What is Dispersive Power?

What is Dispersive Power?

In order to understand Dispersive Power, first of all it is necessary to understand dispersion of light and angular dispersion. 

If you already know what dispersion and angular dispersion is and want to skip to the good part then CLICK HERE.

When a narrow beam of sunlight is passed through a glass prism and emergent light from the prism is incident on a white screen then we see many colourful bands. These colours are Violet, Indigo, blue, green, yellow, orange and red. (VIBGYOR). This splitting of white light into its component colours when it is made to pass through the prism, is called dispersion of light and bands of colours is called spectrum of light.




Here it must be noted that the red colour bends the least while the violet colour bends the most, which can be easily verified by the relation δ=(µ-1)A & µ∝1/λ.

Now, 

Let 

δV = Angle of deviation for violet colour

δR = Angle of deviation for Red colour

δ = Angle of deviation for yellow colour (Mean)

µV = Refractive index of prism for violet colour
µR = Refractive index of prism for Red colour
µ = Refractive index of prism for yellow (mean)

A = Angle of the prism



δV=(µV-1)A
δR=(µR-1)A
δ=(µ-1)A

Angular Dispersion 

The angular separation between the violet and red colur (extreme colours) in the spectrum produced after the dispersion of light through a prism is called the angular dispersion. 

Angular dispersion 
= δV-δR
= (µV-1)A-(µR-1)A
= A(µV-1- µR+1)
= A(µV-µR)

We can see that the angular dispersion of a prism depends on 
i) Angle of the prism (A)
ii) Nature of the material of the prism (µV and µR)

Dispersive Power (ω)

It is defined as the ability of a prism to cause the dispersion of light. It is equal to the ratio of the angular dispersion to the mean deviation.


Clearly, dispersive power depends on the nature of the material of the prism and not on the refractive angle (Angle of Prism) of the of the prism (A).