Eli5 why are you able to see lights far away but the light it projects doesn’t go nearly as far? (Car lights, street lights, etc)
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Think about a slice of toast which you want to spread cream cheese on. The toast represents an object at a distance (d) from the light. This toast is special in that as you move it away from the light it gets larger. You move it twice the distance (2d) it’s sides grow twice as large.
The light is like the cream cheese we want to spread on the toast, but the light is a fixed amount, it doesn’t grow like the toast.
The surface area (A) of the side of toast facing the light is calculated by multiplying the width of the toast (w) by the height of the toast (h). Then (A=w*h). At distance (d) there is (A) amount of cream cheese spread over it, but remember the amount of cream cheese is fixed.
Now at twice the distance (2d) the toast is twice as wide (2w) and also twice as tall (2h). This means that the area of this slice of toast at (2d) (let’s call it B to not confuse it with the size of A) is (B=2w*2h), or in other words (4wh) which is 4 times the original slice (recall originally A=wh), thus we can say (B=4A).
The amount of cream cheese is fixed at A, but now we have 4 times the toast to spread it across! So we see that the further we get the thinner we must spread the cream cheese to cover the ever growing surface.
Now, our eyes are a fixed size, much like our mouths. Imagine taking a bite out of that slice of toast. The closer you are to the source the more cream cheese would be in this fixed size bite, and similarly the further away you are the less cream cheese there will be.
In the same way our eyes will be hit by less light the further we are from the object.
The name of this rule is called the inverse square law. If you were 3 times the distance at (C), then we get (C=3w*3h=9A).
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