Chapter
24 & 25
Geometrical
Optics &
Physical Optics
ThinFilm
Interference
Light
reflected from the top and bottom of the film interferes to create
a fringe pattern.
Optical
Path Length: The optical path length is the actual length of the
path taken by light, multiplied by the index of refraction of the
medium through which it travels.
The
optical path length divided by the vacuum wavelength () equals
the number of wavelengths corresponding
to the route taken.
The
phase difference between the waves is given by:
(13)
Case
1 applies when the index of the film lies between the indices of
the surrounding two media: or .
Maxima:
(14)
where:
m = 1, 2, 3, ...
Case
2 applies when the index of the film is greater or less than
the indices of the surrounding two media: or .
Maxima:
(15)
Example
19
A
beam consisting of red light ()
and blue light ()
is directed at right angles onto a thin soap film. If the film
has
an index of refraction
n = 1.33 and is suspended in air (n = 1.00), find the smallest
nonzero thickness for which it appears red in reflected light.
Solution:
Example
20
Camera
lenses (n = 1.52) are often coated with a thin film of magnesium
flouride (n = 1.38). These "nonreflective coatings" use destructive
interference to reduce unwanted reflections. Find the condition
for destructive interference in this case, and calculate the
minimum thickness required to give destructive interference for
light in the middle of the visible spectrum (yellowgreen light, ).
Solution:
The
rays need to be out of phase:
(Maxima
in normally reflected light occur when the film thickness is
a whole number multiple of half the wavelegth ().
Minima occur when the thickness is an odd multiple of onequarter
of the wavelength ().)
Michelson
Interferometer
On
to Diffraction
