interference in thin films, final an example of different indices of refraction an example of...
Post on 04-Jan-2016
217 Views
Preview:
TRANSCRIPT
Interference in Thin Films, Interference in Thin Films, finalfinal
An example of An example of different indices different indices of refractionof refraction
A coating on a A coating on a solar cellsolar cell
Problem Solving with Thin Films, 3
Equation1 phase reversal
0 or 2 phase reversals
2nt = (m + ½) constructive destructive
2nt = m destructive constructive
Problem Solving Strategy Problem Solving Strategy with Thin Films, 1with Thin Films, 1
Identify the thin film causing the Identify the thin film causing the interferenceinterference
The type of interference – The type of interference – constructive or destructive – that constructive or destructive – that occurs is determined by the phase occurs is determined by the phase relationship between the upper relationship between the upper and lower surfacesand lower surfaces
Problem Solving with Thin Problem Solving with Thin Films, 2Films, 2
Phase differences have two causesPhase differences have two causes differences in the distances traveleddifferences in the distances traveled phase changes occurring on reflectionphase changes occurring on reflection Both must be considered when determining Both must be considered when determining
constructive or destructive interferenceconstructive or destructive interference The interference is constructive if the path The interference is constructive if the path
difference is an integral multiple of difference is an integral multiple of λ and λ and destructive if the path difference is an odd destructive if the path difference is an odd half multiple of λhalf multiple of λ The conditions are reversed if one of the waves The conditions are reversed if one of the waves
undergoes a phase change on reflectionundergoes a phase change on reflection
DiffractionDiffraction Huygen’s principle Huygen’s principle
requires that the requires that the waves spread out after waves spread out after they pass through slitsthey pass through slits
This spreading out of This spreading out of light from its initial line light from its initial line of travel is called of travel is called diffractiondiffraction In general, diffraction In general, diffraction
occurs when wave pass occurs when wave pass through small openings, through small openings, around obstacles or by around obstacles or by sharp edgessharp edges
Diffraction, 2Diffraction, 2
A single slit placed between a distant A single slit placed between a distant light source and a screen produces a light source and a screen produces a diffraction patterndiffraction pattern It will have a broad, intense central bandIt will have a broad, intense central band The central band will be flanked by a The central band will be flanked by a
series of narrower, less intense series of narrower, less intense secondary bandssecondary bands
Called secondary maximaCalled secondary maxima The central band will also be flanked by The central band will also be flanked by
a series of dark bandsa series of dark bands Called minimaCalled minima
Diffraction, 3Diffraction, 3
The results of the single slit cannot The results of the single slit cannot be explained by geometric opticsbe explained by geometric optics Geometric optics would say that light Geometric optics would say that light
rays traveling in straight lines should rays traveling in straight lines should cast a sharp image of the slit on the cast a sharp image of the slit on the screenscreen
Single Slit DiffractionSingle Slit Diffraction According to Huygen’s According to Huygen’s
principle, each portion principle, each portion of the slit acts as a of the slit acts as a source of wavessource of waves
The light from one The light from one portion of the slit can portion of the slit can interfere with light interfere with light from another portionfrom another portion
The resultant intensity The resultant intensity on the screen on the screen depends on the depends on the direction direction θθ
Single Slit Diffraction, 2Single Slit Diffraction, 2 All the waves that originate at the slit are in All the waves that originate at the slit are in
phasephase Wave 1 travels farther than wave 3 by an Wave 1 travels farther than wave 3 by an
amount equal to the path difference (a/2) sin amount equal to the path difference (a/2) sin θ θ
If this path difference is exactly half of a If this path difference is exactly half of a wavelength, the two waves cancel each other wavelength, the two waves cancel each other and destructive interference resultsand destructive interference results
In general, In general, destructive interferencedestructive interference occurs for occurs for a single slit of width a when sin a single slit of width a when sin θθdarkdark = mλ / a = mλ / a m = m = 1, 1, 2, 2, 3, …3, …
Single Slit Diffraction, 3Single Slit Diffraction, 3 The general features of The general features of
the intensity distribution the intensity distribution are shownare shown
A broad central bright A broad central bright fringe is flanked by fringe is flanked by much weaker bright much weaker bright fringes alternating with fringes alternating with dark fringesdark fringes
The points of The points of constructive interference constructive interference lie approximately lie approximately halfway between the halfway between the dark fringesdark fringes
QUICK QUIZ 24.1
In a single-slit diffraction experiment, as the width of the slit is made smaller, the width of the central maximum of the diffraction pattern becomes (a) smaller, (b) larger, or (c) remains the same.
QUICK QUIZ 24.1 ANSWER
(b). The outer edges of the central maximum occur where sin θ = ± λ/a. Thus, as a, the width of the slit, becomes smaller, the width of the central maximum will increase.
