Optics

OpticsChapter 11Shanghai Normal UniversityDepartment of Physics

Development of OpticsGeometrical opticsWave opticsQuantum opticsWave opticsInterference? Diffraction?Polarization?

11-1 Coherent Light 11-5 Michelson Interferometer 11-4 Wedge, Newtons Ring 11-3 Optical Path, Film Interference 11-2 Youngs Double slit Interference, 11-0 Teaching Basic requirements 11-6 The Diffraction of Light117 Single slit DiffractionCatalog of Chapter 11Lloyd Mirror

11-12 The Birefringence11-11 The Polarization of Reflected Light and Refracted Light11-10 The Polarization of Light, Malus Law11- 9 Diffraction Grating 11- 8 Hole Diffraction, the Resolution Capability of Optical Instruments*11-13 The Liquid Crystal Display*11-14 Geometrical OpticsCatalog of Chapter 11

Interference of Light 1. Understand the interference condition and the method of getting coherent light2. Master concept of optical path as well as relationship of the optical path difference and the phase difference, and understand under what circumstances the reflected light has phase jump.

11-0 Teaching Basic requirements

3. Analyze position of Youngs double-slit interference fringes and film thickness interference fringe .

4. Understand principle of Michelson interferometer.11-0 Teaching Basic requirements

2. Understand using zone method to analyze distribution of single-slit Fraunhofer diffraction fringes, and analyze the effect of the slit width and wavelength on distribution of diffraction fringes.

1. Understand the Huygens-Fresnel principle and its qualitative interpretation of diffraction phenomenon of light.11-0 Teaching Basic requirements The Diffraction of Light

3. Understand grating diffraction formula, determine the position of grating diffraction line, analyze the effect of grating constant and the wavelength on the grating diffraction spectrum. 4. Understand the effect of the diffraction of optical instrument resolution.. 5. Understand the x-ray diffraction phenomenon and the physical meaning of Prague formula.11-0 Teaching Basic requirements

The Polarization of Light1. Understand difference of Nature light and Polarized light.2. Understand Brewster law and Marius's law.4. Understand the method of getting and testing linearly polarized light.3. Understand birefringence of light.11-0 Teaching Basic requirements

I. Light wave is the electromagnetic wave (traverse wave) Light vectorthe component who can produce the vision of eyes and the sensitization on the photographic plate is the vector E called light vector. E oscillation is called light oscillation. 11-1 Coherent Light

The speed of light in vacuum c and the speed of light in transparent medium u are 11-1 Coherent Light

Light source: object of emitting light.Ordinary light emitting mechanism is the spontaneous radiation of the atomic. (Atoms and molecules in the absorption of energy are in an unstable excited state, even in the absence of any external forces, they would spontaneously return to low excited state and ground state, at the same time sending out light.) 11-1 Coherent Light

The light source and the mechanical wave source detected difference: mechanical wave source is often a vibrating object, while the light source is thousands on thousands of atoms which randomly emits light as one falls. 11-1 Coherent Light

Heat light source: exciting light utilizing heat energy (Incandescent lamp) Cold light source: exciting light utilizing chemical energy (such as phosphor), power (such as fluorescent lamps) or light energy (such as fluorescent, phosphorescent)According to the light excited method, the light source can be divided intoRange of visual light 11-1 Coherent Light

The monochromatic light a sine (cosine) light wave with a constant frequency and an infinite lengthThe monochromatic light 11-1 Coherent Light

Polychromatic light can produce dispersion phenomenon through the three prism. Polychromatic light: light composited by various frequency light ( such as white light ).

11-1 Coherent Light

II. Coherent Light1. light emitting mechanism of the normal light source the spontaneous radiation of atoms (molecules). 11-1 Coherent Light

Light-emitting characteristics of normal light source: is intermittent, each light to form a short wavAtomic emission e train, the atoms of each luminous independently of each other, each wave train irrelevant.

