Birefringence
Created | Updated Jan 16, 2005
Some materials known as birefringent materials have the quality that two light rays depending on their orientation can pass through the material at different speeds so that when they leave the material they will be slightly out of phase, the magnitude of the phase shift will depend on the thickness, t, of the material.
Cellotape is an example of a birefringent material, if we pass white light through a polariser we have a plane polarised wave which can be broken up into it’s components as shown on the diagram. These components then pass through the birefringent medium, their alignment relative to the medium means that they will pass through it at different velocities, they leave the medium with the same wavelength, period and amplitude but they are out of phase, the difference in phase depends on the difference between the optical path lengths in the medium and can be given by the formula f = (2n + 1)p = 2p/l(h3 - h4)t. n is an arbitrary value assigned to the dark lines seen in the spectrum, l is the wavelength of light in air, h are the relative refractive indices of the light waves passing through the medium which can be denoted as Dh and t is the thickness of the medium. These formulae can be rearranged to get the equation n = l-1Dht-1/2. This can be seen as the formula for a straight line y = mx + c, the slope in this case is Dht and for this experiment we need not worry abut the constant c.
The optical path length is the time it takes the ray to pass through the medium multiplied by the refractive index of the medium, i.e. ht. There will be a difference between these as the very definition of birefringence gives that a medium can have two refractive indices depending on the alignment of the ray that passes through it.
They then pass through another polariser that is crossed relative to the first polariser; this aligns them in the same plane. They then undergo diffraction and interference in the spectrometer, which is viewed through the telescope of the spectrometer. The spectrum will appear to have dark lines in it. The position of these dark lines can be used to calculate the wavelength of the light from the equation ml = dsinq.
From a graph of n, arbitrary number given to the dark lines, versus 1/l we can calculate the slope which is equal to Dh.t, where Dh is the difference in the refractive indices of the medium and t is the thickness of the medium. This formula can be rearranged so that we have Dh = slope/t.
Which will give us a measurement of birefringence.
Cellotape is an example of a birefringent material, if we pass white light through a polariser we have a plane polarised wave which can be broken up into it’s components as shown on the diagram. These components then pass through the birefringent medium, their alignment relative to the medium means that they will pass through it at different velocities, they leave the medium with the same wavelength, period and amplitude but they are out of phase, the difference in phase depends on the difference between the optical path lengths in the medium and can be given by the formula f = (2n + 1)p = 2p/l(h3 - h4)t. n is an arbitrary value assigned to the dark lines seen in the spectrum, l is the wavelength of light in air, h are the relative refractive indices of the light waves passing through the medium which can be denoted as Dh and t is the thickness of the medium. These formulae can be rearranged to get the equation n = l-1Dht-1/2. This can be seen as the formula for a straight line y = mx + c, the slope in this case is Dht and for this experiment we need not worry abut the constant c.
The optical path length is the time it takes the ray to pass through the medium multiplied by the refractive index of the medium, i.e. ht. There will be a difference between these as the very definition of birefringence gives that a medium can have two refractive indices depending on the alignment of the ray that passes through it.
They then pass through another polariser that is crossed relative to the first polariser; this aligns them in the same plane. They then undergo diffraction and interference in the spectrometer, which is viewed through the telescope of the spectrometer. The spectrum will appear to have dark lines in it. The position of these dark lines can be used to calculate the wavelength of the light from the equation ml = dsinq.
From a graph of n, arbitrary number given to the dark lines, versus 1/l we can calculate the slope which is equal to Dh.t, where Dh is the difference in the refractive indices of the medium and t is the thickness of the medium. This formula can be rearranged so that we have Dh = slope/t.
Which will give us a measurement of birefringence.
