Why we can't multiply the energy received from the Sun?

One day when I and my sister were talking on the basic Physics concepts then we came across a very puzzle question. The question is, “How it’s possible to multiply the energy coming from the Sun by mirrors in the Earth by violating the Energy Conservation Law!"

Now you might be thinking actually what I want to say or point out at. For that I need your kind attention for next 5 minutes. Because the depth of this question may also puzzled you like us!

We know that we receive approximately a constant amount of energy from our one and only nearest star the Sun. Let’s assume that the Sun has the capacity to emit 100 cd ( candela ) of intensity per day. And out of 100 cd let’s suppose only 1 cd is directed towards our Earth i.e. we receive only 1 cd intensity from the Sun in a particular day.

Now what we’re going to do is that we want to multiply this 1 cd of intensity or energy into 10 or 20 cd. For that we'll put 10 Mirrors in such angles that they can focus the 1 cd intensity of light incident on each 10 mirrors into a single point. That means what we’re doing here is that we’re able to multiply the limited amount of intensity or energy into our desired quantity.

But if you can visualise the situation and think for a moment then we’re actually violating the Law of Conservation of Energy. How? Here’s is how –

Look, what we’re assuming is that the earth receives only 1 cd of intensity from the Sun out of total 100 cd intensity emitted by Sun in a particular day. And we’re multiplying this 1 cd intensity or we can say energy into 10 cd or 20 cd by using mirrors. So that’s why we’re doing this experiment by violating the universal law of energy conservation. For simplicity in understanding let the intensity of sun as the energy which we can obviously feel when sun light fall into our body.

If you’re still can’t able to visualise the scene let me give you a baby example.
So when we let the sun light fall into our hand, we just feel a bit of warmth but when we put our hand in the sun light coming from 10 mirrors then it may burn our hand. That means we’ve multiplied 10 times the energy in the earth coming from the Sun with the help of mirrors. That means we’re creating more energy or multiplying energy from a single source of energy, which is against the law.

Probably I am able to inject the puzzle into your head. Yeah or nah – comment below!

Now, let me clear some precise assumptions we’re making here.

1. We’re assuming that the Sun can emit only 100 cd per day. It’s actually true because all the Energy sources in the universe are limited. One day in future the sun will also become out of fuel. You know these stuff, but I’m just helping you to remember this basic things. And from this very basic things I’ll show you the path and take you to complex things.
   
2. Here we’re assuming that out of 100 cd only 1 cd is received by the earth. It’s actually true because all the stars and planets are spherical. And if you can visualise it clearly then you’ll see that we cannot receive all the intensity or energy coming from a star at any angle with respect to the Star. We only receive a fraction of the total intensity/energy emitted by that star. That’s why here we’re assuming that the earth can able to receive only 1 cd out of 100 cd.

So till now I’ve proved that we can multiply the constant energy coming from the sun into much more energies by simply using mirrors. If still confused then read again till here!

Now think by yourself that how we’re multiplying energy by violating rules and then look at my explanation. If your and my explanation doesn’t match then feel free to comment down below or text me personally for further research on this topic.

Okay let’s reveal the very simple but tricky solution.

Here in this experiment we’re not actually multiplying the constant source of energy or violating the Universal law of Conservation of energy. The very basic explanation for this experiment is that we’re just accumulating or collecting the scattered energy coming from the sun with the help of the mirrors. Here’s how –

Assume that we’re able to capture the whole 1 cd coming from the Sun by placing huge mirrors on the surface of the earth and we’ve focused it into a point. Now if you try to precisely analyse the scene here then you’ll find that we’re no longer multiplying the 1 cd intensity or energy into 10 or 20 cd. We just collected the scattered 1 cd intensity from the whole surface of the earth. What I mean to say is that even we’re using multiple big mirrors for e.g. 10 big mirrors placed on the surface of earth and after focusing the light incident in these 10 mirrors into a single point we’ll get the net 1 cd of intensity actually coming from the Sun. So we’re no longer multiplying the 1 cd into 10 or 20 cd. That’s why we can write this basic energy or intensity equation in this particular situation as –

Intensity/energy incident on Earth's surface = Intensity/energy obtained after focusing the scattered light into a single point

For more clarity, in the baby example we’ve said that when the sun light falls into our hands, we just feel some warmth. But when we put our hand in the same sun light coming from 10 mirrors then it’ll burn our hand. What’s happening here is that the area of our hand at which the sun light is falling is not equal to the area of 10 mirrors from where sun light is falling into our hand.

I hope you got this very clearly and that’s why it’s impossible to violate the Energy conservation law.

Technically you got the answer up to this point very clearly. But if you want to dive deep more then this last part is for you!

Forget about earth and sun, let’s visualise this experiment with a candle.
Why I’m saying this because in this earth & sun system there are thousands of other factors which are affecting this experiment. For example here we’re assuming that the Sun can emit 100 cd per day and out of 100 cd only 1 cd is directed towards earth. Now this 1 cd is also travelling a long way through the dense atmosphere of earth. Due to which a major portion will get absorbed and only a fraction of 1 cd will received by the earth surface. That’s why taking a small & simple energy source will eliminate maximum of such conditions.

Now we’re taking a candle and will try to multiply the energy coming from the candle. For that we place 10 mirrors in such angles so that it focuses 10 candle light beam into a single point (a). Now if you measure the temperature of a point (b) from a distance ‘x’ from the candle and temperature of point (a), then you’ll obviously get high temperature at point (a). The reason is same as specified above i.e. we’re accumulating or collecting the scattered light at point (a) with the help of mirrors and hence it shows high temperature. And point (b) showing low temperature.

You can also get the exact same temperature of the flame if you cover the candle with a hollow spherical mirror. Because the hollow spherical mirror will focus all the light beams coming from the candle into a single point, which temperature will be same as the flame temperature.

So this is how the energy remains conserved in both the situations and we can’t multiply the energy sources.

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