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Question
A parallel beam of light of wavelength 560 nm 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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Solution
Given:-
Wavelength of light used,
\[\lambda = 560 \times {10}^{- 9} m\]
Refractive index of the oil film, \[\mu = 1 . 4\]
Let the thickness of the film for strong reflection be t.
The condition for strong reflection is
\[2\mu t = \left( 2n + 1 \right)\frac{\lambda}{2}\]
\[ \Rightarrow t = \left( 2n + 1 \right)\frac{\lambda}{4\mu}\]
where n is an integer.
For minimum thickness, putting n = 0, we get
\[t = \frac{\lambda}{4\mu}\]
\[ = \frac{560 \times {10}^{- 9}}{4 \times 1 . 4}\]
\[ = {10}^{- 7} m = 100 nm\]
Therefore, the minimum thickness of the oil film so that it strongly reflects the light is 100 nm.
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