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Transcript
```Young's double-slit experiment
© 2014 Pearson Education, Inc.
Qualitative wave-based explanation of
Young's experiment
© 2014 Pearson Education, Inc.
Interference
• An interference pattern can be explained using the idea
of interference of wavelets.
– Constructive interference occurs when the crests
from the wavelets overlap, resulting in double-sized
crests.
– Destructive interference means no light is present:
the wavelets are out of phase and cancel each other
out.
© 2014 Pearson Education, Inc.
Quantitative analysis of the double-slit
experiment
• Waves in phase give constructive interference.
• Waves completely out of phase give destructive
interference.
© 2014 Pearson Education, Inc.
Mathematical location of the mth bright
band
• Using trigonometry, we find:
© 2014 Pearson Education, Inc.
Mathematical location of the mth bright
band
• We can find the distance between the zero-order
maximum and the mth maximum:
• If the angle is very small, we can approximate
and find:
© 2014 Pearson Education, Inc.
Double-slit interference
© 2014 Pearson Education, Inc.
Tip
© 2014 Pearson Education, Inc.
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.
Refractive index
© 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.
Tip
© 2014 Pearson Education, Inc.
Chromatic aberration in lenses: A practical
problem in optical instruments
• The image locations for each wavelength of light
are slightly different, leading to distortions:
© 2014 Pearson Education, Inc.
Monochromatic and coherent waves
• We don't observe an interference pattern from
two light bulbs.
• The waves are not coherent; they add together
randomly and produce no interference pattern
on the wall.
© 2014 Pearson Education, Inc.
Monochromatic and coherent waves
© 2014 Pearson Education, Inc.
Coherent monochromatic waves
© 2014 Pearson Education, Inc.
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.
© 2014 Pearson Education, Inc.
Tip
© 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.
CDs and DVDs: Reflection gratings
• The grooves in a CD play the role of the slits: the
reflected white light forms interference maxima
for different colors at different angles.
© 2014 Pearson Education, Inc.
Spectrometer
• A spectrometer is used
to analyze wavelengths
of light from different
sources.
© 2014 Pearson Education, Inc.
Thin-film interference
• The beautiful, swirling colors on soap bubbles,
oil slicks, butterfly wings, and a peacock's tail
feathers are the result of thin-film interference.
© 2014 Pearson Education, Inc.
Bright and dark bands due to reflected
monochromatic light
© 2014 Pearson Education, Inc.
Bright and dark bands due to reflected
monochromatic light
• Two factors affect the way in which the light
reflected from the front surface combines with
the light reflected from the back surface.
– Phase change upon reflection
– Phase difference due to path-length
difference
© 2014 Pearson Education, Inc.
Path-length difference due to refractive
index
• If the refractive index of the thin film is greater
than 1.0, then the wavelength of the light in the
film is:
© 2014 Pearson Education, Inc.
Thin film on glass surface
• Glass surfaces are often covered with a thin film.
Waves reflecting from the film interfere with one
another destructively, minimizing reflected light.
© 2014 Pearson Education, Inc.
Examples of thin-film interference for
monochromatic incident light
© 2014 Pearson Education, Inc.
Examples of thin-film interference for
monochromatic incident light
© 2014 Pearson Education, Inc.
Reflection patterns on a soap bubble in
white light
• Usually white light (wavelengths from 400 to 700 nm) is
incident on a thin film.
– Due to different wavelengths, different thicknesses,
and different angles, light of only a small wavelength
range is destructively reduced in intensity at any
particular location on a soap bubble.
© 2014 Pearson Education, Inc.
Complementary colors
• Complementary colors are the white light colors that are
left when light of a small wavelength range is subtracted.
• Complementary colors are not the same as the spectrum
produced by a grating or a prism.
– These devices separate in space the primary colors
that are combined spatially inside a beam of white
light.
© 2014 Pearson Education, Inc.
Tip
© 2014 Pearson Education, Inc.
Lens coatings
• We can reduce the reflected light of a particular
wavelength if we have a film of a particular
thickness.
– The thickness of the coating on glass lenses
for cameras, microscopes, and eyeglasses is
usually chosen to reduce light at a
wavelength of 550 nm, the center of the
visible spectrum.
• A lens with a thin-film coating has a purple hue
because it reflects red and violet light more than
other colors.
© 2014 Pearson Education, Inc.
Bird and butterfly colors
• Many colors in the natural world, such as those
of flower petals and leaves, are caused by
organic pigments that absorb certain colors and
reflect others.
• Some feathers and insect bodies consist of
microscopic translucent structures that act like
thin films to produce destructive and constructive
interference of light.
© 2014 Pearson Education, Inc.
Tip
© 2014 Pearson Education, Inc.
Diffraction of light
• If you look carefully at the pattern produced by
light passing through two slits on the screen, you
will notice that in addition to the alternating
bright and dark bands, there is an overall
periodic modulation of the brightness in the
pattern.
© 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.
Quantitative analysis of single-slit
diffraction
• In the single-slit situation, the slit is not infinitely
narrow.
© 2014 Pearson Education, Inc.
Tip
© 2014 Pearson Education, Inc.
Single-slit diffraction
© 2014 Pearson Education, Inc.
The Poisson spot: A historical testing of the
wave model of light
© 2014 Pearson Education, Inc.
Resolving power: Putting it all together
© 2014 Pearson Education, Inc.
Resolving ability of a lens
© 2014 Pearson Education, Inc.
Rayleigh criterion
© 2014 Pearson Education, Inc.
Tip
© 2014 Pearson Education, Inc.
Skills for analyzing processes using the
wave model of light
• When problem solving:
– Decide if the sources in the problem produce
coherent waves.
– Decide if the small-angle approximation is valid.
– Decide if the slit widths for multiple slits are wide
enough that you have to consider single-slit
diffraction as well as multiple-slit interference.
– If useful, represent the situation with a wave front
diagram showing the overlapping crests and troughs
of the light waves from different sources.
© 2014 Pearson Education, Inc.
Summary
© 2014 Pearson Education, Inc.
Summary
© 2014 Pearson Education, Inc.
Summary
© 2014 Pearson Education, Inc.
Summary
© 2014 Pearson Education, Inc.
Summary
© 2014 Pearson Education, Inc.
Summary
© 2014 Pearson Education, Inc.
Summary
© 2014 Pearson Education, Inc.
Summary
© 2014 Pearson Education, Inc.
```
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