A thin paper of thickness 0.02 mm having a refractive index 1.45 is pasted across one of the slits in a Young’s double slit experiment. The paper transmits 4/9 of the light energy falling on it. (a) Find the ratio of the maximum intensity to the minimum intensity in the fringe pattern. (b) How many fringes will cross through the center if an identical paper piece is pasted on the other slit also? The wavelength of the light used is 600 nm.
(a)Let the original intensity of light be 
and that after passing from the paper be 
.
Given,
We know that intensities are directly proportional to the square of the amplitude. Let the initial amplitude be 
and that from the paper be 
.
Here, k is some constant.
Therefore, 
and 
.
Now, the maximum amplitude is 
And minimum amplitude is 
Therefore, ratio of maximum intensity to minimum is
(b)Here, the refractive index is 
Wavelength of light, 
Here, the optical path difference is 
Therefore, the number of fringe shifts is 