An optical engineer is calibrating a double-slit interferometry system used in high-precision sensor manufacturing. Initially, coherent light of wavelength λ\lambdaλ is shone through a double slit with a separation sss onto a photodetector array placed at a distance DDD from the slits. This configuration produces interference fringes with a spacing www on the array.
To accommodate a new sensor casing, the distance from the slits to the photodetector array is changed to 2.5D2.5D2.5D.
Which combination of modified slit separation and wavelength produces a target fringe spacing of 0.5w0.5w0.5w on the array?
Slit separation s′=1.5ss' = 1.5ss′=1.5s; Wavelength λ′=0.60λ\lambda' = 0.60\lambdaλ′=0.60λ
Slit separation s′=2.5ss' = 2.5ss′=2.5s; Wavelength λ′=0.50λ\lambda' = 0.50\lambdaλ′=0.50λ
Slit separation s′=0.8ss' = 0.8ss′=0.8s; Wavelength λ′=0.40λ\lambda' = 0.40\lambdaλ′=0.40λ
Slit separation s′=1.2ss' = 1.2ss′=1.2s; Wavelength λ′=0.30λ\lambda' = 0.30\lambdaλ′=0.30λ
