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Okay, you've isolated your test chamber.

Heat (same as light in this case) travels through 3 methods: radiation, convection, and conduction. Convection means that essentially something physically moves, such as the blower on a forced air heating system blowing heated air around the house. Conduction means that heat travels through objects in contact, such as getting burned from holding onto the handle of a pan on the stove.

Radiation means that any object with a temperature above absolute zero emits energy. The sun and a light bulb are just two examples. They both emit radiation. And light is a form of radiation.

Here's the problem: All objects also ABSORB radiation of one sort or another. When it does, it gets "hot" (temperature rises). In fact, the device that you intend on sticking in your box to measure temperature is going to affect the experiment. AND, air is a very good absorber of certain microwave frequencies (water vapor absorbs the radiation from a microwave oven, and oxygen absorbs 60 GHz among others which limits the upper frequency on microwave relay towards)...But they don't necessarily absorb it the same way. Your "transparent" box is transparent to light, which means radiation of a specific frequency. However, it might also NOT be transparent to infrared radiation.

In a similar way, your radiation sources (light bulbs and the sun) emit different amounts of radiation at different frequencies. Which also affects the outcome. Don't forget...everything is emitting radiation. So even if the first box was completely solid, it wouldn't matter. It would absorb light radiated from your light source (and via conduction from the air). Then via conduction it would spread the heat throughout the box. And then the box itself would radiate energy, which would STILL be picked up by the second box.

If the box and/or the air and/or whatever you are using to measure temperature absorb any of the radiation emitted from your other box, the temperature will rise above absolute zero.

So I know you think you've figured out every angle to avoid allowing any energy to be absorbed by the second box, but it's simply not possible. You will still measure something, even if it is very small. Light is just a very narrow fraction of the frequency energy can occur in.

Also, some of the radiation is reflected in addition to being absorbed or just passing right through. So don't forget to add that one to your list of complications. They use "front surface mirrors" with high powered lasers. This means the reflective part is on the surfeace instead of the back of the mirror. Why? Because if it's on the back, then the glass gets hit first and it either causes reflection problems (reflecting off two different surfaces) or else because the glass will melt/break when it absorbs some of the laser light.

Also, it does matter how big the boxes are. For instance, titanium oxide pigment is sold in 50 nm sizes. But they can make it much smaller (say 10 nm). The trouble is that the titanium oxide at that point is optically transparent (too small to reflect light). If it is much larger, then it starts to absorb instead of reflecting/refracting.
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