The spacing of interference fringes can be calculated using the formula

where $\lambda$ represents the wavelength of light, $D$ is the distance from the slits to the screen, and $d$ is the separation between the slits.

To elaborate, the phenomenon of interference fringes arises from the behavior of light. When light passes through two closely spaced slits, it undergoes diffraction and subsequently interferes with itself. This interference can be either constructive, leading to bright fringes, or destructive, resulting in dark fringes. The resulting pattern of these fringes can be observed on a screen positioned at a certain distance from the slits.

The formula for calculating the fringe spacing, denoted as $y$, is

In this equation, $\lambda$ is the wavelength of the light used, $D$ is the distance from the slits to the screen, and $d$ is the separation between the slits. This relationship is derived from the path difference between the two waves and the conditions necessary for constructive interference.

To apply this formula, you must know the values of $\lambda$, $D$, and $d$. The wavelength of light is often provided in the problem statement or can be found in reference tables. The distance to the screen and the slit separation can be measured directly in the experiment.

It is important to note that this formula assumes that the angle $\theta$ (the angle between the central maximum and the fringe being considered) is small. For larger angles, a more complex formula that incorporates the sine of the angle should be used.

In summary, to determine the spacing between interference fringes, use the formula

where $y$ is the fringe spacing, $\lambda$ is the wavelength of the light, $D$ is the distance to the screen, and $d$ is the slit separation. This illustrates how light waves passing through slits create a pattern of alternating bright and dark bands on a screen due to their wave-like behavior.