11-1 Coherent Light

Coherent Light: If light vectors of two light beams satisfy the interference condition, they are the coherent light. The relative light sources are called the coherent light source. 11-1 Coherent Light

Reason: Atomic emission is random as well as intermittent, so vibration directions of two columns of light can not be the same, and phase difference may not be constant. Two independent light sources may not be a pair of coherent light source. 11-1 Coherent Light

The basic idea of realizing optical interferometer:The light from each light were decomposed into two sub-light columns, and then let the two sub-light columnsin the same area and produce interference. 11-1 Coherent Light

Two kinds of specific practices:1 Method of dividing wave front (Fig. a)e.g. , Youngs two slit interference.2Amplitude segmentationFig. b 11-1 Coherent Light

11-1 Coherent Light

2 Production of coherent light 11-1 Coherent Light

experimental deviceI. Experiment of Youngs Double slit Interference 11-2 Youngs Double slit Interference, Lloyd Mirror

11-2 Youngs Double slit Interference, Lloyd Mirror

p 11-2 Youngs Double slit Interference, Lloyd Mirror

Distribution of the bright and dark fringesIf white light is used, color fringes appear. The bright and dark fringes distribute in eaual distance. 11-2 Youngs Double slit Interference, Lloyd Mirror

Distance Light intensity of each fringe is equal. 11-2 Youngs Double slit Interference, Lloyd Mirror

Example 1 In Youngs double slit interference experiment, a Sodium light with the wavelength =589.3 nm is used as the light source. The distance d=800 nm between the screen to the double-slit. The question:When the distance between two slits is 1 mm, how much is the distance between the centers of adjacent bright fringes?Assuming the distance between two slits is 10 mm, how much is the distance between the centers of adjacent bright fringes?

11-2 11-2 Youngs Double slit Interference, Lloyd Mirror

Solution(1) As d=1 mm, (2) If d=10 mm, then Known=589.3 nmd`=800 nmAsk (1) d=1 mm (2) d=10 mm 11-2 Youngs Double slit Interference, Lloyd Mirror

Example 2: Two slits with the gap of 0.2 mm are irradiated by the monochromatic light, and the distance between double-slit and the screen is 1 m. Question:(1)The distance is 7.5 mm from the first order bright fringe to the fourth order bright fringe in the same side, what the wavelength of the monochromatic light is? (2)If the wavelength of the incident light is 600 nm, how much the distance is from the center of the central bright fringe to the center of the closest adjacent dark fringe? 11-2 Youngs Double slit Interference, Lloyd Mirror

Solution(1)(2) KnownAsk(1) (2) 11-2 Youngs Double slit Interference, Lloyd Mirror

II The effect of the slit width to the fringes, space coherenceIn the experiment, meanwhile the slit width is increasing gradually, the fringes on the screen is going to be faintness gradually, and disappear finallyspace coherence 11-2 Youngs Double slit Interference, Lloyd Mirror

III Lloyd MirrorPM 11-2 Youngs Double slit Interference, Lloyd Mirror

The half wave expense will occur when light eradicates from the optically thinner medium to optically denser medium and is reflected by the interface. The refraction of light is without half wave expense. 11-2 Youngs Double slit Interference, Lloyd Mirror

Example 3 as shown in the figure, there is an electromagnetic wave receiver on the C position where is with the height h=0.5 m above the lake surface. As a radio star is rising gradually from the ground level on the left side, the receiver measured brokenly a serious of maximum value. It is known that the wavelength of the electromagnetic wave emitted by the radio star is 20.0 cm, what the azimuth angle is between the radio star and the ground level as the first maximum value is measured? 11-2 Youngs Double slit Interference, Lloyd Mirror

Solution: calculate wave path-difference 11-2 Youngs Double slit Interference, Lloyd Mirror

IV Optical path, optical path-difference 11-2 Youngs Double slit Interference, Lloyd Mirror

The physical meaning: The optical path is the distance in vacuum which is equally calculated from the geometric distance of light in the medium according to the phase difference .

