Q. Describe the method of measurement of the thickness of a thin transparent mica slit using Fresnel's Bi-prism. Give necessary theory. Draw suitable diagram.

Measurement of the Thickness of Refractive Index of a given Thin Slit by Fresnel's Bi-prism: The Bi-prism experiment can be used to determine the thickness of thin transparent material slit like silicon chip of mica slit etc.

When a given thin film whose thickness is to be determine is introduced in path of one of the interfering beam emitting from two virtual coherent sources S1 and S2, the whole fringe pattern is shifted towards the beam in path of which, the plate is introduced. If one can measure this fringes shift, then thickness of the film can be determined easily,

Theory: Let S1 and S2 be the two virtual coherent light source giving light of wavelength ¥. Let a thin transparent film of thickness't' and refractive index 'µ' is introduced in path of the light from S1. Due to this the fringe which was originally at 'O' shifts to 'P'.

Here the light form S1 travel partial in air and partially in a plate of thickness 't' and refractive index 'µ'. The distance travelled from S1 to P in air is (S1P-t) and in the plate is 't'.

Thus, the effective optical path for the wave from S1 to P becomes longer by an amount (µ-1) t due to introduction of plate.

Here 'O' is a point such that in the absence of the optical path length S1o and S2o becomes equal i.e. 'O' is the position of central maxima. But in presence of plate the optical path length S1O and S2O do not arrive simultaneously at point 'O'.

Expression (8), suggest us that the fringe shift is independent of order 'n', i.e. all the fringes are displaced through the same amount and no other change in the appearance of fringes in found.

If we know that fringe shift then by using expression (9) and (10) we can calculate the thickness and refractive index of given sheet.

Note : It should be noted that this method is not applicable for thick sheets.