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A plane wave of monochromatic light is incident normally on a uniformly thin film of oil that covers a glass plate. The wavelength of the source can be varied continuously. Fully destructive interference of the reflected light is observed for wavelengths of 517 and 632 nm and for no wavelengths in between. If the index of refraction of the oil is 1.33 and that of the glass is 1.50, find the thickness of the oil film.

Answer :

davidlcastiblanco

Answer:

The thickness of the oil film is

L=1068.98nm

Explanation:

Using the thickness of the film in the case of condition for destructive interference

[tex]L=(m+\frac{1}{2})*\frac{Y}{2*n}[/tex]

Y=517

n=1.33

[tex]L=(m+\frac{1}{2})*\frac{517}{2*1.33}[/tex]

In the other case the thickness can be calculated by

[tex]L=(m-1+\frac{1}{2})*\frac{632}{2*1.33}[/tex]

Both equation equal to find m so:

[tex](m-1+\frac{1}{2})*\frac{632}{2*1.33}= (m+\frac{1}{2})*\frac{517}{2*1.33} \\632m-316=517m+258.5\\115m=574.5\\m=4.9956[/tex]≅5

So the thickness is:

[tex]L=(5+\frac{1}{2})*\frac{517}{2*1.33}[/tex]

[tex]L=1068.98nm[/tex]

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