I saw a puddle of water on the road and I noticed that I can very clearly see the reflection on its surface in almost 8k high definition of each cars and buses that drove by. I went to the canteen and ordered drinks, I also noticed the reflection of patrons on the surface of the steaming hot coffee. I wonder why do so many liquids displaying this property? I am thinking a mirror has a smooth surface and the molecules don't move around but it is a completely different story for a liquid, the molecules are moving non stop bumping against every other molecules but somehow it can produce a clear reflection, why?
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$\begingroup$ My guess is that the mean free path of the surface molecules is much less than the wavelength of reflected light. $\endgroup$– Apoorv PotnisCommented Dec 19, 2023 at 7:50
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$\begingroup$ I agree with @ApoorvPotnis. It's not a matter of how much molecules move, but more about how much space between molecules, where light can go through (and then transmit). Then Snell and Fresnel laws tell you about the relation with the angle of incidence, at a macroscopic level: qualitatively, at microscopic level, the lower the angle of incidence, the smaller the "projection" of the void between molecules seen by light, the higher the probability of reflection $\endgroup$– basicsCommented Dec 19, 2023 at 9:36
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1 Answer
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As noted in the comments, reflections from water are not affected by molecular motion because the size of the molecules and the distances they move are a thousand times less than the wavelength of visible light.
Any flat dielectric interface such as air-water (or air-coffee) has a reflectivity described by the Fresnel Equations, and this reflection is unaffected by features much less than the wavelength $\lambda$ of light. In general, scattering from a sub-wavelength feature with size $d$ falls off dramatically with wavelength, as illustrated by the $d^6/\lambda^4$ dependence of Rayleigh scattering.
A surface with a roughness smaller than $\sim \lambda/2-\lambda/4$ is considered to be "optical quality", and the the best mirrors are flatter than $\lambda/50$. Visible light has wavelengths roughly in the range 380-750 nm. This is more than a thousand times greater than the size and spacing of liquid water molecules, so the roughness due to molecular motion is $<\lambda/1000$. This is far too small to affect reflectivity.
Reflections from liquid surfaces are, however, more susceptible than solid surfaces to large collective molecular movements with dimensions $>\lambda$. For example, reflections from a puddle will be distorted by ripples caused by the wind or a passing truck, and liquid surface mirrors require great care to reduce vibrations.
answered Dec 30, 2023 at 17:59
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$\begingroup$ [more sensitive than solid surfaces] do you mean "more susceptible"? $\endgroup$– g sCommented Dec 30, 2023 at 19:14
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$\begingroup$ Thanks @g-s. I agree, so I have replaced "sensitive" with "susceptible". $\endgroup$ Commented Dec 30, 2023 at 19:30