Answer:
[tex]\lambda_0=\frac{\lambda}{n_0}[/tex]
[tex]t=\frac{\lambda_0}{2}[/tex]
[tex]t=\frac{\lambda}{2n_0}[/tex]
[tex]1.27551\times 10^{-4}\ mm[/tex]
Explanation:
[tex]n_0[/tex] = Oil index of refraction = 1.47
[tex]\lambda[/tex] = 375 nm
We have the relation of wavelength and refractive index as
[tex]\frac{\lambda}{\lambda_0}=n_0\\\Rightarrow \lambda_0=\frac{\lambda}{n_0}[/tex]
Thickness relation is
[tex]t=\frac{\lambda_0}{2}[/tex]
From the above equations we have
[tex]t=\frac{\frac{\lambda}{n_0}}{2}\\\Rightarrow t=\frac{\lambda}{2n_0}[/tex]
Thickness will be
[tex]t=\frac{375\times 10^{-9}}{2\times 1.47}\\\Rightarrow t=1.27551\times 10^{-7}\ m=1.27551\times 10^{-4}\ mm[/tex]
The thickness is [tex]1.27551\times 10^{-4}\ mm[/tex]
