How does scotch tape make frosted glass clear?

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How does scotch tape make frosted glass clear?

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By filling the irregularities of the surface with its soft transparent material, it helps the glass becoming smoother and thus, transparent.
Basically, it cancels the effect of frosting by making the glass smoother instead of frosted

Consider something flat and shiny, like the hood of a car. If you look at it from most angles, it will simply look the color that it is. But if you find a very precise angle between you and the light source (say, the sun), you’ll catch a very bright sheen spot reflecting off of that surface. It’s essentially acting as a mirror and showing you a reflection of the light source, like a weaker version of looking directly at it. Most of our light sources happen to be white, so when you find this precise angle, that surface will look a brilliant white color, regardless of whatever color it actually is.

Now consider a cut gemstone, like a diamond. The reason they get cut into such intricate shapes is because sharp corners cause a similar effect to the “precise angle” effect you’d get with the hood of a car. The gemstone itself is transparent to light, but as it gets reflected and lensed about by all the corners created by the cutting process, it causes little patches of the gem to reflect the light source directly to your eye. With enough carefully-placed cuts, this effect can be all but guaranteed to be visible from any angle, no matter how you hold it, and no matter where the light source is. This is what makes gems like diamonds “sparkle”.

Now imagine taking that diamond and giving it a ton of random, jagged cuts. It won’t be professional, so it probably wouldn’t look very nice, but it should still sparkle all the same, as hundreds of randomly-aligned cuts will make that outcome pretty certain. Now shrink that diamond down to a very, very small size, say a grain of sand. When it’s that small, and the cuts are random, it probably won’t sparkle so brightly. It’ll probably just give off a dull, whitish color. Now add a bunch of these tiny little microdiamonds and you have yourself a pile of white sand.

Step back and think for a moment. We started with a perfectly transparent thing, a diamond, and just by cutting it up, making it very small, and adding a lot of them, now we have something that just looks white. Isn’t that kind of crazy?

You may be amazed to learn that this effect is actually what makes a lot of things white in color. White sand? Put grains of sand under a microscope and you’ll find that many sand grains are transparent, like diamonds, but since they’re rough and tiny, a pile of them looks white. Snow? Tiny, transparent ice crystals in a pile, but the result is a white powder. Clouds, fog, steam? Tiny droplets of water hanging in the air, white. Several of the powders in your kitchen, like salt, sugar, baking soda? White. Even when you take, say, a clear piece of plastic and bend it in a way you aren’t supposed to, the bent area will turn white–that’s because you’re creating a ton of microcracks in it that create the same effect as having lots of tiny randomly cut crystals. All white.

Now let’s get to frosted glass. A flat pane of glass is obviously see-through. To create the frost effect, they essentially just scrape up one side of the glass to create that rough, randomly-cut texture. As we just covered, that makes it appear white due to all of the random cut edges and corners scattering light in all random directions.

Now consider a piece of Scotch tape. It’s a clear strip of plastic, where one side is coated in a clear glue. Press the tape on the roughed up side of a frosted glass pane. What happens? You essentially press the glue in to fill all the tiny rough cracks, smoothing them out. The result is now a pane of glass that’s smooth on the one side, and now, thanks to the tape and the layer of glue, smooth on the other. Since it’s no longer rough, the white effect disappears!

If it bothers you to know that the roughed-up glass still exists, all you’ve really done is cover it up, you can think about it another way. That roughed-up glass has a certain shape that causes light rays coming from a given direction to scatter in a certain way. When you press the film of glue onto the frosted glass, you’re essentially creating a negative version of the roughed-up surface. An anti-lens, so to speak. When you make a lens that’s opposite in shape to another, it can reverse the effect of the first lens. So what you’ve effectively created here is a lens made of glue perfectly tailored to cancel out the scattering of the roughed-up glass. This straightens the light back out on the other end, allowing you to see through the pane.

Frosted glass contains a bunch of surface irregularities – basically lots of dents and bumps – which scatter light. That is, instead of light rays passing straight through, like they do through a smooth & flat pane of glass, the bumps and dents throw the light rays “off course” in random directions as the surfaces of the bumps and dents are angled in all different directions. So, what you get from the other side of the glass is a somewhat random mix of light rays, instead of light rays that went in a straight line from their point of origin. So the glass is still translucent – it still lets light through. But because the origin of the light has been somewhat randomized, the glass is no longer transparent – you can’t see exactly what’s behind it.

Scotch tape has glue on one side, and this glue fills in the irregularities in the surface of the frosted glass. Meanwhile, the other side of the tape is flat and smooth. So, when you apply the tape to the frosted glass you’re effectively undoing all of the roughing-up that was done to it, and making it into a sheet of normal glass with a flat, smooth surface.

This works only because the material in the scotch tape happens to have a refractive index that is the same as the glass (or close enough). A surface between materials will bend light unless those surfaces have the same index of refraction. So, if the tape (including glue) and the glass had different indices, then the light wouldn’t pass straight through and it wouldn’t work – the tape wouldn’t be able to “undo” the dents and bumps.

This also means there’s nothing special about scotch tape – any material with a refractive index sufficiently similar to glass can work, if you can make one side of it conform to the irregularities of the frosted glass, while the other side forms a smooth, flat surface. For instance, you could cover the frosted glass with mineral oil to achieve the same effect (though that would probably require the glass to be horizontal w.r.t. gravity so that the layer of mineral oil can sit on top of it).