Re: Why can you see your fingerprints on the side of a glass

The question: "Why can you see your fingerprints on the side of a glass? If a glass of water is peered into from above all that can be seen is the inside of the glass. The sides of the glass reflect what's inside. If you touch the outside of the glass, suddenly you can see through, except in the valleys of the finger prints which still display a reflection. This only works if the outside of the glass is wet. What physics are involved? Why doesn't the side of the glass just continue to reflect the inside of the glass?"

The phenomenon you are experiencing is total internal reflection (TIR) without the finger on the outside, or the lack of TIR when the wet finger is present on the outside. You can find out details of TIR in many places, one of them being here at hyperphysics.

Look at this sketch:

From the hyperphysics site you know that it is possible to calculate the minimum angle of incidence that will be totally internally reflected (the critical angle), if you know the two substances. And we do know. For light that enters the side of the glass from the water and then encounters the glass-air interface at the outside surface of the glass, assuming that the refractive index of the glass is 1.50 and that of air is 1.00, the minimum angle of incidence for TIR (the critical angle) is about 41.8 degrees. It is very easy to exceed that angle: For light that enters the glass material at an angle of incidence of, say, 80 degrees at the inside water-glass interface, the incident angle of the ray at the glass-air interface is about 60.8 degrees and so is totally reflected.

So why does the surface of the glass appear mirror like? Because no light can enter your eye from the outside of the glass, so any light that does get to your eye is mostly reflecting by TIR at the glass-air interface and originates from the bottom of the glass. These rays are represented in black in the lefthand glass. But now look at the red rays. Any ray entering the glass from the outside can have at most an angle of refraction, inside the glass material, of 41.8 degrees (which is the critical angle of a glass-air interface with glass of refractive index 1.50), and such a ray will have an angle of refraction at the inside glass-water interface of at most 48.8 degrees, and will go through the water at an angle similar to the inside red ray shown. If your eye is intercepting the black rays, it will not see the red rays!

But when one applies a wet finger (or any other object that can trap water so that it is in good contact with the outside surface of the glass) as shown in the righthand glass, the incident angle of 60.8 degrees no longer exceeds the critical angle! The critical angle at a glass-water interface (the refractive index of water is about 1.33) is about 62.5 degrees for our glass material, which you can verify by calculating. So, much of the light that previously reflected totally at the glass-air interface and reached you eye is now entering the finger (or other object) and being absorbed or scattered so that it no longer makes it to your eye, and you see it as a dark area.

You can see ridges of your fingerprint because there are valleys in your fingerprint which may not have water trapped in them. Indeed, if your finger is too wet you will see a uniformly dark area rather than fingerprint ridges. (A secondary effect that allows you to see fingerprint ridges is the different amounts of absorption or scattering by the different thicknesses of the skin represented by the fingerprint.)

John Link, MadSci Physicist