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Physics 272 December 2 Fall 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_fall_272_uhm.html Prof. Philip von Doetinchem [email protected] Phys272 - Fall 14 - von Doetinchem - 139 Standing electromagnetic waves ● Electromagnetic waves can be reflected on surfaces – ● ● ● Dielectrics or conductors can serve as reflectors Superposition principle of electric and magnetic fields also applies to electromagnetic waves Superposition of incident and reflected wave forms a standing wave Electric force is conservative → it is not possible to do work on a test charge like that: Phys272 - Fall 14 - von Doetinchem - 140 Standing electromagnetic waves ● Electric field cannot have a net component parallel to the surface ● Superposed incident and reflected wave must be zero at all times on the conductor ● Incident wave is not zero at all times on the conductor → oscillating currents are induced in surface → additional field that cancels out the electric field of the incident electromagnetic wave ● This also creates the reflected wave: ● The sum of incident and reflected wave must be 0 at all times on the surface: Phys272 - Fall 14 - von Doetinchem - 141 Standing electromagnetic waves ● ● The sum of incident and reflected wave must be 0 at all times on the surface: Position and time factorize for electric field Phys272 - Fall 14 - von Doetinchem - 142 Standing electromagnetic waves ● ● ● What does the magnetic field look like? → Faraday's law still applies Integrate: A standing wave that was reflected on a conductor shows a 90deg phase angle between electric and magnetic field Phys272 - Fall 14 - von Doetinchem - 143 Standing waves in a cavity ● ● ● ● ● Insert a second conducting plane: cavity → example: microwave oven On both planes the electric field has to vanish A standing wave is created when the electromagnetic wave wavelength is an integer multiple of /2 Measuring the node positions → measurement of wavelength Reflections generally also happen on surfaces of two materials: – Part of the wave is transmitted and a part is reflected Phys272 - Fall 14 - von Doetinchem - 144 The nature and propagation of light ● ● Understanding the properties of light: – Blue color of the sky – Red color of a sunset – Rainbows – Cameras – Glasses – Human eye – lasers Wave properties of light began to be discovered 1665 ● ● ● ● The wave picture is only describing one side of light Several aspects reveal particle properties Particles and wave properties combined → photon Propagation can be well understood in wave picture Phys272 - Fall 14 - von Doetinchem - 146 Waves, wave fronts, and rays ● ● ● ● ● A wave front is the leading edge of a wave All points on a wave front are at the same part of the cycle of their variation Electromagnetic waves emitted by a point-like source: – spherical surface concentric with source is a wave front – Far away from the source (i.e., the radius is large) → spherical wave front can be treated as plane wave Light rays use the particle properties of light and denote the direction of travel of the wave front Light rays are straight lines in a homogeneous material → we will study what happens when light travels from one medium into another Phys272 - Fall 14 - von Doetinchem - 147 Reflection and refraction ● ● ● ● When a light ray strikes a plane → light is partly reflected → light is partly transmitted Incident, reflected, and refracted rays and the normal to the surface all lie in the same plane Incident angle = reflected angle Keep in mind most objects we see do not emit light → they reflect light in a diffuse manner No reflection → no wonderful mirror selfies → what a sad world that would be Phys272 - Fall 14 - von Doetinchem - 148 The laws of reflection and refraction ● Optical materials have an important property → index of refraction air glass Incident light ray Source: http://en.wikipedia.org/wiki/Refractive_index ● ● Light travels slower in a material than in vacuum Index of refraction is 1 for vacuum and larger than 1 for any other material ● Snell's law: Ratio of sines of the angles and is equal to the inverse ratio of the two indexes of refraction Phys272 - Fall 14 - von Doetinchem - 149 The laws of reflection and refraction air glass ● If a ray passes into a material with higher index of refraction → refraction angle is smaller in material Incident light ray Source: http://en.wikipedia.org/wiki/Refractive_index ● At normal incident on the surface: zero refraction angle ● The path of a refracted ray is reversible ● Intensities of reflected and refracted rays depend on angle of incidence, index of refraction, polarization ● Index of refraction of air: ~1.0003 (increases with density) ● Glasses have index of refraction of 1.5-2.0 Phys272 - Fall 14 - von Doetinchem - 150 Index of refraction and the wave aspects of light ● When light passes from one medium to the other: – Frequency stays constant: ● ● – number of wave cycles