# Polarization and Photon Concept A. Polarization

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1 Polarization and Photon Concept A. Polarization Physics 102 Workshop #8A Name: Lab Partner(s): Instructor: Time of Workshop: General Instructions Workshop exercises are to be carried out in groups of three. One report per group is due by the end of the class. Each week s workshop session would typically contain three sections. The first two sections must be completed in class. The third section should be attempted if there is time. 1. A pre-lab reading and assignment section 2. Experiment section 3. Practice questions and problems Polarization A polarized wave is a wave in which there is only one vibration-direction. That is, if we are stationary at a chosen point in space, then the vibration-direction does not change, as time progresses. This unique direction is called the polarization-direction (PD) of the wave. The concept of a polarized wave is meaningful only for transverse waves (and hence light). Recall that for a transverse wave, it is required that the vibration-direction be perpendicular to the travel-direction. For any given travel direction, (let us say it travels along the positive x direction) every line in the plane perpendicular to the x axis fits the requirement. That is, each line in this plane (the yz-plane) is at right angles to the x direction. For unpolarized light, the vibration direction takes on, as time progresses, many directions in the yzplane, in random fashion. For polarized light, there is just one direction in the yz-plane, (say, the +y direction), for which there is vibration. A filter is a sheet or set of sheets, made of material consisting of long, parallel chains of atoms. Further, when light is incident on the filter, the chains absorb any part of the energy of the light wave that vibrates parallel to the chain direction. The part of the wave that vibrates perpendicular to the chain direction passes through the polarizer. 1

2 SOME SIMPLE EXPERIMENTS Overhead Lights Look at the room lights through one of the filters provided. Is the intensity of the light through the filter reduced, compared to the intensity that reaches your eye in the absence of a filter? Rotation of a Single Filter Does rotating the filter have any effect on the intensity of light from the overhead lights that reaches your eye? Nature of the Overhead Lights Consider your above observations. Do you conclude that the overhead lights emit polarized light or unpolarized light? Explain. Light through Two Filters Look at the room lights through two overlapping filters. Rotate one of the filters, keeping the other filter steady. Record below your observations on the intensity of light transmitted through both filters, as the rotation takes place. 2

3 We define the transmission axis (TA) of a filter as the PD of the polarized light that emerges through the filter. Consider the particular case in which minimum (close to zero) intensity of light gets through both filters. How do the directions of the two TAs of the two filters compare? (For this case, we say that the filters are crossed.) Explain. Light through three polarizers Use the small sized filters provided for this part of the lab. Orient two of the filters (call them 1 and 2) so that they are crossed. That is, minimum intensity of light goes through both. Now, put a third filter (call it 3) behind or in front of the first pair (filters 1 and 2). Put filter C in any orientation, relative to A and B. Does it still look dark? Now, put filter 3 in between the two crossed filters. Try various orientations of filter 3. What is seen through all three? Does what you see depend on the orientation of filter 3? Record your observations. 3

4 B. Discussion You may have noted an apparent paradox in your observations. It appears that adding absorbers can lessen absorption! Write a short paragraph on why this happens. Light Outdoors Go outdoors, and look at the trees through a single filter. Also, look at the ivy on the sides of buildings. Finally, look at the sky (NOT AT OR NEAR THE SUN). Do you observe any intensity change, as the filter is rotated, for any of these three cases? Trees: Buildings: Sky: Would you say that skylight is polarized, unpolarized, or partly polarized light? Explain. 4

5 The Polarization of Reflected Light A very interesting occurrence is observed when unpolarized light is reflected from a non-metallic surface. The reflected light is observed to be polarized or partly polarized. The one exception occurs when the angle of incidence is zero. That is, at normal incidence, the reflected light remains unpolarized. There is a particular angle of incidence for which the reflected light is completely polarized. This angle of incidence is known as the Brewster angle (θb). For this case, the vibration of the reflected light is exclusively in a direction parallel to the surface. At other angles of incidence, (excluding normal incidence), the reflected light is partly polarized in a direction parallel to the surface. Brewster angle is determined by the very simple relation: tan θb = n. Here, n is the index of refraction of the reflecting material. It is assumed that the ray travels in air, and that the index of refraction of air is equal to one. Observations Go the lobby on the west side of the Physics Building (in front of the elevator). Observe the reflection of light from the sign Experience Physics. Keep in mind that the mirror is in a vertical plane, behind the sign. To do this, stand halfway between the water fountain and the staircase door. Observe the reflection of the sign through your filter (and not the neon sign). Use the large filter with the handle. Rotate your filter through all possible orientations. Record your observations below. In the event you see a minimum intensity for the reflected light, record the orientation of the filter when this occurs. Is the reflected light polarized or unpolarized? Are you at or close to the Brewster angle? Explain your conclusions. Repeat the above procedure, standing directly in front of the sign. Explain your observation. 5

