Q15 of 79 Page 380

In a Young’s double slit experiment using mono-chromatic light, the fringe pattern shifts by a certain distance on the screen when a mica sheet of refractive index 1.6 and thickness 964 micron (1 micron = 10-6 m) is introduced in the path of one of the Interfering waves. The mica sheet is then removed and the distance between the screen and the slits is doubled. �t is found that the distance between the successive maxima now is the same as the observed fringe-shift upon the introduction of the mica sheet. Calculate the wavelength of the monochromatic light used in the experiment.

Given, refractive index of mica,

Thickness of mica,


Let D be the distance between the slits and the screen, “d” be the distance between two slits and be the wavelength of light.


Now, the fringe width is given by


The path difference when the mica sheet is present is


Therefore, the number of fringe shifted,


And the shift in the fringes is given by the fringe width multiplied by the number of fringes shifted.



And for the second case, the fringe width is,



Here, there’s no shift present.


From the question,






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13

A plate of thickness t made of a material of refractive index μ is placed in front of one of the slits in a double slit experiment. (a) Find the change iii the optical path due to introduction of the plate. (b) What should be the minimum thickness t which will make the intensity at the center of the fringe pattern aero? Wavelength of the light used is λ. Neglect any absorption of light in the plate.

 14

A transparent paper (refractive index = 1.45) of thickness 0.02 mm is pasted on one of the slits of a Young’s double slit experiment which uses monochromatic light of wavelength 620 nm. How many fringes will cross through the center if the paper is removed?

 16

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?

 17

Two transparent slabs having equal thickness but different refractive indices μ1 and μ2 are pasted side by side to form a composite slab. This slab is placed just after the double slit in a Young’s experiment so that the light from one slit goes through one material and the light from the other slit goes through the other material. What should be the minimum thickness of the slab so that there is a minimum at the point P0 which is equidistant from the slits?