# Sum of intensity of light or radiance?

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If two sources, S1 and S2, of light are shining on a ball, and we are given the formula, L1(P) for the amount of light reflecting off the ball at point P caused by light source S1 and into a pixel, 'p' in the image plane of a camera, and similarly L2(P) is the amount of light reflecting off the ball at point P caused by light source S2 and into the same pixel, 'p', on the same image plane of the same camera. Then can we say the total amount of reflected light at point 'P' into pixel 'p' on the image plane is equal to L(P) = L1(P) + L2(P)?

In other words, is there a superposition principle for the intensity of light? It seems that when two lights shine on a surface, the resulting surface is always brighter.

Edited by Dobob

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If two sources, S1 and S2, of light are shining on a ball, and we are given the formula, L1(P) for the amount of light reflecting off the ball at point P caused by light source S1 and into a pixel, 'p' in the image plane of a camera, and similarly L2(P) is the amount of light reflecting off the ball at point P caused by light source S2 and into the same pixel, 'p', on the same image plane of the same camera. Then can we say the total amount of reflected light at point 'P' into pixel 'p' on the image plane is equal to L(P) = L1(P) + L2(P)?

In other words, is there a superposition principle for the intensity of light? It seems that when two lights shine on a surface, the resulting surface is always brighter.

Intensity is the rate of photons being emitted/reflected. if you have two photons arriving and reflecting off the same point it is twice as intense as one photon being reflected off the same point

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There is an exception if the light is coherent. Then the phase of the light matters, as you can get destructive interference, which reduces the intensity in some regions.

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There is an exception if the light is coherent. Then the phase of the light matters, as you can get destructive interference, which reduces the intensity in some regions.

Right, that makes sense.

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If you look at the lighting models used in computer graphics, they treat light sources as being linearly additive. (We don't normally model laser light!)

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On a large enough scale that's fine; interference tends to be a local effect. Hard to make coherent light that looks like plane waves over a large area. The bottom line is that energy is conserved.

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It seems that when two lights shine on a surface, the resulting surface is always brighter.

Apart from what has been said by other members.

At high enough intensity of light, photons that were absorbed will cause significant increase of temperature of object, and change its physical properties.

Shiny metal ball, after increase of temperature, will change color to red, yellow, white, and won't be reflective anymore.

This could be also done with powerful lasers, instead of blowtorch.

Edited by Sensei

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And, depending on the material, specular reflections are predominantly the colour of the light source, while diffuse reflections will be mainly the colour of the surface.

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If two sources, S1 and S2, of light are shining on a ball, and we are given the formula, L1(P) for the amount of light reflecting off the ball at point P caused by light source S1 and into a pixel, 'p' in the image plane of a camera, and similarly L2(P) is the amount of light reflecting off the ball at point P caused by light source S2 and into the same pixel, 'p', on the same image plane of the same camera. Then can we say the total amount of reflected light at point 'P' into pixel 'p' on the image plane is equal to L(P) = L1(P) + L2(P)?

In other words, is there a superposition principle for the intensity of light? It seems that when two lights shine on a surface, the resulting surface is always brighter.

The intensity will increase if constructive interference takes place, that is, if the phase difference is in multiples of $2\pi$.

The intensity will decrease if destructive interference takes place, that is, if the phase difference is in odd multiples of $\pi$.

Edited by Sriman Dutta

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The intensity will increase if constructive interference takes place, that is, if the phase difference is in multiples of $2\pi$.

The intensity will decrease if destructive interference takes place, that is, if the phase difference is in odd multiples of $\pi$.

Not quite. The intensity goes to zero when the phase difference is $\pi$ and is a maximum for zero or 2$\pi$.(and the multiples). in between there is partial cancellation.

I think that so.

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The sum will not appear twice as bright, though, since our eyes do not observe brightness in a linear way.

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