To solve this problem it is necessary to apply the concepts related to the condition of path difference for destructive interference between the two reflected waves from the top and bottom of a surface.
Mathematically this expression can be described under the equation
[tex]\delta = 2nt[/tex]
Where
n = Refractive index
t = Thickness
In terms of the wavelength the path difference of the reflected waves can be described as
[tex]\delta = \frac{\lambda}{4}[/tex]
Where
\lambda = Wavelenght
Equation the two equations we have that
[tex]2nt = \frac{\lambda}{4}[/tex]
[tex]t = \frac{\lambda}{8n}[/tex]
Our values are given as
[tex]\lambda = 380nm \rightarrow[/tex] Wavelength of light
[tex]n = 1.4[/tex]
[tex]t = \frac{380nm}{8*1.4}[/tex]
[tex]t = 33.93nm[/tex]
Therefore the minimum thickness of the oil for destructive interference to occur is approximately 34.0 nm
