Q. A double slit experiment is performed with light of wavelength 500nm. A thin film of thickness 2 μm and refractive index 1.5 is introduced in the path of the upper beam. The location of the central maximum will

(a) remain unsuited

(b) shift downward by nearly two fringes

(c) Shift upward by nearly two fringes

(d) Shift downward by 10 fringes

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Ans: (c)

Sol: Shift $\displaystyle y_0 = \frac{(\mu -1)t D}{d} $

Fringe width $\displaystyle \beta = \frac{\lambda D}{d} $

Number of fringe shifted ,

$ \displaystyle N = \frac{y_0}{\beta} $

$ \displaystyle N = \frac{(\mu-1)t D/d}{\lambda D/d} $

$ \displaystyle N = \frac{(\mu-1)t}{\lambda} $

$ \displaystyle N = \frac{(1.5-1)2\times 10^{-6}}{500 \times 10^{-9}} $

On solving , N =2