In one puzzle, the code was only revealed upon squeezing a glass tightly. This effect only works because of quantum mechanics. The reason it wasn’t visible initially is internal reflection. When light passes from a region with a higher index of refraction into a region with a lower index of refraction, there is a certain angle, beyond which, all of the light will be reflected. This is a direct result from Snell’s law that describes refraction. In a previous puzzle, refraction was already an important concept. It basically states that depending on the index of refraction, light will be bent at the surface. The precise mathematical formulation is captured in the following equation:
Internal reflection comes into play when the angle outside is 90° which means that the resulting beam is parallel when compared to the surface. This angle can be calculated using the previous formula.
(source: https://slideplayer.com/slide/14640805/)
For any incident angles greater than that critical angle, nothing is transmitted and there is only total internal reflection. Because of that, when looking in a glass from above, the outside isn’t visible anymore. However, there is a way to overcome total internal reflection, but only through quantum mechanics. In quantum mechanics, the position of a particle is probabilistic until it is measured. It is even possible to pass through obstacles in this method, which is called quantum tunnelling. This is what happens to the photons when the message is squeezed closely to bottle. So, total internal reflection is overcome and the previously invisible writing has become visible.