Young's double slit experiment involves the interference of light waves originating from two slits which produce a pattern of bright and dark fringes due to constructive and destructive interference respectively. In this problem, we introduce a glass plate in the path of one of the beams, which causes an additional path difference due to the change in the optical path length.
Given:
Wavelength of light,
λ=500‌nm=500×10−9mRefractive index of the glass plate,
n=1.5Thickness of the glass plate,
t=0.1‌mm=0.1×10−3m The optical path difference introduced by the glass plate is given by:
∆d=(n−1)tSubstituting the given values:
∆d=(1.5−1)×0.1×10−3m=0.5×0.1×10−3m=0.05×10−3m=5×10−5m
The shift in the number of fringes due to this path difference is given by:
Number of fringes
=‌Substituting the values for
∆d and
λ :
Number of fringes
Thus, the number of fringes that will shift due to the introduction of the glass plate is 100 .
The correct option is A.
100