A spacing of the interference fringes on a screen in Young’s experiment

Laser-Diffraction-and-Interference-still
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

ΔX1 = L*λ1/d

and the formula for the red filter

ΔX2 = L*λ2/d

Divide the second equation by the first

ΔX2/ΔX1 = λ21

Finally,

ΔX2/ΔX1 = 750/500 = 1.5

 

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