Light from a helium-neon laser (λ = 633 nm) is used to illuminate two narrow slits. The
interference pattern is observed on a screen 3.0 m behind the slits. Twelve bright fringes are
seen, spanning a distance of 52 mm. What is the spacing (in mm) between the slits?
We can use the equation for fringe spacing in a double-slit interference pattern:
y = λL / d
where y is the fringe spacing, λ is the wavelength of light, L is the distance between the slits and the screen, and d is the spacing between the slits.
In this case, we are given λ = 633 nm = 0.633 μm, L = 3.0 m, and y = 52 mm = 52 x 10^-3 m.
We can now rearrange the equation to solve for d:
d = λL / y
Substituting the given values:
d = (0.633 x 10^-6 m)(3.0 m) / (52 x 10^-3 m)
Simplifying:
d = (1.899 x 10^-6 m)(1/0.052)
d = 36.52 x 10^-6 m
Converting to mm:
d = 36.52 mm
Therefore, the spacing between the slits is 36.52 mm.