Optics Polarization. Lana Sheridan. June 20, De Anza College

Transcription

1 Optics Polarization Lana Sheridan De Anza College June 20, 2018

2 Last time interference from thin films Newton s rings

3 Overview the interferometer and gravitational waves polarization birefringence

4 7 Michelson Wave Optics Interferometer A single ray of light is split into two rays by mirror M 0, which is called a splitter. Light source The path difference between the two rays is varied with the adjustable mirror M 1. Telescope L 2 M 0 L 1 M 1 As M 1 is moved, an interference pattern changes in the field of view. M 2 Invented by Albert Michelson in 1881, this device featured in two target pattern (corresponding to destructive interference) and M 1 is then moved a particularly distance l/4 toward important M 0, the experiments path difference (and changes lotsby more!): l/2. What was a dark circle at the center now becomes a bright circle. As M 1 is moved an additional distance l/4 thetoward Michelson-Morley M 0, the bright circle experiment becomes a dark (1887) circle again. demonstrated Therefore, the fringe there pattern ishifts no by ether one-half fringe each time M 1 is moved a distance l/4. The wavelength of light is then measured by counting the number of fringe shifts for a given displacement of M 1. If the wavelength is accurately known, mirror displacements can be measured to within a fraction of the wavelength. the LIGO experiment (2015) first experimental detection of gravitational waves

5 Gravitational Waves General relativity predicts gravitational waves, similar to electromagnetic waves. However, they are much harder to detect than EM waves! Massive objects that accelerate (for example, rotation of a non-rotational symmetric object) generate gravitational waves. Their effect is to distort spacetime as they propagate. They can tell us about events in the cosmos that we cannot see, and they can travel through matter with almost no scattering.

6 Laser Interferometer Gravitational-Wave Observatory (LIGO) Two miles-long interferometers where constructed in Hanford, Washington, and in Livingston, Louisiana. 1 The LIGO Livingston Observatory in Louisiana. Caltech/MIT/LIGO Lab

7 Detecting Gravitational Waves

8 Laser Interferometer Gravitational-Wave Observatory (LIGO) On Sept 14, 2015, both interferometers observed the same pattern of lengthening and contraction in the arms of their interferometers at basically the same time. They concluded that the source of the waves was the merger of two black holes. This was the first confirmed detection of gravitational waves.

9 Laser Interferometer Gravitational-Wave Observatory (LIGO) On Sept 14, 2015, both interferometers observed the same pattern of lengthening and contraction in the arms of their interferometers at basically the same time. They concluded that the source of the waves was the merger of two black holes. This was the first confirmed detection of gravitational waves. Four black hole collisions have now been observed by LIGO, and one of those also by Virgo, a new interferometer in Italy. They have also detected a collision of neutron stars (Aug 17, 2017), the first time both gravitational and EM waves were seen from the same event. The Fermi gamma ray space telescope detected a coinciding short gamma ray burst.

10 Polarization electromag- Light is composed of oscillation electric and magnetic fields. f this transitted by the e particular on of atomic ed to be the rection hapling in the x ld be at any ration from perposition larized light ve propagaz S B y S E S c Figure Schematic dia- In the diagram the gram E-field of an oscillates electromagnetic in the y-direction. wave The magnetic field must oscillate in perpendicular propagating at velocity S direction (here x) c in the and the direction of propagation is z. x direction. The electric field vibrates in the xy plane, and the magnetic field vibrates in the xz x

11 directions of the e The red dot signifies the We refer to the direction velocity of oscillation vector for ofthe tant. At any thewave E-field as the coming out of the page. tric field vectors ad polarization direction of the light ray. As noted in Sec S S E E electric field S E vi shown in Figure 3 simply polarized.) T the plane of polariz tant of all individu A linearly polar ing all waves from a single plane. We unpolarized light. unpolarized light vertically polarized light Polarization a Polarization by Light can also Figure be horizontally (a) polarized A representation of an unpolarized light or polarized in any other plane. The most common viewed along the direction It can also be circularly of propagation. polarized, The transverse meaning the direction transmits of waves w oscillation of the E-field rotates as the ray propagates. tion and that abso electric field can vibrate in any b

12 Creating Polarized Light: by Selective Absorption When unpolarized light of a long wavelength is shone through a set of closely-placed vertical wires, it becomes polarized horizontally. Any light ray with an electric field oscillation that is vertical causes a current in the wires. The energy is absorbed as the electron flow in the wire heats the wire. The horizontally polarized light has no electric field oscillation vertically, so it passes through the wires without interacting with them.