(1) optical path The product of the refractive index of the medium and the geometry of the light path = 11-2 Youngs Double slit Interference, Lloyd Mirror

(2) optical path-difference 11-2 Youngs Double slit Interference, Lloyd Mirror

Youngs Double slit experimentwhen light obliquely incidents to double slits, optical path is: 11-2 Youngs Double slit Interference, Lloyd Mirror Bright fringesDark fringes

When the optical paths 1,2 are respectively inserted into two transparent medium sheets with the refractive index of n1 and n2, thickness of t1 and t2, the optical path-difference will be: 11-2 Youngs Double slit Interference, Lloyd Mirror

(3) The lens does not introduce the additional optical path difference 11-2 Youngs Double slit Interference, Lloyd Mirror

11-3 Optical path thin film interference=nrBright fringesDark fringes=

In our daily lifethe soap bubbles under the Sun and the oil films on the water show colorful pattern. The phenomena can be attributed to the interference by the light beam reflected on upper and bottom surfaces of the film. Because of the energies of the reflected and transmitted are from the incidenceso it is amplitude segmentation interference. 11-3 Optical path thin film interference

Equal inclination interference 11-3 Optical Oath, Film Interference

LI Film Interference 11-3 Optical Oath, Film Interference

11-3 Optical Oath, Film Interference

Optical path-difference of the transmission lightNote: the interference of the transmission light and of the reflected light is complement with each other. This satisfies the law of conservation energy. 11-3 Optical Oath, Film Interference

The optical path difference is just related with the incident angle, which means that the same level fringe of the same level has the same incident angle. Such interference is equal inclination interference. Half wavelength loss exists only on the upper or bottom surface of thin films, and the optical path difference should include the additional item /2If there is no half wavelength loss on both the surfaces or both have half wavelength loss, then no additional item /2 should be calculated. Additional items /2 Equal inclination interference fringe 11-3 Optical Oath, Film Interference

Example The oil (refractive index n1=1.20) leaked out by an oil tanker pollutes an ocean area, and forms a thin dirty oil film on the surface of ocean (2=1.30). (1) If the sun is just in the sky above this ocean area, a pilot observes the just down direction from the helicopter, and the thickness of the oil layer faced to him is 460 nm, what is the color of the oil layer he watched? (2) If a diver dives under the water in this area, what is the color of the oil layer he observed when he looks a his up direction? 11-3 Optical Oath, Film Interference

GreenKnownn1=1.20n2=1.30d=460 nm 11-3 Optical Oath, Film Interference

The reflection and transmission increasing filmThin film interference can improve the optical transmittance. 11-3 Optical Oath, Film Interference

As shown in the Figurea wedge can be formed by two transparent glass. If the two glass are in air ambientan air wedge is formed; If it is placed in translucent liquid, then it is a liquid wedge. The interferences by wedges are called wedge interference which is a kind of equal thickness interference.A wedge formed by two inclined glassI Production of a wedge 11-4 Wedge, Newtons Ring

SMII Optical path of Optical path difference of the two reflected light by the up and down surfaces of the wedge with thickness d is 11-4 Wedge, Newtons Ring

The interference condition of wedge 11-4 Wedge, Newtons Ring

Wedge interference 11-4 Wedge, Newtons Ring

(2)Thickness difference of the adjacent bright (dark)fringes 11-4 Wedge, Newtons Ring

11-4 Wedge, Newtons Ring

(4 )The shift of the fringes 11-4 Wedge, Newtons Ring

DiscussionEqual thickness interferenceTo the same order fringethe film thickness should be the same. 1. With wedge interference, small angle small thickness and the wavelength of incidence can be meausured. 3. Questiondark fringe or bright fringe 11-4 Wedge, Newtons Ring

(2)Measure film thicknessThe applications of wedge interference 11-4 Wedge, Newtons Ring

(3) The surface inspection of the optical component 11-4 Wedge, Newtons Ring

(4) Diameter of thin wires 11-4 Wedge, Newtons Ring

Newtons RingA convex A with one flat surface, which curvature R is very big, touches a flat glass Bas shown in the figureso that forms an air wedge which is called Newtons ring film.BA 11-4 Wedge, Newtons Ring

The experimental setuup of Newtons RingInterference patternMicroscopeSLM beam splitting lensT 11-4 Wedge, Newtons Ring

