Answer:
The minimum thickness of the oil is 77.55 nm
Explanation:
Given:
Refractive index of oil [tex]n_{o} = 1.47[/tex]
Refractive index of water [tex]n_{w} = 1.35[/tex]
Wavelength of light [tex]\lambda= 456 \times 10^{-9}[/tex] m
From the equation of thin film interference,
The minimum thickness is given by,
[tex]2n_{o} t = (n+\frac{1}{2}) \lambda[/tex]
Where [tex]n = 0,1,2,3.........[/tex],[tex]t =[/tex] thickness
Here we have to find minimum thickness so we use [tex]n = 0[/tex]
[tex]2n_{o} t =( 0+\frac{1}{2} )\lambda[/tex]
[tex]t = \frac{\lambda }{4 n_{o} }[/tex]
[tex]t = \frac{456 \times 10^{-9} }{4 \times 1.47}[/tex]
[tex]t = 77.55 \times 10^{-9}[/tex] m
[tex]t = 77.55[/tex] nm
Therefore, the minimum thickness of the oil is 77.55 nm
