2 nd & 3 th N.U.T.S. Workshops Gulu University Naples FEDERICO II University 7 – Polarization

9- Polarization 2nd & 3th NUTS Workshop ( Jan 2010) 2 Transverse Waves Exhibit Polarization Effect Oscillation of a rope in a plane along the slit, it passes through the slit Oscillation of a rope in a plane perpendicular to the slit, it does not pass through the slit

9- Polarization 2nd & 3th NUTS Workshop ( Jan 2010) 3 zz xx E.M. Wave Polarization … is a property that specifies the electric field (E) direction. Why do we pick the electric field out of the two (E, B)? Aren’t they on an equal footing? They are on an equal footing, but it is mostly the electric field, which interacts with matter – atoms, electrons, nuclei. Both E.M. waves are propagating in the +z direction but have different polarization. The polarization direction is that of the Electric field: in (a) it is vertically polarized (i.e. E is along y axis); in (b) it is horizontally polarized (i.e. E is along x axis). Unpolarized light would be a mix of such waves, with their E oriented at random in many different directions.

9- Polarization 2nd & 3th NUTS Workshop ( Jan 2010) 4 Polarization -2 EM waves from a TV tower are perfectly polarized – the Electric field has a very well defined direction, which stays always the same. In contrast, the light coming from the Sun or from a light bulb is unpolarized. What does it mean unpolarized? Doesn’t the electric field have some direction? It certainly does at every instant. BUT this direction does not stay constant and changes very rapidly and randomly. So, averaging over any reasonable time interval you do not find any particular polarization! polarized unpolarized The frequency of light (at the center of its spectrum) is about 5×10 14 Hz, which means 5×10 14 wave crests per second. If the polarization changes once every 500 crests it will still change times per second. Too fast to be detectable!

9- Polarization 2nd & 3th NUTS Workshop ( Jan 2010) 5 Polarizing the Light -1 Any way to make a polarized wave (light) out of unpolarized wave? Yes, but it is going to cost us some intensity loss… (No free meals…) We can use a polarizer - a piece of material, whose molecular or crystal structure has a preferred direction called the transmission axis. A polarizer “decomposes” the e.m. wave into a component with the electric field, E║, parallel to the transmission axis, which passes through, and a component with the E ┴ field perpendicular to the transmission axis, which gets totally absorbed.

9- Polarization 2nd & 3th NUTS Workshop ( Jan 2010) 6 Polarizing the Light - diff. view Natural light incident on a linear polarizer: the transmitted light is only the light component polarized in the plane defined by transmission axis and light propagation direction

9- Polarization 2nd & 3th NUTS Workshop ( Jan 2010) 7 Polarizing the Light -2 transmission axis z The magnitude of the component of the electric field along the transmission axis : Intensity of the wave is proportional to the square of the amplitude Law of Malus In an unpolarized wave the angle  changes randomly After passing through a polarizer the average intensity is The light gets polarized, but it looses 1/2 of its intensity...

9- Polarization 2nd & 3th NUTS Workshop ( Jan 2010) 8 Crossing the polarizers If the axis of a polarizer is set at  = 90° to the axis of polarization: A system of two crossed polarizers never lets any light through. Whatever passes through the first one is blocked by the second. no light is passing through!

9- Polarization 2nd & 3th NUTS Workshop ( Jan 2010) 9 I1I1 I2I2 I = I 3 IoIo I Stack of polarizers Without the second polarizer: E E E What happens to the intensity, I, and axis of polarization of unpolarized light upon passing through three polarizers (fig.) ?

9- Polarization 2nd & 3th NUTS Workshop ( Jan 2010) 10 Types of Polarization

9- Polarization 2nd & 3th NUTS Workshop ( Jan 2010) 11 Linear Polarization States Polarization by Reflection from Dielectric Media It’s the most common source of polarized light Wave pointing to you Wave moving this direction The reflected beam is partially polarized, in a plane perpendicular to the incidence plane. θiθi β For the incidence angle θ i = θ B (Brewster's angle) such that the angle between the reflected and refracted beam, β, is 90 0, the reflected ray is totally polarized ! n1n1 n2n2

9- Polarization 2nd & 3th NUTS Workshop ( Jan 2010) 12 Brewster's Angle Exercises N1: Derive the Brewster's angle formula, tan( θ B )=n2/n1, from the reflection and refraction laws. N2: Which is the Brewster's angle for the air - water (n=1.33) surface ?

9- Polarization 2nd & 3th NUTS Workshop ( Jan 2010) 13 Skylight is polarized if the Sun is to your side. Multiple scattering yields some light of the other polarization. In clouds, much multiple scattering occurs, and light there is unpolarized. Right-angle scattering is polarized Polarizer transmitting vertical polarization This polarizer transmits horizontal polarization (of which there is very little). Polarized Skylight