Answer:
The split separation d = 2.12 * 10^-4 m
Explanation:
Mathematically, for a double split interference, the relation between separation of slit and fringe width is given by the formula;
d = Rλ/Δy
Where R represents the distance of screen from the slit given as 1.86m , λ is the wavelength of incident light given as 460 nm ,
Δy is the fringe width given as 3.90 nm
plugging these values into the equation, we have;
d = (1.86)(460 * 10^-9)/(3.9 * 10^-3)
d = 2.12 * 10^-4 m
The slit separation of the given experiment will be [tex]2.1938\times 10^{-4}[/tex] m or 0.21938 mm.
Given information:
The wavelength of the coherent light which falls on a pair of slits is [tex]\lambda=460[/tex] nm.
The distance between slits and screen is [tex]R=1.86[/tex] m.
The fringe width is given as [tex]\Delta y=3.9[/tex] mm.
For a double-slit experiment, the slit separation, d, can be calculated as,
[tex]d\Delta y=R\lambda\\d=\dfrac{1.86\times 460\times10^{-9}}{3.90\times 10^{-3}}\\d=219.38\times 10^{-6}\\d=2.1938\times 10^{-4}[/tex]
Therefore, the slit separation of the given experiment will be [tex]2.1938\times 10^{-4}[/tex] m or 0.21938 mm.
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