per time is conserved A surface cannot destroy or create waves The wavelength changes: ● ● Wavelength becomes shorter after refraction into medium with higher index of refraction Wave gets squeezed at lower velocities and stretched at higher velocities Phys272 - Fall 14 - von Doetinchem - 151 Reflection and refraction Phys272 - Fall 14 - von Doetinchem - 152 Total internal reflection Source: http://en.wikipedia.org/wiki/Optical_fiber ● ● ● AMS-02 AntiCoincidence Counter All the light can be reflected from a surface → no transmission Important effect to transport light without losses from one place to the other → light guides Used in cars for sending signals to sensors → does not feel electric interference → more reliable signal Phys272 - Fall 14 - von Doetinchem - 156 Total internal reflection ● If a ray passes from a higher refractive index medium to a lower refractive index medium – At a certain critical incident angle the refracted angle in the second medium becomes 90deg → no transmission possible Phys272 - Fall 14 - von Doetinchem - 157 Applications of total internal reflection ● ● In contrast to polished metallic surfaces total reflection can really totally reflect light without losses (inhomogeneities in material make this statement a bit weaker) Diamonds have a large refractive index (2.417 → critical angle: 24.4deg): – light enters a cut diamond – internal total reflection on the back surface – light leaves the light in the front → wonderful sparkle! Phys272 - Fall 14 - von Doetinchem - 158 Dispersion ● ● ● White light is a superposition of electromagnetic waves with a wide variety of wavelength Speed of light is the same for all wavelength in vacuum Speed of light in matter is different for different wavelength → index of refraction depends on wavelength (dispersion) Source: http://de.wikipedia.org/wiki/Prisma_%28Optik%29 ● In most materials the index of refraction decreases with longer wavelengths ● Violet light is the slowest in this case, red light the fastest inside the prism ● Different wavelengths (colors) have different refractive angles ● Prism reveals the spectrum of colors ● Diamonds also have a large dispersion → wide spectrum of colors adds to the sparkling effect Phys272 - Fall 14 - von Doetinchem - 160 Rainbows ● Dispersion, refraction, and reflection are important ● White light is reflected on the back of a water droplet ● Waves of different wavelength feel different index of refraction ● Exit angle of water droplet is different for different wavelength ● ● ● Observation at a quite narrow angle: the refracted, reflected spectrum from the water droplets meet in observer's eye Rainbow is visible from different locations: for example the red color is now coming from a different region of the sky → angle between sun, water droplet and sun has to be just right (reason for arc) Double rainbow comes from two internal reflections in water droplet (→ reversed colors) Phys272 - Fall 14 - von Doetinchem - 161 Rainbow ● ● ● How large is the angle between incident and exit ray → add up all refraction angles: Snell's law: depends on wavelengths Water droplet is spherical: Angle between incident and deflected ray: Phys272 - Fall 14 - von Doetinchem - 162 Rainbow ● ● ● ● This is the deflection angle for a particular wavelength using the index of refraction for this particular wavelength Deflection angle Change of deflection angle is small Change of deflection angle is too large to form one bright region on the sky Incident angle the deflection angle varies with the incident angle of the light on the water droplet To form a bright region on the sky in a particular color: incident light needs to be reflected at the same (or very similar) deflection angle: Larger index of refraction → lower deflection angle → light comes from a lower position on the sky Phys272 - Fall 14 - von Doetinchem - 163 Polarization ● ● ● ● ● ● If an electromagnetic wave has an electric field that only varies in one direction: linear polarization Electromagnetic waves can be composed of different modes with different polarizations Unpolarized light can be filter in a way such that is polarized Waves from a radio transmitter are usually linearly polarized (electric field only changes in vertical direction of the antenna) Electromagnetic waves from light are different – The total composition of light waves is not emitted from a single antenna – Waves are emitted from different sources (atoms, molecules) with random order → light from (e.g., a light bulb) is the superposition of electromagnetic waves with different polarizations Please don't confuse a polarized wave with shifting of electric charges inside material Phys272 - Fall 14 - von Doetinchem - 164 Polarizing filters https://www.youtube.com/watch?v=nCAKQQjfOvk Phys272 - Fall 14 - von Doetinchem - 165 Polarizing filters ● ● Simple filter for microwaves (~cm wavelength) with isolated conducting wires: Polaroid material → sun glasses: – Selective