In fact, behind this observation is almost the principle of fingerprint optical collection.
Let's first look at the case of filling the glass with water, because the refractive index of water and the refractive index of glass are greater than air, so according to the law of refraction, when the angle is right, the light will enter the human eye after a total reflection on the outer surface of the glass. From a geometric optical point of view, it seems that the light does not "pass" through the interface when it is fully reflected, and the fingerprint outside the glass seems to have no effect on the optical path. But in fact, according to electromagnetic theory, when light is fully reflected at the interface, it will produce a "hidden wave" within a certain thickness on the other side of the interface. The reason why it is said "within a certain thickness" (as shown below) is because the hidden wave decays beyond the wavelength of a few light from the interface to the point where it can be ignored.
When the finger is pressed outside the glass, the raised part of the fingerprint fits more closely with the glass, so that it affects the propagation of the hidden wave, which also affects the total reflection of the light, so this part looks darker. The depth of the part of the fingerprint depression is about 100 microns, and the wavelength of visible light is about a few tenths of a micron, so the gap of this fingerprint is enough for the hidden wave to decay to be ignored, so the light can be fully reflected normally, and this part looks brighter. So we can see the fingerprint pattern on the glass.
So why is it so difficult to see this phenomenon when the glass is not filled with water? This is because total reflection is not prone to occur at this time. Assuming that the glass is thinner, the situation near a point on the cup can be equivalent to a larger thin glass plate with air on both sides, and light enters the glass from the air. Then by the law of refraction, light can be refracted normally with reflection without total reflection. (As shown below) The phenomenon we see is similar to that of normal fingerprints.
Through the above principles, combined with some specific technologies, the optical acquisition of fingerprints can be realized.
bibliography:
[1] Li Zhipeng,He Xiaotong,Hu Jinxin,Liu Ruolin,Zhu Ling,Zhang Zengming,Tao Xiaoping. Optical Fingerprint Acquisition and Processing[J].Physical Experiments,2017,37(S1):4-8.
by pilot