Diffraction GratingDiffraction Grating
The diffracting grating consists of The diffracting grating consists of many equally spaced parallel slitsmany equally spaced parallel slits A typical grating contains several A typical grating contains several
thousand lines per centimeterthousand lines per centimeter The intensity of the pattern on the The intensity of the pattern on the
screen is the result of the screen is the result of the combined effects of interference combined effects of interference and diffractionand diffraction
Diffraction Grating, contDiffraction Grating, cont The condition for The condition for
maximamaxima is is d sin d sin θθbrightbright = m λ = m λ
m = 0, 1, 2, …m = 0, 1, 2, … The integer m is the The integer m is the
order numberorder number of the of the diffraction patterndiffraction pattern
If the incident radiation If the incident radiation contains several contains several wavelengths, each wavelengths, each wavelength deviates wavelength deviates through a specific through a specific angleangle
Diffraction Grating, finalDiffraction Grating, final All the wavelengths are All the wavelengths are
focused at m = 0focused at m = 0 This is called the zeroth This is called the zeroth
order maximumorder maximum The first order maximum The first order maximum
corresponds to m = 1corresponds to m = 1 Note the sharpness of Note the sharpness of
the principle maxima and the principle maxima and the broad range of the the broad range of the dark areadark area This is in contrast to to This is in contrast to to
the broad, bright fringes the broad, bright fringes characteristic of the two-characteristic of the two-slit interference patternslit interference pattern
Polarization of Light Polarization of Light WavesWaves
Each atom produces Each atom produces a wave with its own a wave with its own orientation of Eorientation of E
All directions of the All directions of the electric field E vector electric field E vector are equally possible are equally possible and lie in a plane and lie in a plane perpendicular to the perpendicular to the direction of direction of propagationpropagation
This is an unpolarized This is an unpolarized wavewave
Polarization of Light, contPolarization of Light, cont A wave is said to be A wave is said to be linearly linearly
polarizedpolarized if the resultant if the resultant electric field vibrates in the electric field vibrates in the same direction at all times same direction at all times at a particular pointat a particular point
Polarization can be obtained Polarization can be obtained from an unpolarized beam from an unpolarized beam by by selective absorptionselective absorption reflectionreflection scatteringscattering
Polarization by Selective Polarization by Selective AbsorptionAbsorption
The most common technique for polarizing lightThe most common technique for polarizing light Uses a material that transmits waves whose Uses a material that transmits waves whose
electric field vectors in the plane parallel to a electric field vectors in the plane parallel to a certain direction and absorbs waves whose certain direction and absorbs waves whose electric field vectors are perpendicular to that electric field vectors are perpendicular to that directiondirection
Selective Absorption, contSelective Absorption, cont
E. H. Land discovered a material E. H. Land discovered a material that polarizes light through that polarizes light through selective absorptionselective absorption He called the material He called the material polaroidpolaroid The molecules readily absorb light The molecules readily absorb light
whose electric field vector is parallel to whose electric field vector is parallel to their lengths and transmit light whose their lengths and transmit light whose electric field vector is perpendicular to electric field vector is perpendicular to their lengthstheir lengths
Selective Absorption, finalSelective Absorption, final
The intensity of the polarized beam The intensity of the polarized beam transmitted through the second transmitted through the second polarizing sheet (the analyzer) varies polarizing sheet (the analyzer) varies asas I = II = Ioo cos cos22 θθ
IIoo is the intensity of the polarized wave is the intensity of the polarized wave incident on the analyzerincident on the analyzer
This is known as This is known as Malus’ LawMalus’ Law and applies to any and applies to any two polarizing materials whose transmission two polarizing materials whose transmission axes are at an angle of axes are at an angle of θ to each otherθ to each other
Polarization by ReflectionPolarization by Reflection When an unpolarized light beam is reflected When an unpolarized light beam is reflected
from a surface, the reflected light isfrom a surface, the reflected light is Completely polarizedCompletely polarized Partially polarizedPartially polarized UnpolarizedUnpolarized
It depends on the angle of incidenceIt depends on the angle of incidence If the angle is 0° or 90°, the reflected beam is If the angle is 0° or 90°, the reflected beam is
unpolarizedunpolarized For angles between this, there is some degree of For angles between this, there is some degree of
polarizationpolarization For one particular angle, the beam is completely For one particular angle, the beam is completely
polarizedpolarized
Polarization by Reflection, Polarization by Reflection, contcont
The angle of incidence for which the The angle of incidence for which the reflected beam is completely polarized is reflected beam is completely polarized is called the called the polarizing anglepolarizing angle, , θθpp
Brewster’s Law relates the polarizing Brewster’s Law relates the polarizing angle to the index of refraction for the angle to the index of refraction for the materialmaterial
θθpp may also be called Brewster’s Angle may also be called Brewster’s Angle
pp
p tancos
sinn
Polarization by ScatteringPolarization by Scattering
When light is incident on a system When light is incident on a system of particles, the electrons in the of particles, the electrons in the medium can absorb and reradiate medium can absorb and reradiate part of the lightpart of the light This process is called This process is called scatteringscattering
An example of scattering is the An example of scattering is the sunlight reaching an observer on sunlight reaching an observer on the earth becoming polarizedthe earth becoming polarized
Polarization by Scattering, Polarization by Scattering, contcont
The horizontal part of The horizontal part of the electric field the electric field vector in the incident vector in the incident wave causes the wave causes the charges to vibrate charges to vibrate horizontallyhorizontally
The vertical part of the The vertical part of the vector simultaneously vector simultaneously causes them to causes them to vibrate verticallyvibrate vertically
Horizontally and Horizontally and vertically polarized vertically polarized waves are emittedwaves are emitted
top related