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# A mica strip and a polystyrene strip are fitted on the two slits of a double slit apparatus. The thickness of the strips is 0.50 mm and the separation between the slits is 0.12 cm. The refractive index of mica and polystyrene are 1.58 and 1.55 respectively for the light of wavelength 590 nm which is used in the experiment. The interference is observed on a screen a distance one meter away. (a) What would be the fringe-width? (b) At what distance from the center will the first maximum be located?

Answer :

Given, separation between the slits

The distance between the screen and the slit,

Wavelength of light,

refractive index of mica,

refractive index of polystyrene,

(a)The fringe width is given by

(b) The optical path difference is

Now we know that

Therefore, number of fringe shifts is

This means that there are 25 full fringe shifts from the center with 0.42w shift on one side and (1-0.42) w=0.58w on the other side

Hence, maximum on one side =

And on the other side,

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