Absorption of light

When light is incident upon a homogeneous medium, a part of the incident light is reflected, a part is absorbed and the rest is transmitted.

I₀ = I_a + I_t + I_{r                                                                        ...........................(1)}

Where, I₀ = Incident light

            I_a = Absorbed light

            I_t = Transmitted light

            I_r = Reflected light.

_{Ir is very small, so eq.(1) becomes,}

I₀ = I_a + I_t                                                                   ......................(2)

Lambert's law: 

" When a beam of light is allowed to pass through a transparent medium, the rate of decrease of intensity with the thickness of medium is directly proportional to the intensity of the light."

 "This law states that decrease in the intensity of monochromatic light with the thickness of the absorbing medium is proportional to the intensity of incident light."

-dI/dx ∞ I      or     -dI/dx = KI,                                  ......................(3)

Where, I = intensity of incident light of wavelength(λ)

            x = Thickness of the medium 

            K = Proportionality constant.

Now, Integration of equation (3) and putting I = I₀ when x = 0,

I = I₀e^{-Kx                                                                                 ............................(4)}

^{Where I₀ = Intensity of incident light.}

             ^{I = Intensity of transmitted light.}

             ^{K = Absorption coefficient.}

Definition of  Absorption Coefficient (K) : 

"It is the reciprocal of the thickness which is required to reduce the light to 1/10 of its intensity."

^{The ratio Ix/I₀ is known as transmittance (T).}

^{log I₀/Ix is known as absorbance (A).}

^{I₀/Ix is known as opacity.} 

^{Beer's Law:}

It states that a decrease in the intensity of monochromatic light with the thickness of the solution is not only proportional to the intensity of the incident light but also the concentration 'c' of the solution.

Beer's law gives the relationship between transmittance and the concentration of the solution.

Mathematically,            

-dI/dx ∞ Ic

-dI/dx = ЄIc

on integration I = I₀e^-ЄCX

^Where,

 Є = molar absorption coefficient or molar extinction coefficient.

Applications of Beer's law:

Beer - Lambert's law is used to determine unknown concentration by comparison with a solution of known concentration by using a colourimeter or spectrophotometer.

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