critical angle can only be approximately determined, because the intensity of the image changes from maximum to minimum value over some interval of angles. For this purpose, Fresnel’s equations were proposed in the paper. They give information about total intensity of reflected and transmitted light for a given incident angle and indices of refraction. By using these equations and connecting the angle of incidence (from air to glass) with the observing angle, we made theoretical graph showing the transmittance in dependence on the observing angle, i.e. how the visibility of finger changes. Experiment The experiment consisted of a few parts: measuring indices of refraction for 5 liquids (water with different concentrations of sugar), determining critical observing angle, and determining the intensity of light for different observing angles. Indices of refraction were determined using a semi-circular vessel in which the liquid was put. With three needles one light ray was defined, and by measuring the incident and transmitted angle, one could determine the index of refraction. For determining critical observing angle, experimental setup was made. Rectangular vessel with water had one glass side for observing the patterns. This setup was observed through which enabled us to control the height of observing. “windows” For every height, the distance from the pattern was determined (for critical observing angle). From the height-distance graph, observing angle was determined. This was done for every measured index and compared to the theoretical result. Relevance of Fresnel’s equations was investigated by taking a photo of an image and analyzing it in a computer program. The graph showing the intensity of light in dependence on the depth of observed image was obtained. Dependence of depth on the observing angle can easily be derived using a little geometry and trigonometry by → transforming depth axis to observing angle axis, we got the graph that was compared to theoretical graph that we got using Fresnel’s equations. Results 5 indices of refraction were determined. For every index, the critical angle was determined experimentally and then compared to the theoretical value. Indices of refraction n1 = 1,31 ± 0,02 (pure water) n2 = 1,34 ± 0,01 n3 = 1,346 ± 0,014 n4 = 1,350 ± 0,03 n5 = 1,36 ± 0,02
critical angle can only be approximately determined, because the intensity of the image changes from maximum to minimum value over some interval of angles. For this purpose, Fresnel’s equations were proposed in the paper. They give information about total intensity of reflected and transmitted light for a given incident angle and indices of refraction. By using these equations and connecting the angle of incidence (from air to glass) with the observing angle, we made theoretical graph showing the transmittance in dependence on the observing angle, i.e. how the visibility of finger changes. Experiment The experiment consisted of a few parts: measuring indices of refraction for 5 liquids (water with different concentrations of sugar), determining critical observing angle, and determining the intensity of light for different observing angles. Indices of refraction were determined using a semi-circular vessel in which the liquid was put. With three needles one light ray was defined, and by measuring the incident and transmitted angle, one could determine the index of refraction. For determining critical observing angle, experimental setup was made. Rectangular vessel with water had one glass side for observing the patterns. This setup was observed through “windows” which enabled us to control the height of observing. For every height, the distance from the pattern was determined (for critical observing angle). From the height-distance graph, observing angle was determined. This was done for every measured index and compared to the theoretical result. Relevance of Fresnel’s equations was investigated by taking a photo of an image and analyzing it in a computer program. The graph showing the intensity of light in dependence on the depth of observed image was obtained. Dependence of depth on the observing angle can easily be derived using a little geometry and trigonometry → by transforming depth axis to observing angle axis, we got the graph that was compared to theoretical graph that we got using Fresnel’s equations. Indices of refraction n1 = 1,31 ± 0,02 (pure water) n2 = 1,34 ± 0,01 n3 = 1,346 ± 0,014 n4 = 1,350 ± 0,03 n5 = 1,36 ± 0,02 Results 5 indices of refraction were determined. For every index, the critical angle was determined experimentally and then compared to the theoretical value.
2011_11_Fingerprints_Croatia_KK_v2.docx