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Question

In biprism experiment, 10th dark band is observed at 209mm from the central bright point on the screen with red light of wavelength 6400˚A. By how much will fringe width change, if blue light of wavelength 4800˚A is used with the same setting?

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Solution

In the biprism experiment, the 10th dark band is observed.
The distance between the mth dark band with the central bright band is
Xm=(2m1)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:
XrXb=0.220.165=0.055mm

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