chapter 24the intensity distribution are shown ... slit interference pattern. an x-ray diffraction...
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Chapter 24
Wave Optics II
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hitt1
An object and a screen are separated by 20.00 cm. Aconvex lens is placed between them, 5.00 cm from theobject. In this position it causes a sharp image of theobject to form on the screen. What is the focal lengthof the lens?
a. 15.0 cm b. 5.00 cm c. 10 cm d. 2.00 cm e. noneof these
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Diffraction Huygen’s principle
requires that thewaves spread out afterthey pass through slits
This spreading out oflight from its initial lineof travel is calleddiffraction In general, diffraction
occurs when wavespass through smallopenings, aroundobstacles or by sharpedges
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Diffraction, 2 A single slit placed between a distant
light source and a screen produces adiffraction pattern It will have a broad, intense central band The central band will be flanked by a series
of narrower, less intense secondary bands Called secondary maxima
The central band will also be flanked by aseries of dark bands
Called minima
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Diffraction, 3 The results of the
single slit cannot beexplained bygeometric optics Geometric optics
would say that lightrays traveling instraight lines shouldcast a sharp image ofthe slit on the screen
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Fraunhofer Diffraction Fraunhofer Diffraction
occurs when the raysleave the diffractingobject in paralleldirections Screen very far from the
slit Converging lens (shown)
A bright fringe is seenalong the axis (θ = 0)with alternating brightand dark fringes on eachside
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Single Slit Diffraction According to Huygen’s
principle, each portionof the slit acts as asource of waves
The light from oneportion of the slit caninterfere with light fromanother portion
The resultant intensityon the screen dependson the direction θ
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Single Slit Diffraction, 2 All the waves that originate at the slit
are in phase Wave 1 travels farther than wave 3 by
an amount equal to the path difference(a/2) sin θ
If this path difference is exactly half ofa wavelength, the two waves canceleach other and destructive interferenceresults
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Single Slit Diffraction, 3
In general, destructiveinterference occurs for a single slitof width a when sin θdark = mλ / a m = ±1, ±2, ±3, …
Doesn’t give any information aboutthe variations in intensity alongthe screen
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Single Slit Diffraction, 4 The general features of
the intensity distributionare shown
A broad central brightfringe is flanked bymuch weaker brightfringes alternating withdark fringes
The points ofconstructive interferencelie approximatelyhalfway between thedark fringes
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Diffraction Grating
The diffracting grating consists ofmany equally spaced parallel slits A typical grating contains several
thousand lines per centimeter
The intensity of the pattern on thescreen is the result of thecombined effects of interferenceand diffraction
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Diffraction Grating, cont The condition for
maxima is d sin θbright = m λ
m = 0, 1, 2, …
The integer m is theorder number of thediffraction pattern
If the incidentradiation containsseveral wavelengths,each wavelengthdeviates through aspecific angle
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Diffraction Grating, final All the wavelengths are
focused at m = 0 This is called the zeroth
order maximum The first order maximum
corresponds to m = 1 Note the sharpness of the
principle maxima and thebroad range of the darkarea This is in contrast to the
broad, bright fringescharacteristic of the two-slit interference pattern
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an X-ray diffraction image of sodium saltof DNA. B configuration
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Diffraction Grating in CDTracking
A diffraction grating canbe used in a three-beam method to keepthe beam on a CD ontrack
The central maximumof the diffractionpattern is used to readthe information on theCD
The two first-ordermaxima are used forsteering
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Polarization of Light Waves Each atom produces a
wave with its ownorientation of
All directions of theelectric field vector areequally possible andlie in a planeperpendicular to thedirection ofpropagation
This is an unpolarizedwave
Er
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Polarization of Light, cont
A wave is said to be linearlypolarized if the resultantelectric field vibrates in thesame direction at all times at aparticular point
Polarization can be obtainedfrom an unpolarized beam by selective absorption reflection scattering
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Polarization by SelectiveAbsorption
The most common technique for polarizinglight
Uses a material that transmits waves whoseelectric field vectors in the plane are parallel toa certain direction and absorbs waves whoseelectric field vectors are perpendicular to thatdirection
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Selective Absorption, cont E. H. Land discovered a material
that polarizes light throughselective absorption He called the material Polaroid The molecules readily absorb light
whose electric field vector is parallelto their lengths and transmit lightwhose electric field vector isperpendicular to their lengths
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Selective Absorption, final The intensity of the polarized beam
transmitted through the secondpolarizing sheet (the analyzer) varies as I = Io cos2 θ
Io is the intensity of the polarized wave incidenton the analyzer
This is known as Malus’ Law and applies to anytwo polarizing materials whose transmission axesare at an angle of θ to each other
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Polarization by Reflection When an unpolarized light beam is
reflected from a surface, the reflectedlight is Completely polarized Partially polarized Unpolarized
It depends on the angle of incidence If the angle is 0° or 90°, the reflected beam is
unpolarized For angles between this, there is some degree
of polarization For one particular angle, the beam is completely
polarized
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Polarization by Reflection,cont The angle of incidence for which the
reflected beam is completely polarizedis called the polarizing angle, θp
Brewster’s Law relates the polarizingangle to the index of refraction for thematerial
θp may also be called Brewster’s Angle
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Polarization by Scattering
When light is incident on a systemof particles, the electrons in themedium can absorb and reradiatepart of the light This process is called scattering
An example of scattering is thesunlight reaching an observer onthe earth becoming polarized
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Polarization by Scattering,cont The horizontal part of the
electric field vector in theincident wave causes thecharges to vibratehorizontally
The vertical part of thevector simultaneouslycauses them to vibratevertically
Horizontally and verticallypolarized waves areemitted
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Optical Activity
Certain materials display theproperty of optical activity A substance is optically active if it
rotates the plane of polarization oftransmitted light
Optical activity occurs in a materialbecause of an asymmetry in theshape of its constituent materials
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Liquid Crystals A liquid crystal is a substance with
properties intermediate between thoseof a crystalline solid and those of aliquid The molecules of the substance are more
orderly than those of a liquid but less thanthose in a pure crystalline solid
To create a display, the liquid crystal isplaced between two glass plates andelectrical contacts are made to theliquid crystal A voltage is applied across any segment in the
display and that segment turns on
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Liquid Crystals, 2
Rotation of a polarized light beam by a liquidcrystal when the applied voltage is zero
Light passes through the polarizer on the rightand is reflected back to the observer, whosees the segment as being bright
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Liquid Crystals, 3
When a voltage is applied, the liquid crystaldoes not rotate the plane of polarization
The light is absorbed by the polarizer on theright and none is reflected back to theobserver
The segment is dark
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Liquid Crystals, final
Changing the applied voltage in aprecise pattern can Tick off the seconds on a watch Display a letter on a computer display
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hitt2For a converging lens with two curved surfaces,
the radius of curvature for both surfaces is 10cm. If the focal length is 10 cm, what mustthe index of refraction be?
a. 1.5b. 2.0c. 2.5d. 3.0