The Newtons ring is still equal thickness interference, which means the film thicknesses of bright and dark fringes obey the equal thickness interference rules.With monochromic parallel light incidence, concentric circles with their center O can be observed on the convex surfacewhich are called Newtons ring.A small wedge can be regarded in every part of the wedge, however, their inclinations are not the same at different places, leading to unequal distance of the fringes which are denser in inner circles and sparser in outer part. 11-4 Wedge, Newtons Ring

Bright fringeOptical path difference 11-4 Wedge, Newtons Ring

11-4 Wedge Newtons Ring

(1) On the reflection sideIt is dark or bright of the center pointOn the transmission sidehow about the center point? (2)It belongs to equal thicknessbut the fringe distances are not uniformwhy 11-4 Wedge, Newtons Ring

(4) Application example: measuring the optical wavelengthconvex quality inspectionand curvature radius etc.. (3) Put the setup in liquids with , how about the fringes? 11-4 Wedge, Newtons Ring

If the Newtons Ring setup is put into other ambient (e.g. water), then 11-4 Wedge, Newtons Ring

Measuring the curvature radius 11-4 Wedge, Newtons Ring

Summary (1) The interference pattern are tracing point aggregation with the same optical path difference, i.e., those with the same film thickness. 11-4 Wedge, Newtons Ring

(2)The fringe distance increases linearly with the film thickness. 11-4 Wedge, Newtons Ring

4 The additional optical path needs to be analysis specifically. 11-4 Wedge, Newtons Ring

The structure drawing of Michelson interferometerMonochromic light source 11-5 Michelson Interferometer

Monochromic light sourceOptical path difference 11-5 Michelson Interferometer

11-5 Michelson InterferometerMonochromic light source

The main features of Michelson Interferometer (1)seperation of two light beam (2)tunable of the optical path differentce. 11-5 Michelson Interferometer

Moving of the interference fringes 11-5 Michelson Interferometer

The optical path after the dielectric slice insertionThe change of the optical differenceThe optical difference 11-5 Michelson Interferometer

11-5 Michelson Interferometer

Large slit (much larger than wavelength)light is propagating straightlySmall slit (comparable with light wavelength) DiffractionThe diffraction phenomena of light11-6 The Diffraction of Light

We introduced Huygens principle which can explain refraction, reflection and scattering of mechanical waves. Huygens principle can explain diffraction of light qualitatively, however, it can not quantitatively demonstrate the light intensity distribution.After studying light interference, Fresnel, according to the principle of the wave superposition and interference, raised the concept of wavelet coherent addition. He thought, wavelets emitted by each point on a same wave front are coherent, and as propagating on the certain point in the space, the result of which each wavelet makes the coherent addition determine the wave amplitude on the place. This developed Huygens principle is named as Huygens-Fresnel principle.Huygens-Fresnel principle11-6 The Diffraction of Light

Huygens-Fresnel principlethe wavelet from the same wave front can interfere with each other when they meet at some point in space.11-6 The Diffraction of Light

The formula is Fresnel diffraction theory integration equation. Generally speaking, the integration is very complicated. In college physics, we only require to master the Fresnel half wave zone approach.Light osillation at P pointthe mathematic formisKey of Huygens-Fresnel: interference of wavelets. Diffraction originates from interferences of infinite wavelets.11-6 The Diffraction of Light

Fresnel diffraction and Fraunhofer diffractionThe setup to observe light diffraction includes three parts: sourcediffraction objectsslit or hole etc.screenThe diffraction can be classified into two types according to position of the three parts. At least one non-parallel light beam of incidence and emergence11-6 The Diffraction of LightSourcescreen and slit: infinite distance Parallel light beam of incidence and emergence

S*Setup of single-slit diffractionL1KL2

Single-slit Fraunhofer diffraction experimental setup. The light from source S is changed to parallel light beam via convex L1 and perpendicular incident on the single-slit. The diffracted light is then focused on the screen, where diffraction fringes can be observed, via convex L2.11-6 The Diffraction of Light

