Angular dispersion and Mean deviation

  Angular dispersion and Mean deviation

Introduction: We know that when the polychromatic source of light is incident on a refracting surface, it gets separated into its constituent colors. This phenomenon is called the dispersion of light. Let us understand it in detail.

Dispersion of light

Deviation through a thin prism.

Thin prism: A prism having a very small refracting angle of prism is called as thin prism

If 𝜭 is small, sin𝜭 = 𝜭

Thus prism formula for thin prism changes to,

𝛅 + A = 𝝻A

𝛅 =  𝝻A - A

𝛅 = A(𝝻-1)  --(1)

Angular Dispersion: The angular separation between two extreme colors in the dispersed beam of light is called angular dispersion.

Note: For white light, red and violet are the extreme colours and yellow is the mean colour.

Angular dispersion =  𝛅v- 𝛅r

𝛅v- 𝛅r = [A (𝝻_v -1) - {A(𝝻_r -1)}]

𝛅v- 𝛅r = [𝝻_v A -A) - {𝝻_rA - A)}]

𝛅v- 𝛅r = [𝝻_v A - A - 𝝻_rA + A]

𝛅v- 𝛅r =  𝝻_v A - 𝝻_rA 

𝛅v- 𝛅r =  A(𝝻_v - 𝝻_r) ----(2)

Eq (2) gives the expression for angular dispersion.

SI unit for angular dispersion is degree  or radian

Dispersive power (⍵): The dispersive power of a prism is its ability to disperse a beam of light into its constituents colours.

It can also be defined as the ratio of the angular dispersion between the extreme colours to the deviation of mean colour is called the dispersive power of material of a prism.

_{│<<<Prism formula│   │Formation of rainbow>>>│}

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