Light from a helium-neon laser $(\lambda =633\mathrm{nm})$is used to illuminate two narrow slits. The interference pattern is observed on a screen $3.0m$behind the slits. Twelve bright fringes are seen, spanning a distance of$52mm$. What is the spacing (in mm) between the slits?

Helium-neon (He-Ne) lasers are often used for interferometry because they are inexpensive and produce a consistent, visible output. They generally work at a wavelength of $633nm$, however customized versions with useable outputs at other visible and infrared wavelengths are also available.

The distance between two adjacent fringes is calculated as follows:

$\Delta y=\frac{\lambda L}{d}$

$L=3.0m$is the distance between two subsequent slits, and $d$is the distance between two successive slits.

We have $12$bright fringes in this problem, which means there are $11$spaces between them. If $h=52mm$, the distance between successive brilliant fringes is calculated as follows:

$\Delta y=\frac{h}{11}$

When we combine the two equations for$∆y$, we get

$\frac{h}{11}=\frac{\lambda L}{d}$

This results in,

$d=\frac{11\lambda L}{h}$

We get numerical values and return them.

$d=0.40\mathrm{mm}$