MainPage:Nuclear:Summer2018:Diana

Refractive Index of Lead Tungstate Crystal (J21)

The extraordinary index of refraction was measured to be 1.006 and the ordinary index of refraction was measured to be 1.007. This was calculated utilizing the following equation:Θr = γ − (π/2 + α) + sin−1 [ (sin α)(sin γ) + (cos α) q (n^2 – sin^2 γ)]. These values are quite off, possibly because the equation is limited to n<1.225 at a 45 degree angle. This is because sine of any angle will always be less than or equal to one, and in the equation, if the angle of incidence is 45, then the maximum value of n to result in a sine value less than or equal to one would be 1.225. While the angle of incidence could be increased to 89 degrees to maximize the largest possible n value determined, the greatest value of n would still be 1.5.

An alternative method of determining refractive index may be with the following equation: n^2 = 1 + 0.438*rho. That refractive index value will be determined once an appropriate scale has been located. However, that method would only result in one value for index of refraction. This crystal is anisotropic and should have extraordinary and ordinary indices of refraction. It will be interesting to see how the density method might relate to the two indices.

6/21:

The density method of determining the refractive index resulted in an n value of 2.17. Although, there are supposed to be two values of n to account for the anisotropic nature of the crystal. This may be accounted for by the systematic uncertainty mainly caused by the chipped nature of the crystal sample. This will be quantified.

6/26:

Tool uncertainty for the refractive index has been propagated to be ±0.2. The propagation process can be followed in the spreadsheet linked below.

https://docs.google.com/spreadsheets/d/19or7L6fUpRY_mJiaQoGpr46ZWl_RE42wAtRgJJEKHG4/edit?usp=sharing

Geometric Deviations on Light Collection and Resolution

Using a measuring stick with millimeter delineations, the length of the crystal was measured as 20cm, and each side of the bottom ends was measured as 2cm. Therefore, this sample of Lead Tungstate Crystal (J21) is not tapered. Utilizing snell’s law and a predetermined refractive index of 2.17, the maximum and minimum initial emission angles were calculated with the spreadsheet linked below. The calculated range of initial emission angles is 0.46°<θ<27.44°.

https://docs.google.com/spreadsheets/d/1neQI7LniWMYyUP0Q0-bgnIFC5drDTiN7zaUKt_JVRZY/edit?usp=sharing

The scintillation light is emitted isotropically, thus the range of initial emission angles by which the scintillation photons are emitted determines the fraction of light that reaches the sensor. Therefore, the fraction of scintillation light that will theoretically reach the sensor will be proportional to the range of initial emission angles. Thus, the detected light will be the emitted light reduced by a factor of .075.

Presentation Link

https://docs.google.com/presentation/d/1wihv7zX6HOTCHfR3l9qJnHa2r59lceJo0mfW5a9PCoc/edit?usp=sharing