A parallel beam of light of wavelength 560nm falls on a thin film of oil (refractive index = 1.4). What should be the minimum thickness of the film so that it strongly reflects the light?
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Given that, $\lambda=560\times10^{-9}\text{m},\mu=1.4.$
For strong reflection, $2\mu\text{d}=(2\text{n}+1)\frac{\lambda}{2}\Rightarrow\text{d}=\frac{(2\text{n}+1)\lambda}{4\text{d}}$
For minimum thickness, putting n = 0.
$\Rightarrow\text{d}=\frac{\lambda}{4\text{d}}\Rightarrow\text{d}=\frac{560\times10^{-9}}{14}=10^{-7}\text{m}=100\text{nm}.$
For strong reflection, $2\mu\text{d}=(2\text{n}+1)\frac{\lambda}{2}\Rightarrow\text{d}=\frac{(2\text{n}+1)\lambda}{4\text{d}}$
For minimum thickness, putting n = 0.
$\Rightarrow\text{d}=\frac{\lambda}{4\text{d}}\Rightarrow\text{d}=\frac{560\times10^{-9}}{14}=10^{-7}\text{m}=100\text{nm}.$
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