Answer:
572.3 nm
Explanation:
[tex]n_{oil}[/tex] = refractive index of the oil film = 1.48
[tex]t_{oil}[/tex] = thickness of the oil film = 290 nm
[tex]\lambda[/tex] = wavelength of the dominant color
m = order
Using the equation
[tex]2 n_{oil} t_{oil} = (m + 0.5) \lambda[/tex]
For m = 0
[tex]2 (1.48) (290) = (0 + 0.5) \lambda[/tex]
[tex]\lambda[/tex] = 1716.8 nm
For m = 1
[tex]2 (1.48) (290) = (1 + 0.5) \lambda[/tex]
[tex]\lambda[/tex] = 572.3 nm
For m = 2
[tex]2 (1.48) (290) = (2 + 0.5) \lambda[/tex]
[tex]\lambda[/tex] = 343.4 nm
Hence the dominant color wavelength is 572.3 nm