Determination of detector rotation angle in the experiment based on the total internal reflection using an equilateral right angle prism

We present a relation between incident angle and rotation angle detector in the Total Internal Reflection (TIR) experiments when using a right angle prism. In the TIR method, the light coming toward the prism will experience reflection and out of the prism at a certain angle direction. Results of analysis of the geometry and Snell’s law shows that the angular position of the detector is not only determined by the angle of incidence of light alone but also by the size of the prism and the detector position from the rotation axis of goniometer. The experimental results show relation between the angle of detector and angle of goniometer. When the prism rotated 45 °, position of goniometer detector is 2×45 °. However, when the prism rotated at an angle instead of 45 °, detector position µ is not always equal to twice the rotation angle goniometer ψ, so that this relationship needs to be corrected. This correction is also determined by the value of the refractive index of the prism is used. By knowing the relationship between detector position and the incident angle of light, this formulation can be used to control the position of the sample and the detector in the experiments based on ATR.