Q. The contrast in the fringes in any interference pattern depends on-
NTA AbhyasNTA Abhyas 2022
Solution:
Contrast of fringes means, fringes should be clearly visible and its separation can be perfectly visible and this can be perfect only when, bright fringes are perfectly bright and dark fringes are perfectly dark.
It can also be measure by an index known as fringe visibility and is given by,
$V=\frac{2 \sqrt{\frac{I_{1}}{I_{2}}}}{1 + \frac{I_{1}}{I_{2}}}$ , where $I_{1}\&I_{2}$ represents intensity of both sources.
$\Rightarrow V=\frac{2 \sqrt{N}}{1 + N},\left(\because N = \frac{I_{1}}{I_{2}}\right)$
It is clear from above expression that $V$ is maximum for $N=1$ , which represents $I_{1}=I_{2}=I$ , at this case, $I_{m a x}=4I\&I_{m i n}=0$ , it gives perfectly bright and dark fringe and gives the best contrast of fringes.
So we can say that contrast depends on intensity of the sources.
It can also be measure by an index known as fringe visibility and is given by,
$V=\frac{2 \sqrt{\frac{I_{1}}{I_{2}}}}{1 + \frac{I_{1}}{I_{2}}}$ , where $I_{1}\&I_{2}$ represents intensity of both sources.
$\Rightarrow V=\frac{2 \sqrt{N}}{1 + N},\left(\because N = \frac{I_{1}}{I_{2}}\right)$
It is clear from above expression that $V$ is maximum for $N=1$ , which represents $I_{1}=I_{2}=I$ , at this case, $I_{m a x}=4I\&I_{m i n}=0$ , it gives perfectly bright and dark fringe and gives the best contrast of fringes.
So we can say that contrast depends on intensity of the sources.