absorption of different polarization directions – ~80% are transmitted when light is polarized parallel to the polarizing axis – ~1% for other directions – Explanation goes back to certain long-chain molecules → similar to the filter above Phys272 - Fall 14 - von Doetinchem - 166 Using polarizing filters ● ● Ideal polarizer definition: – 100% of incident light polarized parallel to polarizing axis transmitted – 0% transmission in all other directions Polarized wave carries exactly 50% of the energy of the incident waves – Superposition of incoming waves can be decomposed into a parallel and perpendicular component with respect to polarizer – If light is completely unpolarized → all directions appear equally often → perpendicular and parallel component have the same value Phys272 - Fall 14 - von Doetinchem - 167 Using polarizing filters ● ● A combination of two filters allows to find the polarization direction: – Intensity is at maximum when both polarizing axis are align – Intensity is zero when polarizing axis are perpendicular Intensity of light transmitted (Malus's law): Phys272 - Fall 14 - von Doetinchem - 168 Polarization by reflection ● ● ● ● Unpolarized light can be polarized by reflection Components that are polarized perpendicular to the plane of incidence are stronger reflected than parallel components Assumption in the following: – Light composed of a linear polarized component parallel to the plane of incidence – and a component linear polarized to the plane of incidence Example on water: – The polarization of most reflected light is aligned with the water surface – Sun glasses with polarization have vertical polarizing axis and filter the reflections from the water – At the same time the intensity is also reduced by ~50%. Phys272 - Fall 14 - von Doetinchem - 170 Polarization by reflection ● ● ● Reflection can be described by inducing Hertzian dipole in the reflecting surface Reflection can only occur if the induced Hertzian dipoles actually emit electromagnetic waves in the direction of reflection angle When induced dipoles in material do not emit in the direction of the reflected ray → reflected parallel ray disappears when the reflected ray and the refracted ray enclose 90deg → only perpendicular component left → polarized Phys272 - Fall 14 - von Doetinchem - 171 Polarization by reflection ● =0 for vanishing of parallel component: Brewster angle Phys272 - Fall 14 - von Doetinchem - 172 Polarization filter in photography ● ● without polarization filter ● ● with polarization filter reflecting surface is not horizontal incidence plane is determined for each drop by the plane containing the sun, the drop, and the observer → the rainbow is polarized tangential to the arch vertical polarizing filter will produce a gap at the top of the rainbow and enhances the contrast of the sides Grey sky is not polarized → filter reduces background Phys272 - Fall 14 - von Doetinchem - 173 Additional Material Phys272 - Fall 14 - von Doetinchem - 175 Flattened sun at sunset Deviation from circular shape ● Rays path through atmosphere ● Atmosphere gets denser at lower altitudes ● rays from the lower limb of the sun and from the upper limb path through different densities of the atmosphere → different refraction Phys272 - Fall 14 - von Doetinchem - 176 AMS-02 AntiCoincidence Counter Plastic optical fiber light guides are part of a detector for cosmic ray measurement AMS-02 during ground testing Connecting plastic optical fiber light guides AMS-02 on the International Space Station Phys272 - Fall 14 - von Doetinchem - 177 Reflection from a swimming pool ● ● ● ● Sunlight reflects from a smooth swimming pool surface Reflected light is completely polarized at this incident angle: Corresponding refraction angle: If you would turn on a spot under water during the night → completely polarized reflected beam under water at 36.9deg → angles are reversed Phys272 - Fall 14 - von Doetinchem - 178 Circular and elliptical polarization ● ● ● Circular polarized light can be produced when running two antennas in a 90deg angle at a quarter cycle phase difference The two electric fields superpose in the following way at a fixed position: If the phase angle is different from 90deg, the light is elliptically polarized Phys272 - Fall 14 - von Doetinchem - 179 Circular and elliptical polarization ● Nature is also able to produce circular polarized light: – Light composed of two perpendicular polarizations – enters a material with different indexes of refraction for different directions of polarization (e.g., calcite) – Light travels at different velocities through material – After leaving material → light not any longer in phase → circular/elliptical polarization ● ● If such a material has the right thickness to produce quarter-wave phase angle → circular polarization It also works in reverse → circular polarized light is linear polarized after going through a quarter-wave plate Phys272 - Fall 14 - von Doetinchem - 180