The width of the slit is approximately 0.0589 mm, or 58.9 micrometers.
When light passes through a narrow slit, it diffracts, meaning it spreads out and bends around the edges of the slit. This creates an interference pattern on a screen behind the slit, with bright fringes where the light waves reinforce each other and dark fringes where they cancel each other out.
Relate the fringe spacing to the slit width using the formula:
The distance between dark fringes (d) is related to the slit width (w), the wavelength of the light (λ), and the distance from the slit to the screen (D) by the formula:
d = λD / w
Given values:
λ = 589 nm (wavelength of sodium light)
D = 75 cm = 0.75 m (distance from slit to screen)
d = 7.5 mm = 0.0075 m (distance between first and third dark fringes)
Solve for the slit width:
Rearranging the formula to solve for w:
w = λD / d
w = (589 nm * 0.75 m) / 0.0075 m
w ≈ 58.9 mm