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In optics, the transparency, T, of a substance equals the ratio of the intensity of light transmitted through the substance (Jt) to the intensity of incident light (Jt) where incident light is the light falling on the surface of a substance. The opacity of a substance equals the reciprocal of transparency. The density, D, of a substance equals the common logarithm of the opacity. Find density in terms of intensity of transmitted and incident light then expand the equation to a difference of two logarithms.



Answer :

sqdancefan

Answer:

  • D = log(Ji/Jt)
  • D = log(Ji) -log(Jt)

Step-by-step explanation:

You want optical density in terms of intensity of transmitted (Jt) and incident (Ji) light, written as a single term and as the difference of logarithms.

Transparency

Optical transparency is the ratio of transmitted to incident light intensities:

  T = Jt/Ji

Opacity

Opacity is the inverse of transparency:

  O = 1/T = Ji/Jt

Density

Optical density is the common log of opacity:

  D = log(O)

  D = log(Ji/Jt)

As the difference of logarithms, this is ...

  D = log(Ji) -log(Jt)

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Additional comment

The relevant rule of logarithms is ...

  log(a/b) = log(a) -log(b)

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