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

###### Solution.

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.

Hence,

the formula for the green filter is

ΔX_{1} = L*λ_{1}/d

and the formula for the red filter

ΔX_{2} = L*λ_{2}/d

Divide the second equation by the first

ΔX_{2}/ΔX_{1} = λ_{2}/λ_{1}

Finally,

ΔX_{2}/ΔX_{1} = 750/500 = 1.5

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