When Albert turns on his small desk lamp, the light falling...

When Albert turns on his small desk lamp, the light falling on his book has intensity $I_{0}$. When this is not quite enough, he turns the small lamp off and turns on a high intensity lamp so that the light on his book has intensity $4 I_{0}$. What is the intensity of light falling on the book when Albert turns both lamps on? If there is more than one possibility, give the range of intensity possibilities.

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Key Concepts

Intensity Addition for Incoherent Light

When light sources are incoherent, meaning they have no stable phase relationship, the intensities simply add together without interference effects. In this case, the total intensity on a surface is just the sum of the individual intensities from each source, independent of any phase considerations.

Coherence

Coherence refers to the fixed phase relationship between light sources. When sources are coherent, their amplitudes can interfere constructively (maximizing the total intensity) or destructively (reducing the total intensity). This coherence is crucial in determining whether the added amplitudes lead to interference effects or simply result in the arithmetic sum of intensities.

Superposition of Waves

This concept involves the principle that wave amplitudes add where they overlap. For light, the resulting intensity is related to the square of the sum of the amplitudes. The contributions from different sources can add in a way that depends on their relative phases, potentially leading to constructive or destructive interference.

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