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deviation 

Deviation
Deviation, measured in degrees, is the angle an incident ray is turned through after passing through a prism(or other optical component).
This deviation is a minimum for a prism when the path of a light ray is symmetrical about its axis of symmetry.
Derivation of Minimum Deviation D
In
(i
(D external angle of )
around points P and Q respectively,
substituting into equation (i
(ii
In
(iii
adding together equations (ii & (iii,
(iv
rearranging equation (iii,
(v
Using Snell's Law equation,
and substituting for i and r from equations (iv & (v above,
n_{1} is the refractive index of air which approximates to 1. Hence the equation becomes:
Example
So for a 60^{o} equilateral prism made of glass(n = 1.5 approx.), the minimum deviation angle D is given by:
It follows that:
remembering that sin^{1}(x) means the angle whose sine is 'x',
Chromatic Dispersion
The term Chromatic Dispersion describes how refractive index changes with wavelength for a particular medium.
Medium 
Violet 
Red 
Crown glass 
10.00 
10.37 
Acrylic 
10.46 
10.87 
Fused quartz 
11.30 
11.58 
data courtesy of Serway & Jewett
Using refractive index theory we can formulate equations in terms of the wavelength of the light involved:
Remembering that: n_{m} is defined as the absolute refractive index
where,
c_{o} is the velocity of white light in a vacuum
c_{m} is the velocity of white light in the medium
It follows that: n_{v} is defined as the absolute refractive index for violet light
(i
where, c_{m(v)} is the velocity of violet light in the medium
Similarly, n_{r} is defined as the absolute refractive index for red light
(ii
where, c_{m(r)} is the velocity of red light in the medium
Since frequency f is constant throughout,
and
where,
λ_{o} is the wavelength of white light in a vacuum
λ_{m(v)} is the wavelength of violet light in the medium
λ_{m(r)} is the wavelength of red light in the medium
Substituting for c_{m(v)} , c_{m(r)} and c_{o} into equations (i and (ii ,
cancelling f in each equation,
Minimum Angle of Dispersion
This is measure of the angle of 'spread' of a spectrum when it leaves a prism.
For minimum angular dispersion, the angle is derived from the difference in deviation between red and violet rays of light.
Using the equation(below) we can calculate values of deviation D for each colour.
Subtracting the deviation angles gives the minimum dispersion angle for white light.
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