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A certain luminous surface obeys Lambert...

A certain luminous surface obeys Lambert's law. Its luminance is equal to `L`. Find:
(a) the luminous flux emitted by a element `DeltaS` of this surface into a cone whose axis is normal to the given element and whose aperture angle is equal to `theta`,
(b) the luminosity of such a source.

Text Solution

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For a Lambert source `L =` const The flux emitted into the cone is
`Phi = L Delta S cos alpha d Omega`
`= L DeltaS int_(0)^(theta) 2pi cos alpha sin alpha d alpha`
`= L Delta S pi (1- cos^(2) theta) = pi Ldelta S sin^(2)theta`
(b) The luminosity is obtained from the pervious fromula for `theta = 90^(@)`
`M = (Phi (theta = 90^(@)))/(Delta S) = piL`
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