Calculating Distance Between Interference Fringes for Yellow Light with 583 nm Wavelength

Calculating the Angle θ

Given: Wavelength (λ) = 583 nm = 583 x 10^-9 m, Slit Separation (d) = 0.075 mm = 0.075 x 10^-3 m

Using the small angle approximation: θ = tanθ = λ/d

θ = (583 x 10^-9 m) / (0.075 x 10^-3 m)

θ ≈ 7.77 x 10^-3 radians

Calculating the Distance Between Interference Fringes

For the first order maximum (m=1):

d = mλ / sinθ = (1 x 583 x 10^-9 m) / sin(7.77 x 10^-3 radians)

d ≈ 7.49 x 10^-5 m

Therefore, the distance between the interference fringes for yellow light with a wavelength of 583 nm falling on a pair of slits separated by 0.075 mm is approximately 7.49 x 10^-5 m.