Let the refractive index of mica be 'μ ' and the thickness of the thin sheet be 't'. If the mica sheet is introduced into the path of one of the interfering beams, the optical path length is increased by 2(μ-1)t. If 'n' is the number of fringes shifted in the fringe system then,
2(μ-1)t = nλ ------------------------------------ (1)
But as fringes with monochromatic light are exactly alike, it is not possible to count the number fringes shifted due to the introduction of mica sheet.To overcome this difficulty, localized fringes are formed with a white light source and central dark fringe is made to coincide with the vertical cross wire.The paths AB and AC are then exactly equal.
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| Localized White Light Fringes Credit: By Stigmatella aurantiaca at English Wikipedia, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=20155966 |
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| Michelson Interferometer Setup |
The mica sheet is then introduced between the glass plate G1 and M1 such that light passes through it normally.Mirror M1 is adjusted till the central dark fringe again coincide with the vertical cross wire of the telescope. The distance 'l ' through which the mirror moved is noted. The white light is now replaced with monochromatic light of wavelength 'λ' .Mirror M1 is moved back and number of fringes 'n' contained in length 'l ' is found out . Then from equation (1),thickness of the mica sheet is given by,