13 Figure represents an unpolarized light incident on a first polarizing sheet, Creating called the Polarized polarizer. Because Light: the transmission by Selective axis is oriented Absorption vertically in the figure, For the shorter light transmitted wavelengthsthrough a material this called sheet polariod is polarized will do vertically. the same A second polarizing thing. sheet, called the analyzer, intercepts the. In Figure 38.26, the ana lyzer transmission axis is set at an angle u to the polarizer axis. We call the electric field vector It is composed of the first oftransmitted long-chain hydrocarbons S E 0. The component that have been of S E 0 treated perpendicular to the analyzer axis is completely absorbed. The component of S E to become better conductors. 0 parallel to the Unpolarized light The polarizer polarizes the incident light along its transmission axis. S E 0 The analyzer allows the component of the light parallel to its axis to pass through. u Transmission axis Polarized light

14 lyzer transmission axis is set at an angle u to the polarizer axis. We call the electric field vector of the first transmitted S E 0. The component of S E 0 perpendicular Dependence to the analyzer axis of is Intensity completely absorbed. on Angle The component of the of S E Polarizers 0 parallel to the Unpolarized light The polarizer polarizes the incident light along its transmission axis. The analyzer allows the component of the light parallel to its axis to pass through. ng es her. ed is Transmission axis S E 0 Polarized light u When the analyzer is at an angle θ with respect to the transmission axis of the polarizer, the intensity of light transmitted through both is: I = I max cos 2 θ where I max is the intensity of the light after the first polarizer. This is called Malus s law.

15 Question Quick Quiz A polarizer for microwaves can be made as a grid of parallel metal wires approximately 1 cm apart. Is the electric field vector for microwaves transmitted through this polarizer (A) parallel (B) perpendicular to the metal wires? 1 Serway & Jewett, page 1181.

16 Question Quick Quiz A polarizer for microwaves can be made as a grid of parallel metal wires approximately 1 cm apart. Is the electric field vector for microwaves transmitted through this polarizer (A) parallel (B) perpendicular to the metal wires? 1 Serway & Jewett, page 1181.

17 Creating Polarized Light: by Reflection When light strikes a smooth surface of a transparent material, some light is reflected and some is transmitted. Interestingly, the polarization of the transmitted is not the same as of the reflected! If the incident ray is unpolarized, the transmitted and reflected rays will be partially polarized.

18 the reflecting surface and perpendicular to those the reflected ray (perpendicular to the dots and parallel to the blue arrow) send no energy in this direction. perpendicular to the page. represented by the dots. Creating Polarized Light: by Reflection Incident u 1 u 1 Reflected Incident u p u p Reflected n 1 n 2 90 n 1 n 2 u 2 u 2 a Refracted We can obtain an expression relating the polarizing angle to the index of refraction of the reflecting substance by using Figure 38.28b. From this figure, we see that When u p 1 90 the 1 ureflected ; therefore, and refracted u rays 2 uare p. Using perpendicular, Snell s law of the refraction (Eq. 35.8) gives n 2 n 1 5 sin u 1 sin u 2 5 sin u p sin u 2 b Refracted The dipoles in the surface cannot create a ray that has an E-field oscillating in the direction that the ray travels. reflected ray is completely polarized parallel to the surface.

19 y m es field oscillations parallel to the reflecting surface and perpendicular to those Creating Polarized Light: by Reflection perpendicular to the page. electric field oscillations represented by the dots. oscillating in the direction of the reflected ray (perpendicular to the dots and parallel to the blue arrow) send no energy in The value of the incident angle for the reflected and transmitted this direction. rays to be perpendicular, θ p is called Brewster s angle. - Incident u 1 u 1 Reflected Incident u p u p Reflected n 1 n 2 90 n 1 n 2 u 2 u 2 a Refracted Notice, θ 2 = 90 θ p. From Snell s Law: We can obtain an expression relating the polarizing angle to the index of refraction of the reflecting substance by using Figure 38.28b. From this figure, we see that u p u ; n 1 therefore, sin θ p u= n 2 cos(θ 2 u p. Using p ) Snell s law of refraction (Eq. 35.8) gives So, n 1 sin θ p = n 2 sin(90 θ p ) n 2 5 sin u 1 5 sin ( u p nθ 1 p = sin tan u 1 n2 2 sin u n 2 1 Because sin u 5 sin (90 2 u ) 5 cos u, we can write this expression as n /n 5 b ) Refracted

20 Summary the interferometer polarization Final Exam 9:15-11:15am, Tuesday, June 26. Homework Serway & Jewett: prev: Ch 37, onward from page OQs: 1, 5, 7; Probs: 43, 54, 63, 68 new: Ch 38, onward from page OQs: 1, 7; Probs: 45, 49, 51, 63, 65, 70