How many times will increase a spacing of the interference fringes on a screen in Young’s experiment (Double-slit experiment), if a green (λ1 = 500 nm) filter is replaced by a red filter (λ2 = 750 nm)?
Image Credit: MIT
The spacing of the fringes ΔX at a distance L from the slits is given by
ΔX = L*λ/d
where λ is the wavelength of the light and d is the distance between the two slits.
the formula for the green filter is
ΔX1 = L*λ1/d
and the formula for the red filter
ΔX2 = L*λ2/d
Divide the second equation by the first
ΔX2/ΔX1 = λ2/λ1
ΔX2/ΔX1 = 750/500 = 1.5