Expression for Fringe Width in Double Slit Experiment I YDSEI

In Young’s Double Slit Experiment, a monochromatic light source illuminates two closely spaced slits, resulting in an interference pattern of alternating bright and dark fringes on a screen. These fringes are formed due to the constructive and destructive interference of light waves emerging from the slits.
The fringe width (denoted by 𝛽) is the distance between two consecutive bright (or dark) fringes in the interference pattern.
The expression for fringe width is derived from the path difference condition for constructive interference and is given by:
β=λD/d
Where:
β = fringe width
λ = wavelength of the light used
D = distance between the slits and the screen
d = distance between the two slits
This equation shows that the fringe width is:
-Directly proportional to the wavelength (λ) and the screen distance (𝐷)
-Inversely proportional to the slit separation (d)
Hence, using light of a longer wavelength or increasing the screen distance results in wider fringes, while increasing the slit separation leads to narrower fringes.

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