Example of Wave optics
Example of wave optics: in Young’s double slit experiment using monochromatic light, the fringe pattern shifts by a certain distance on the screen when a mica sheet of refractive index 1.6 and thickness 1.964 micron is introduced in the path of one of the interfering waves. The mica sheet is then removed and the distance between the slits and the screen is doubled. It is found that the distance between successive maxima (or minima) now is the same as the observed fringe shift upon the introduction of mica sheet. Calculate the wavelength of monochromatic light used in the experiment.
Solution:
Here, µ = 1.6,
t= 1.964 µ m = 1.964 × 10-6 m
if d is distance between the slits and D is distance of screen from the slits, then shift in the pattern is :
x = (µ -1)t D/d
Fringe width β = λD/d
When D is doubled, fringe width β’ =λ (2D)/d
This is the distance between successive maxima/minima.
As per question x =β’
(µ -1)t D/d = λ (2D)/d
λ = (µ -1)t /2=5.892 × 10-7 m= 5892 Angstrom