Mirror and its glories…

There are a lot of flabbergasting phenomena associated with these glasses, mirrors, lenses, etc. I won’t be taking a class on optics, regarding the Snell’s law relating the sines of the angles between surfaces, rays of light falling on a surface, etc. Don’t you worry. And, we won’t be going much into the atomic level in order to understand the reflection, refraction, interference, etc (at least, not this time). Instead, we’ll be addressing a few basic funny things associated with the mirrors. For now, we’ll stick to the fact that light is made of photons. Okay? Okay..!!!

A mirror (as everyone know) is just a piece of glass of some thickness with some amount of silver coated at the back. Wait… not simply “back”..!!! It cannot be defined under these circumstances. I mean, the silver is coated at one of the two surfaces, so that it reflects light, producing an illusion that a copy of the object in front of it is sitting right inside the mirror.

Index of Refraction

Before we get into the subject, we need to know about the refractive index of a material. It’s just a number that gives the ratio of speed of light in vacuum to that in air (“1.5” for glass, “1.33” for water). Different materials can have different values of this number. And, this thing is also a function of density. Mostly, it increases linearly with the density of material, which explains a strange activity going on inside the sun.

  • A high energy photon released at the core by fusion of hydrogen atoms has to suffocate to get out. Because, it has to traverse through a lot of layers (around 700,000 km) before it reaches the surface. Common sense may suggest that it’d take less than 5 seconds (which isn’t true). Mind you..!!! That happens only in vacuum. The density is around 0.0002 kg/m³ in the photosphere. But in the core, it goes to an unimaginable 150,000 kg/m³. Moreover, the layers are moving around chaotically. As a result, an average photon can take from at least 17,000 years to as long as 50 million years to reach the surface. Then, the next eight minutes of further travel to reach your town and finally arrive at your retina…

But, this linear variation of density doesn’t hold good sometimes. In case of materials like ethanol, which is less dense than water, the refractive index has a greater value. That’s Physics. It can make fool of you by lot of its tricks…

Reflection at surfaces

Now that we’ve seen the index, let’s go deeper into reflection. Light falling on the surface of any material (occuring between media having different refractive indices) gets reflected and transmitted (absorbed or refracted) at the same time. And, I’m speaking about ordinary stuff. Not blackholes and blackbodies..!!! (where this isn’t applicable). A set of equations by Fresnel provide the way for calculating the amount of light that is reflected & transmitted. For glass, about 4% of light is reflected off from the surface (i.e) 1 in 25 photons get reflected (2% for water). The reason why it’s like that, is not yet known. But, in order to explain the observations, and in order to continue our quest of exploring nature, we settled with the fact and moved on (with the agreement that it’s as it is…)

I suggest you spend about an hour or so, watching Richard Feynman’s QED lecture on “Fits of Reflection and Transmission“, where he explains about these astonishing making-others-go-crazy phenomena…

As we’ve seen so far, reflection happens only when a difference in refractive index is encountered. And, this reflection can be of two kinds. It can either be specular or, be diffuse, which is based on the material and also, the state of it.

Diffuse reflection “magic”

The difference between both reflections can be realized by the following experiment. A mirror, being a flat & smooth surface, reflects the incident light at equal angles, without scattering it, thereby cloning the environment in the mirror. This is specular reflection. Now, let’s blend the mirror and have a look at the remains, the powder (which is essentially, grains of silica). It should appear white. Hmm… Why should the powder be white? What’s happening here is diffuse reflection.

The silica-air interface does have the refractive index mismatch, but the conditions are slightly different here. Because, they’re in their fine powdery state (i.e) the gap between individual grains is more than enough for thousands of air molecules to fill into. So, light incident on this mixture encounters a lot of mismatches (unlike mirror where there’s only a single mismatch) by which it gets scattered by the grains at different angles. The net effect is that all of these subsequent reflections add up to produce the white appearance of the powder. Let’s bring this situation more realistic. We will now fill up the spaces with some magic fluid of refractive index “1.5” (same as that of glass). Now that there are no mismatches in refractive indices of both materials, the mixture acts like glass. It’s transparent.

Hey, we experience this phenomenon everyday (more or less). What happens when you soak a cloth? It appears dark. Of course. And, that happens due to this thing going on. The reflection at the air-cloth interface is not the same as that of water-cloth and the effect of this – relatively less light is reflected. It appears dark… Hence, we can now conclude that transparency, translucency, opaqueness, etc. depend on these air-material interfaces.

In addition to this, there’s one more thing. What’s the color of a mirror? A perfect mirror (in reality, there’s is nothing as “perfect”, there are losses) has exactly the same color as that of a perfectly white piece of paper. The difference is what I said all the way down. The reflection in a mirror is specular, while reflection in a paper is diffuse (i.e) it’s scattered.

Windows at night…

The effect of the 4% reflection previously mentioned, can also be seen in windows & other glass panes with light filters (like car doors). Let’s take a normal glass window. During daytime, large amount of light from the inside is refracted out, while 4% is reflected back inside. The sunlight from outside also gets refracted through the window by large amount and reflected back out by 4%. The intensity of light (number of photons striking the glass) outside being large, the reflection due to it can be easily noticed.

For instance (as a rough number), if 100 photons strike the window from the inside, only 4 reflect back. On the other hand (in case of sunlight), if a million photons strike the window from outside, about 40k reflect back. It’s this 40k, you’d be seeing when you’re zooming past a house. Only if you get close enough and notice very carefully, you’d be able to see the 96 photons refracted from the inside, which shows you enough information about the insides of the house. Again, it’s just a rough number which totally depends on the number of photons striking from the inside. Here comes another issue which determines how your eye recognizes the reflected image in both situations. First, you’d require at least 50-100 photons to excite your cones and second, the irises contract & open up depending on the intensity of light, which limits your daytime recognition.

And, the situation gets inverted at night when you can see the insides of the house with no issues at all. That’s due to the absence of sunlight. What you’re seeing is just the light refracting from the inside of the room. This explains how a window can also act as a mirror at night. If you look at the mirror from inside the room, you can see the reflection (due to absence of sunlight refraction from outside)…

Inspired by this post written by John Rennie (a scientist) and this post written by Manish Goregaokar    (an undergrad student) at Physics Stack Exchange.

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