A small transparent slab containing material of μ=1.5 is placed along AS (figure). What will be the distance from O of the principal maxima and of the first minima on either side of the principal maxima obtained in the absence of the glass slab?
             

AC=CO=D,S1C=S2C=d<<D

Hint: The position of the maxima or minima depends on the path difference.

Step 1: Find the path difference.

ln case of transparent glass slab of refractive index, the path difference will be calculated 

as x=2dsinθ+(μ-1)L

Step 2: Find the condition for maxima.

For the principal maxima, the path difference= 0 

2dsinθ+(μ-1)L=0
orsinθ0=-L(μ-1)2d=-L(0.5)2dL=d/4
orsinθ0=-116
OP=Dtanθ0=Dsinθ0=-D16

Step 2: Find the condition for minima.

For the first minima, the path difference is ±λ2.

2dsinθ1+0.5L=±λ2sinθ1=±λ/20.5L2d=±λ/2d/82d=±λ/2λ/82λ=±14116

[ The diffraction occurs if the wavelength of waves is nearly equal to the slit width (d)] 

On the positive side, sinθ1+=14-116=316

On the negative side, sin θ1-=14-116=-516

The first principal maxima on the positive side is at distance:

tanθ1+=Dsinθ1+1sin2θ1=D316232=3D247above point O

The first principal minima on the negative side is at distance 

D tan θ1+=5D162-52=5D231belowpointO.