of refraction of the Amoco and the Witco mineral oil as a fuction of wavelength. The apparatus consists of a atomic line source (we used helium and mercury for the prism calibration and just a mercury line source for the oil measurements), a spectrometer table which measured angles to a minute of arc, and an approximately equilateral plexiglass container (wall thicknesses of 1/8"). The triangular container was first filled with distilled water to calibrate the interior angle and then with the two samples of mineral oil. For each measurement, the container was rotated on the spectrometer table until the minimum deflection was observed. Under these conditions, the incoming angle with respect to the normal to the front face is equal to the outgoing angle with respect to the normal of the back face and the relationship between the total angular deflection (t), the interior angle of the prism (a), and the index of refraction (n) is given by:

Sin[(t+a)/2] = n Sin[a/2]

Table 1 gives the indices of refraction as a function of wave length.

**Table 1**

Water Indices of Refraction at 20 C

Wave
Length (A) |
Frequency
(PHz) |
Index | Calculated
Index |

7065 | 2.6680 | 1.3300 | 1.3301 |

5893 | 3.1986 | 1.3330 | 1.3328 |

5016 | 3.7579 | 1.3364 | 1.3361 |

4047 | 4.6577 | 1.3427 | 1.3428 |

The indices of refraction are fit to a "one resonance" model for dense media:

n^2 - 1 a ----- = ------------- n^2 + 2 (w_0^2 - w^2)where a and w_0 are fit parameters. For the calculated values given in table 1, a=88.42 (PHz)^2 and w_0=20.98 PHz.

With distilled water in the prism, we measured the angular deviations given below in Table 2.

**Table 2**

Measured Angles with Distilled Water

Wave
Length |
Index | Angle | Measurement
Sigma |
Number of
Measurements |
Prism
Angle |

Mercury | |||||

5790 | 1.3331 | 23.083 | .13 | 6 | 59.044 |

5461 | 1.3342 | 23.289 | .10 | 6 | 59.272 |

4358 | 1.3402 | 23.578 | .19 | 6 | 58.976 |

Helium | |||||

6563 | 1.3311 | 23.172 | .08 | 3 | 59.489 |

4861 | 1.3369 | 23.256 | .07 | 3 | 58.839 |

4340 | 1.3403 | 23.794 | .05 | 3 | 59.352 |

The prism angle is calculated as:

alpha = 2 ArcTan[Sin[gamma/2]/(n-Cos[gamma/2])]where alpha is the interior angle of the prism and gamma is the measured deflection angle.

From these measurements, we conclude that

- The average error on a single measurement is +/- .13o; and
- The interior angle of the prism is 59.14 +/- .04.

**Table 3**

Amoco Oil Measurements

Wave
Length (A) |
Frequency
(EHz) |
Measured
Angle |
Angle
Sigma |
Calculated
Index |
Index
Error |

6907 | 2.730 | 32.82 | .04 | 1.4572 | .0008 |

5790 | 3.257 | 33.22 | .03 | 1.4621 | .0008 |

5461 | 3.453 | 33.34 | .04 | 1.4636 | .0008 |

4916 | 3.836 | 33.78 | .14 | 1.4689 | .0008 |

4358 | 4.327 | 34.11 | .07 | 1.4729 | .0008 |

4047 | 4.660 | 34.38 | .06 | 1.4762 | .0008 |

**Table 4**

Witco Oil Measurements

Wave
Length (A) |
Frequency
(EHz) |
Measured
Angle |
Angle
Sigma |
Calculated
Index |
Index
Error |

6907 | 2.730 | 32.98 | .12 | 1.4591 | .0008 |

5790 | 3.257 | 33.29 | .08 | 1.4629 | .0008 |

5461 | 3.453 | 33.53 | .17 | 1.4659 | .0008 |

4916 | 3.836 | 33.76 | .09 | 1.4687 | .0008 |

4358 | 4.327 | 34.22 | .08 | 1.4743 | .0008 |

4047 | 4.660 | 34.52 | .08 | 1.4779 | .0008 |

These results are plotted in Figure 1 (click on the picture for a PostScript version) along with a single resonance fit to the data. The parameters of these fits are given in Table 5.

**Figure 1**

**Table 5**

Mineral Oil Index of Refraction Fit Parameters

Oil | a | w_0 | n_D | Dispersive
Index |

Amoco | 112.4 | 20.48 | 1.4616 | 51.3 |

Witco | 114.9 | 20.68 | 1.4627 | 51.4 |