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PHYSICS IN LIFE SCIENCE
Wave diffraction, interference and refraction
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Diffraction and its dependence on obstaclesize.
Constructive and destructive interference.
Light speed in vacuum and refractive index.
Snells law of refraction.
Myopia and hyperopia and how to correctthem.
Key concepts
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Reminder: Wave phenomena
A mechanical wave is the spreading ofvibration in a medium.
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The wave equation
Wave speed = wavelength / period
= wavelength
frequency All forms of wave obey this relationship.
v = l/T = lf
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Difference between particle motion
and wave motion
Visithttp://micro.magnet.fsu.edu/primer/java/particleor
wave/diffraction/ for theparticle-wave simulation.
Classical particles like bullets leave straightshadows.
Wave can bend into the shadow region and reach
places where the wave source is not directly visible.
http://micro.magnet.fsu.edu/primer/java/particleorwave/diffraction/http://micro.magnet.fsu.edu/primer/java/particleorwave/diffraction/http://micro.magnet.fsu.edu/primer/java/particleorwave/diffraction/http://micro.magnet.fsu.edu/primer/java/particleorwave/diffraction/http://micro.magnet.fsu.edu/primer/java/particleorwave/diffraction/http://micro.magnet.fsu.edu/primer/java/particleorwave/diffraction/ -
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Diffraction: when wave meets anobstacle
Part of the wave willbe reflected by theobstacle echo.
Part of the wave willmove around theobstacle, spreading to
points behind theobstacle diffraction.
Waves rejoining after moving
around
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If the obstacle is much smaller than the wavelength,
diffraction is significant, i.e., small obstacles cannotblock a wave.
If the obstacle is much larger than the wavelength,
diffraction is much less obvious, i.e., large obstaclescan leave an obvious shadow region behind it.
Wavelength and size of obstacle
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Diffraction through an aperture
When the obstacle is big but has a small holeon it, a wave can move around it through the
hole still it is the phenomenon of diffraction.
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Wavelength and aperture size
If the aperture is muchlarger than thewavelength, diffraction
is not obvious.
If the aperture is muchsmaller than thewavelength, diffraction is
significant.
wavelength distance between wavefronts
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Examples of diffraction
You can still hearsound from the other
side of the wall.
Water wave diffractsthrough a narrow
opening.
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Two wave pulses are travelling on a string.They pass through as if the other one doesnot exist.
Principle of superposition: the totalwaveform at any moment is simply the
summation of two waveforms.
What happens when waves meet?
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When two waves add up, they can cancel each
other or enhance each other: (a) destructiveinterference (b) constructive interference.
Interference
Watch video wave interference on slinky.
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Interference of 1-D waves
Peak meets peak;Valley meets valley.
Constructiveinterference
Peak meets valley;Valley meets peak.
Destructiveinterference
Peaks and valleysdont meet.
Partialinterference
For stable interference, two waves must have the
same l and f.
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Interference of wave in 2D or 3D medium
Some points have constructive interference;
Some points have destructive interference.
Interference pattern of two spherical waves
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Double-slit Interference
The two slits are two wave sources with the same f.
The interference pattern shows alternating regions
of constructive and destructive interference.
Peak meetspeak
(constructive)
Peak meetsvalley
(destructive)
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Double-slit Interference of light
Constructive or destructive interferencehappens at certain angles.
Light seems to be split into multiple beams.
what you see on ascreen after the slits
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Double slit experiment
Lasers are very good monochromatic (singlefrequency) sources and are commonly used for
double slit experiments
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When a wave goes from one medium intoanother, the direction of the wave often changesat the interface. This is refraction.
Refraction of wave
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Reflection and Transmission of Waves
Refraction
Diffraction
Water waves travel faster on the surface of deep waterthan they do on shallow water.
Faster v longer wavelength or larger distance betweenwave fronts. However, the wave front at the interfaceneeds to be continuous. This leads to a tilted wave frontin shallow water.
Refraction happens because wave speed is changed.
Refraction of water wave
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Light speed in a medium and
refractive index Speed of light:
In vacuum c=3108 m/s.
In a medium v=c/n, n>1 is the refractive index ofmaterial.
Wavelength:
In vacuum l0 = c/f.
In a medium l= v/f = l0/n.
Larger n slower speed and shorter wavelength. Refraction will happen when light goes from one
medium into another medium of different n.
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n2sin
2= n
1sin
1
Snells Law of Refraction
n1
n2
q1
q2
q1: angle of incidence (or reflection)q
2: angle of refraction
q1
Snells law:
Note: all angles are between the light beam and
the normal direction!
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Example
q1
q2
n1=1.00
n2=1.33
q1
q2
n1=1.51
n2=1.33
From air to water From oil to water
q1>q2 q1
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Refraction of light
Light speed is slower in a medium than in air:c/v = n (refractive index)>1.Refraction changes the direction of light,
making things in water look shallower.
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The problem of a fisherman
Fishes in water are merely images ofrefraction. Where should a fisherman aim?
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Refraction of curved surfaces lens
With curved surfaces, lenses can converge ordiverge light rays.
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Convex and concave lens
Concave lens is
thinner in the middle.
It defocuses light.
Convex lens isthicker in the middle.
It focuses light.
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Image projection by a convex lens
Light from differentpoints of a far object isfocused onto differentpoints on the other side
an image is formed. It projects an object
into an inverted image.
The image can be
magnified or reduced,depending on thedistance between theobject and the lens.
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Lens in human eye
The focus of lens is adjusted by the surroundingmuscles.
To see a closer object clearly, the lens need to have
a shorter focus.
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Image projection in our eyes
An inverted reduced image of external objects is
formed on the retina.
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Focusing problems of an eye
Refraction by the eye in (A) emmetropia; (B)hyperopia (farsightedness); and (C) myopia
(nearsightedness).
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Correcting myopia and hyperopia
Nearsightedness: eyesfocusing too tight use
concave lens to relax focusing.
Farsightedness: eyes focusingtoo loose use convex lens to
enhance focusing.
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Next
Nature of light.