Question

A two-slit interference experiment is set up, and the fringes are displayed on a screen. Then the whole apparatus is immersed in the nearest swimming pool. How does the fringe pattern change?

Short answer

The fringe width will decrease, if the apparatus is immersed in water.

Step-by-step solution

Define the principle of superposition.

The principle of superposition states:

When two or more waves overlap, the resultant amplitude at any point and at any instant is the sum of the amplitudes that would be produced at the point by the individual waves.

Determine the change in the pattern.

In a double-slit experiment, for a constant separation between the two slits $\left(\mathrm{d}\right)$and between the slits and screen $\left(\mathrm{D}\right)$, the fringe width is directly proportional to the wavelength of light used. Let the wavelength of light in water is $\mathrm{\lambda }$. Then-

$\mathrm{\lambda }=\frac{{\mathrm{\lambda }}_0}{\mathrm{n}}$

Where, ${\mathrm{\lambda }}_0$is the wavelength of light in air and role="math" localid="1663848236651" $n$is the refractive index.

As the refractive index of water is $1.33$, the wavelength of light decreases. Thus, the fringe width also decreases.

Hence, the fringe pattern becomes narrower.