Worksheet
Thin Film Interference
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Refer to the following information for the next twelve questions.
A thin layer of baby oil (n = 1.50) is floating on the top of the water (1.33) in a wadding pool.
True or False: When the film is illuminated by sunlight and observed from above, it will appear multi-colored.
True
False
In the diagram shown above, will rays 1 and 2 be in-phase or out-of-phase with each other?
In-phase
Out-of-phase
In the diagram shown above, will rays 1 and 3 be in-phase or out-of-phase with each other?
In-phase
Out-of-phase
In the diagram shown above, will rays 3 and 4 be in-phase or out-of-phase with each other?
In-phase
Out-of-phase
In the diagram shown above, will rays 4 and 5 be in-phase or out-of-phase with each other?
In-phase
Out-of-phase
In the diagram shown above, will rays 2 and 5 be in-phase or out-of-phase with each other?
In-phase
Out-of-phase
If a section of the oil appears yellow, what primary color must be cancelled by the two reflected rays?
red
green
blue
We will now use the formula EPD = 2t + Φ to calculate the thickness of the oil film for a given wavelength of light. In this formula,
EPD
represents the
e
xtreme
p
ath
d
ifference traveled by rays 2 and rays 3, 4, and 5 collectively before reaching the eye.
2t
represents twice the thickness of the film since rays 3 and 4 have to travel down and back up through the film.
This thickness will be represented in terms of the number of wavelengths the light rays travel in the film, λ
_{n}
, where λ
_{n}
= λ/n
Φ
represents the net phase inversion (or phase difference) between rays 2 and 5. It will always be equal to either 0 λ
_{n}
or ½ λ
_{n}
.
Remember that all wavelengths must be expressed in terms of what happens in the film: we always use 0 λ
_{n}
or ½ λ
_{n}
Which of the following expressions should be used to mathematically represent the cancellation of these rays resulting from rays 3 and 4 traveling through this thin film of oil?
EPD = mλ
_{n}
where m
{0, 1, 2, 3...}
EPD = ½(2m - 1)λ
_{n}
where m
{1,2,3...}
Which formula correctly summarizes our current information:
mλ
_{n}
= 2t + 0 λ
_{n}
where m
{0, 1, 2, 3...}
mλ
_{n}
= 2t + ½ λ
_{n}
where m
{0, 1, 2, 3...}
½(2m -1)λ
_{n}
= 2t + 0 λ
_{n}
where m
{1, 2, 3...}
½(2m -1)λ
_{n}
= 2t + ½ λ
_{n}
where m
{1, 2, 3...}
Assume that the wavelength absorbed by the film is 490 nm (in air). What is the wavelength of this blue light in oil?
268 nm
327 nm
368 nm
652 nm
735 nm
How thick is the film in terms of λ
_{n}
?
t = ½(m - 1)λ
_{n}
t = ½(m + 1)λ
_{n}
t = ½ λ
_{n}
t = ¼(2m - 1)λ
_{n}
t = ¼ λ
_{n}
What is the first non-zero thickness that will result in a yellow film?
Refer to the following information for the next three questions.
A magnesium fluoride (n = 1.38) film is used to coat a glass camera lens (n = 1.56).
Will rays 2 and 5, the ones that are reflected back to your eye when looking at the front of the camera lens, interfere constructively or destructively?
constructively
destructively
Which thickness of the film will not allow any strong reflections of red light (700 nm)?
63.4 µm
126.8 µm
253.6 µm
367.6 µm
Which of the above thickness of film would encourage red light to be strongly reflected and therefore minimize its transmission to the film?
63.4 µm
126.8 µm
253.6 µm
367.6 µm
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