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What is the gain profile of amplifying medium?

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https://brainmass.com/physics/optics/optic-gain-profiles-66357

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GAIN PROFILE : Constructive interference of the waves within the cavity is required for laser action. The result is the condition of resonance: light waves are amplified strongly if, and only if, they satisfy the equation, 2nL=Nw where L is the ...

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The answer contains the explanation of the gain profile of an amplifying medium.

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Optics Question: Light Traveling Through Different Medias

A beam of light traveling in air (n=1.00) falls on a layer of oil (n1=1.465) which is exactly 1.000cm thick and which rests on a layer of water (n=1.333) of thickness d2 cm. Angle of incidence is 19 degrees.
(a) Find the physical path length, l1 of the ray in the oil.
(b) Find the optical path length, OPL1, of the ray in the oil.
(c) Find the physical path length, l2, of the ray as it passes through the layer of water of thickness d2.
(d) What must be the value of d2 in order for the optical path lengths to be equal (for the oil and water paths)?
(e) What would be the apparent depth (below the air-oil interface) of a small particle at the bottom of the water layer viewed from directly above the container?

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