Will intensity of this light become infinity?

[P.Ramesh]

Dear Friends,

My longtime pending doubt here...!

When we focus a mirror on the wall we get bright spot of the light. Ok.

Now say, there is cube 6" x 6" x 6" whose inner walls are of mirror surfaces and opaque surfaces are the outer surfaces of the cube. In the center of the cube, in the mid space, I install a lamp (say 100W electric bulb).

There are mutiple reflections happening since all the 6 walls are facing each other. Now If I introduce an instrument to measure the intensity or brightness of the light, How much it will be? 2 times, 3 times or 4 times or infinity?

But I feel the answer as the "intensity will be same as that of the light at the given distance". It won't get multipled. Still I want an detailed explanation with convincing reasons. Anybody to explain me please!?

 

[whatta]

Let's say a mirror reflects x amount of light, x < 1. So we have for two opposite mirrors, for every hop,
1: 1(light from bulb)
2: 1(bulb) + x(light from hop 1 reflected by opposite mirror)
3: 1 + x(from hop 2) + x*x(from hop 1)
...
∞: 1 + x + x*x + x*x*x +... = 1/(1-x)
this is if I didn't missed anything. the rest of light, ∞ - 1/(1-x), will be consumed by mirrors and eventually melt them. unless they radiate the heat.

 

[P.Ramesh]

Let's say a mirror reflects x amount of light, x < 1. So we have for two opposite mirrors, for every hop,
1: 1(light from bulb)
2: 1(bulb) + x(light from hop 1 reflected by opposite mirror)
3: 1 + x(from hop 2) + x*x(from hop 1)
...
∞: 1 + x + x*x + x*x*x +... = 1/(1-x)
this is if I didn't missed anything. the rest of light, ∞ - 1/(1-x), will be consumed by mirrors and eventually melt them. unless they radiate the heat.

Thanks for the reply. but it is not convincing because the brightness seems function of the wavelength... even i am also not sure.

 

[whatta]

i mean, x like integral flux reflected in all wavelengthes. oh well.

 

[russ_watters]

If you could get everything perfect (you can't), the intensity would continuously increase. Real mirrors have reflectivities under 100% and real lights are bigger than a single point and get hot.