Download Wave Optics

2/27/2015
Wave Optics
Physics 116
Eyres
Topics
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Double-slit interference
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Diffraction gratings
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Thin-film interference
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Single-slit diffraction
Why do we see
colors in a soap
bubble?
Circular-aperture diffraction
A hummingbird’s feather colors
have are unlike that of ordinary
pigments. Why do they change
subtly depending on the angle at
which they’re viewed?
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Terms
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antireflection
double-slit interference
refraction
diffraction
single-slit diffraction
thin-film interference
sharp-ended shadows
double-slit interference
More?
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Waves: Through a Slit Opening
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Young's double-slit
experiment
© 2014 Pearson Education, Inc.
Mathematical location of the bright & dark bands
• Using trigonometry, we find:
Under what
conditions can
one say:
=
Remember that mλ is simply the extra path
length to point P. It is labelled Delta in the
picture.
You can use the same equation for dark
bands. However, there you have half
wavelengths.
© 2014 Pearson Education, Inc.
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Same equations as written in your text:
© 2014 Pearson Education, Inc.
Example
Two narrow slits 0.04 mm apart are illuminated by light from a
HeNe laser (λ = 633 nm).
A. What is the angle of the first (m = 1) bright fringe?
B. What is the angle of the thirtieth bright fringe?
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Young's interference with white light
• When white light is used in the double-slit experiment, we see the
following:
• Because the angular deflection of red light appears greater than
that of blue light, we can conclude that red light must have a
longer wavelength than blue light.
© 2014 Pearson Education, Inc.
Relating the refractive index
and the speed
of light in a substance
• The wave model of light not
only explains why light bends at
the boundary of two media, but
also explains Snell's law by
connecting the medium's index
of refraction to the speed of
light in that medium.
© 2014 Pearson Education, Inc.
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Refractive index: A review from chapter 21
© 2014 Pearson Education, Inc.
Does the refractive
index depend on the
color of the light?
• The different indexes of
refraction for different colors
mean that light of different
colors and light waves of
different frequencies travel
at different speeds in the
same medium.
© 2014 Pearson Education, Inc.
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Chromatic aberration in lenses: A practical
problem in optical instruments
• The image locations for each
wavelength of light are slightly
different, leading to distortions:
• Remember that the index of
refraction is different for different
colors of light.
© 2014 Pearson Education, Inc.
White light incident on grating
• A spectrum produced by a grating is a result of the light of different
wavelengths interfering constructively at different locations.
© 2014 Pearson Education, Inc.
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Gratings: An application of interference
• A typical grating has hundreds of
slits per millimeter.
• The bright bands are very
intense and narrow, with
almost complete darkness
between them.
Notice that this equation is the same as
that for 2-slit interference!
© 2014 Pearson Education, Inc.
Quantitative analysis of single-slit diffraction
• The width of the central diffraction maximum (the central bright band
on the screen) increases as the width of the slit decreases.
© 2014 Pearson Education, Inc.
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Quantitative analysis of single-slit diffraction
• In the single-slit situation, the
slit is not infinitely narrow.
• Notice that the result is an
interference pattern similar to
that of multiple slit interference.
© 2014 Pearson Education, Inc.
Single-slit diffraction
Compare this to
the 2-slit
equation:
=
© 2014 Pearson Education, Inc.
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Resolving power: Putting it all together
© 2014 Pearson Education, Inc.
Resolving ability of a lens
Rayleigh Criterion
1.22
=
When the lens is small (small D),
then a large angle of separation
is required to resolve the
objects.
© 2014 Pearson Education, Inc.
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Rayleigh criterion
© 2014 Pearson Education, Inc.
Example 23.7
A. What is the limit of
resolution of the human
eye?
B. The rectangular box shown
in the figure has vertical lines
separated by 2 mm (as seen
in your text). At what
maximum distance
(according to Rayleigh's
criterion) will you be able to
resolve the lines in picture?
D for eye is 0.5 cm. Use
wavelength of 550 nm
=
1.22
Solve for θ:
= 1.34 10
Now solve for s, given
that y is 2 mm. S=15 m.
Now try it with the distance as
seen on the screen. You will have
to measure y on the screen.
Distance
between
lines: y
Distance from you
to the lines: s
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