A thin film of liquid 1 (n1 = 1.57) sits on top of a solid. A single beam of mon

Question

A thin film of liquid 1 (n1 = 1.57) sits on top of a solid. A single beam of monochromatic light (wavelength = 619 nm) travels through air (n = 1.00) and falls on the top surface. Some of the light reflects off the top layer; some passes through medium 1, strikes the solid and reflects back upward. Since these two beams are coherent to each other, they can produce interference with each other.

Assume:
- n1 << n2.
- the film is very thin, so the distance the refracted beam travels can be assumed to be 2t, where t is the thickness of the film.
- the thickness of the film is uniform.
HINT: Remember: when light enters a medium, only the frequency (color) of the light does not change.

Find:
i. the thickness of the thinnest film of liquid 1 that will produce total destructive interference between the two upward beams.

ii. the thickness of the thinnest (non-zero) film of liquid 1 that will produce total constructive interference between the two upward beams.

Explanation / Answer

a) 2*n1*t=Lambda/2

==>t=98.56687898089172 nm

b) Â 2*n1*t=Lambda

==> t=197.1337579617834 nm

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