free physics video tutorials for all

 

 

OPTICS

 

Prisms

 

deviation

derivation minimum deviation

chromatic dispersion

minimum angle of dispersion

 

 

 

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.

 

 

deviation angle in a prism

 

 

back to top

 

 

Derivation of Minimum Deviation D

 

 

minimum deviation by a prism

 

 

In triangle PQR

 

deviation in prisms - equation #3            (i          

(D external angle of triangle PQR)

 

 

around points P and Q respectively,

 

prism deviation - equation #3b

 

prism deviation - equation #4

 

substituting into equation (i

 

prism deviation - equation #5                       (ii          

 

 

In triangle OPQ

 

        prism deviation - equation #6

 

prism deviation - equation #7

 

prism deviation - equation #8                             (iii     

 

      

adding together equations (ii & (iii,

 

prism deviation - equation #9              (iv        

 

  

rearranging equation (iii,

 

prism deviation - equation #10                                   (v          

 

 

 

Using Snell's Law equation,

 

prism deviation - equation #11

 

and substituting for i and r from equations (iv & (v above,

 

prism deviation - equation #12

 

n1 is the refractive index of air which approximates to 1. Hence the equation becomes:

 

prism deviation - equation #13

 

 

Example

 

So for a 60o equilateral prism made of glass(n = 1.5 approx.), the minimum deviation angle D is given by:

 

prism deviation - equation #14

 

 

It follows that:

 

prism decviation - equation #15

 

remembering that sin-1(x) means the angle whose sine is 'x',

 

prism deviation - equation #16

 

 

 

back to top

 

 

 

Chromatic Dispersion

 

The term Chromatic Dispersion describes how refractive index changes with wavelength for a particular medium.

 

 

Medium

Violet
400 nm

Red
650 nm

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: nm is defined as the absolute refractive index

 

definition of the absolute refractive index

 

where,

 

co is the velocity of white light in a vacuum


cm is the velocity of white light in the medium

 

 

It follows that: nv is defined as the absolute refractive index for violet light

 

prism dispersion - equation #1                              (i    

 

where, cm(v) is the velocity of violet light in the medium

 

 

Similarly, nr is defined as the absolute refractive index for red light

 

prism dispersion - equation #2                              (ii     

 

where, cm(r) is the velocity of red light in the medium

 

 

Since frequency f is constant throughout,

prism dispersion - equation #3

and

prism dispersion - equation #4

 

where,

 

    λo is the wavelength of white light in a vacuum


    λm(v) is the wavelength of violet light in the medium


    λm(r) is the wavelength of red light in the medium

 

 

Substituting for cm(v) , cm(r) and co into equations (i and (ii ,

 

prism dispersion - equation #5

 

cancelling f in each equation,

 

prism dispersion - equation #6

 

 

 

back to top

 

 

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.

 

 

prism dispersion - diagram

 

 

Using the equation(below) we can calculate values of deviation D for each colour.

 

prism deviation - equation #12

 

Subtracting the deviation angles gives the minimum dispersion angle for white light.

 

 

 

back to top

 

 

 

this week's promoted video

 

 from Physics Trek

 

 

creative commons license

All downloads are covered by a Creative Commons License.
These are free to download and to share with others provided credit is shown.
Files cannot be altered in any way.
Under no circumstances is content to be used for commercial gain.

 

 

 

 

©copyright a-levelphysicstutor.com 2016 - All Rights Reserved