The wavefronts of incidence reach the slitthen the points in the slit forms new wavelet sources which emit wavelets with the same initial phase. The wavelets propagate in different directions and then focuse on the screen. For example, the wavelet in direction focuse on screen Q point. is diffraction angleThe optical paths from different wavelet propagating in direction is different. There exists optical path differences which determine the intensity at Q point.11-7 Single slit interference

Fresnel wave zone approach11-7 Single slit interferenceFraunhofer single-slit diffraction

Half wave zone approach11-7 Single slit interference

11-7 Single slit interference

Light intensity distribution 11-7 Single slit interference

Light intensity distribution11-7 Single slit interference

11-7 Single slit interference

(1)The distance between 1st dark fringe and the central bright fringeThe diffraction angle of 1st dark fringe.11-7 Single slit interference

Straight propagationMaximum diffractionThe diffraction angle of 1st dark fringe11-7 Single slit interference

between the 1st dark fringes(2)Central bright fringe11-7 Single slit interference

How about the central bright fringe if the slit width changes?11-7 Single slit interference

How about the diffraction if the incidence wavelength changes?11-7 Single slit interference

(3)the width of fringethe distance of adjacent orders11-7 Single slit interference

(4) Dynamic changes of single-slit diffractionWith up movement of the slitthe zero order bright fringe is still on axis of the convex. Up and down movements of single-slitthe diffraction pattern does not change according to the convex imaging principle.11-7 Single slit interference

(5)the optical path calculation non-normal incidence The central fringe move downwards11-7 Single slit interference

The central fringe move upwards 11-7 Single slit interference

Double-slit interference and single-slit diffraction can not be used in high-accuracy spectra measurement due to the small distance between fringes and low intensity. If we have a fence-tape optical element which includes many slits with equal distances and is identified as diffraction gratings. We can achieve larger distance, very tiny and higher intensity fringes which is advantageous for measurement with high-accuracy.11-8 Diffraction grating

Slits with equal widthequal distance. Gratings The width of transparent partsslits in gratings are represent by b, and that of opaque parts is b`. And b+b`i.e. the central distance of the slit is grating constant which is das shown in the Figure In practical gratingseveral dozens and even thousands of grooves are etched every millimeter (N/cm)which leads d the order of microns.d=1/N11-8 Diffraction grating

(Diffraction pattern is mixed effect of interference of diffraction)Grating equation11-8 Diffraction grating

Grating equationThe optical path difference of two adjacent slits equals to multiple number of wavelength, leading to interference enhancement and bright fringes.Optical path difference of adjacent slits11-8 Diffraction grating

Slit number N = 4 the diffraction intensity distribution of gratingBright fringeDark fringeThe envelope line is lightintensity of single-slitdiffractionk=1k=2k=0k=4k=5k=-1k=-2k=-4k=-5k=3k=-3Central bright fringek=6k=-6 Light intensity distribution11-8 Diffraction grating

More slits in gratingsmuch thinner of the fringes.(a)1(f)20(e)6(c)3(b)2(d)511-8 Diffraction grating

When N is large, i.e. many slitsThe light intensity distribution:11-8 Diffraction grating

the maximum order of the fringes11-8 Diffraction grating

Thinner the grating is, narrower width is, farer the bright fringes is . Larger wavelength is farer seaperation of the bright fringes.

11-8 Diffraction grating

ABd=b+b`POWith oblique incidencethe grating equation changes toWhen incidence and diffracted light are at the different side of the grating normaladdotherwise minus.11-8 Diffraction grating

Grating spectra

Continuous spectrumBroiling solidLinear spectrumthe gas in a discharge tubeZonary spectrummolecule spectrumClassification of diffraction spectra11-8 Diffraction grating

Due to single-slit diffractionthere is no bright fringes at the positions where should have interference enhancement. The phenomena is called order shortage.The two requirements should be satisfied for order shortage(The condition of order shortage Order shortage11-8 Diffraction grating

11-8 Diffraction grating

k=1k=2k=0k=4k=5k=-1k=-2k=-4k=-5k=3k=-3k=6Order shortage1st dark fringe3rd main brightfringe of grating diffractionOrder shortagek=-6

The end

Optics

Documents