In the biprism experiment, the 10th dark band is observed.
The distance between the mth dark band with the central bright band is
Xm=(2m−1)λD2d
Therefore, the distance for the 10th dark band is
X10=((2×10)−1)λD2d=19λD2d
Now, when red light is used, we have:
(X10)r=19λrD2d------(1)
Similarly, for blue light, we have
(X10)b=19λbD2d------(2)
Now, the fringe width is
X=λDd
∴Xr=λrDd-------(3)
∴Xb=λbDd-------(4)
From equations (1) and (3), we get:
(X10)r=19Xr2=2.09mm
∴Xr=2×2.0919=0.22mm
Dividing equations (1) and (2), we get:
(X10)r(X10)b=λrλb
∴(X10)b=1.57mm
Now, from equations (2) and (4), we get:
(X10)b=19Xb2
∴Xb=2×1.5719=0.165mm
Therefore, the change in fringe width when blue light is used instead of red is:
Xr−Xb=0.22−0.165=0.055mm