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  4. What happens to the fringe pattern when the Young's double slit experiment is performed in water instead of air?

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Q. What happens to the fringe pattern when the Young's double slit experiment is performed in water instead of air?

AFMCAFMC 2005

Solution:

In water, wavelength of light decreases by a factor $\mu$, the refractive index of water. In Young's double slit experiment, let screen is placed at a distance $D,\, d$ is the distance between coherent sources.
image
The fringe width is given by
$W=\frac{D\lambda }{d}$
where, $\lambda$ is wavelength of light used.
When the whole setup is dipped in water, wavelength is $\lambda_{w}=\frac{\lambda_{a}}{\mu}$ hence, it decreases.
Therefore, fringe width decreases and hence, fringe pattern shrinks.