Interference of Light help?

Question

Light passing through a double slit with separation d=6.42*10^-5 creates it's first maximum (m=1) at an angle of .396 deg. What is the wavelength of the light in nanometers?

 

 

Answer 1

mλ = yd/D = d(y/D)

 

m = 1 

d = 6.42 x 10^-5 m

θ = 0.396°

y/D = tanθ = tan(0.396°) ≅ 6.912 x 10^-3

 

λ = (6.42 x 10^-5 m) tan(0.396°) = (6.42 x 10^-5 m)(6.912 x 10^-3) ≅ 4.438 x 10^-7 m = 443.8 nm