Chapter 24

Wave Optics II

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

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

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

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

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

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

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

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

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

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

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

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

an X-ray diffraction image of sodium saltof DNA. B configuration

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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