6 B. The Photon Concept Workshop #8B Physics 102 Introduction The concept of the photon was introduced at the lecture of Thursday, March 24, and also discussed at yesterday s lecture. Briefly put, the photon is the particle of light. Only a whole number of photons (0, 1, 2, 3,..) can exist in a light beam. It follows that only a whole number of photons can be emitted or absorbed. Each photon represents a light particle with a given frequency f. The energy E of the photon is given by the Einstein-Planck relation E = hf. The constant h in this relation is called Planck s constant. It is a universal constant in nature, just as fundamental as the speed of light or the electron charge. Its value is h = 6.6 x Joule seconds. The experimental basis for the concept, used by Einstein in 1905, was the photoelectric effect. (The experimental basis for the concept, as advanced by Planck in 1901, was the character of the radiation emitted by a black body at high frequencies.) In the photoelectric effect, electromagnetic radiation is incident on the surface of a metal. Some of the radiation is absorbed by electrons at the surface of the metal. A certain portion of these electrons consequently escape the metal. The escaping electrons are collected at an electrode and produce an observable current. In this workshop, we will answer questions and solve problems on the subject of photons. The purpose is to strengthen our knowledge of the concept and its applications. 1. The diagram below displays the apparatus used in the demonstration of the photoelectric effect given in Thursday s lecture. (The only exception is that in the experiment done in Stolkin Auditorium, the source of light was from the overhead projector.) 6

7 We used first a red filter to intercept the light from the source, before it reached the metal surface. Then, we repeated, using a blue filter. The meter reads the current going through the circuit for both cases. The size of the current is proportional to the number of electrons emitted from the metal surface. The effect was strong for one of the two choices of filters, and negligible for the other. For which case was the photoelectric effect strong? (This is an observational question. In case, you do not remember, consult with the Teaching Assistant or a Peer TA.) 2. Which type of photon has more energy a photon of red light or a photon of blue light? Why? 3. As discussed in lecture, each metal has its own characteristic value for its work function W 0. The work function is the minimum energy needed to liberate an electron at the surface of the metal. 7

8 The value of the work function for cesium is 1.8 ev. Note that the electron volt (abbreviated as ev) is simply an energy unit that is an alternative to the joule. One definition of the electron volt is that 1eV = 1.60 x Joules. When discussing work function values and electron energies, the ev is a more convenient unit for energy than is the Joule. This is because these energies are usually of the order of a few ev. One then avoids writing down factors of Decide whether or not the photoelectric effect will be seen, if the incident radiation is red light, with frequency of 4.0 x Hz. Take the metal to be cesium. Explain. 4. Repeat question #3 for the case in which blue light is the incident radiation. Blue light has its frequency-value equal to approximately 7.0 x Hz. Hint: It is not necessary to repeat the calculation of Question 3. Simply use ratio reasoning. Note that the frequency of blue light is roughly 7/4 times that of red light. 5. In a photoelectric effect experiment, two different metals (labeled as #1 and #2) are used. a) Metal #1 produces photoelectrons for both blue light and red light. In contrast, metal #2 produces photoelectrons for blue light but not for red light. Which metal produces photoelectrons for ultraviolet radiation? A. Meat #1, only. B. Metal #2, only. C. Both metals. D. Neither. Explain your choice. b) Which metal might produce photoelectrons for infrared radiation? 8

9 Why? c) Which metal has the larger work function? How do you know? 6. A photoelectric material has a work function W 0. Then, the threshold wavelength for the material is given by by a combination of factors of W 0, Planck s constant h, and the speed of light c. Work out the combination of factors that gives the threshold wavelength. In doing this, you cannot use any equations other than those cited on the first page of this photoelectric effect part, plus the wave-relation that connects the wavelength, the frequency and the speed of the wave. 7. Which one of the three completions below is correct? The energy of a photon is A. directly proportional to its wavelength. B. inversely proportional to its wavelength. C. not dependent on its wavelength. Explain. 9

10 8. Conservation of energy is a valid principle in the photoelectric effect, as it is in all of science. Consider how it relates the measured quantities in the photoelectric effect. Take the system to be a single electron, plus a photon of frequency f. For simplicity, choose the energy of the electron in the metal to be zero. Note: This can always be done. There is freedom to choose the zero of energy at any value you desire. However, once the choice has been made, you must remain faithful to this selection of the zero of energy. a) What is the initial energy of the system of photon and electron? b) The electron absorbs the photon and then immediately acquires kinetic energy K. Write down an expression for the energy of the system in terms of K and the work function W 0 of the metal. Hint: If an electron has initial energy zero, and then escapes the metal, then its potential energy is raised to the value of W 0. c) Use the principle of energy conservation to relate K, f and W 0. Your result is the basic relation (derived initially by Einstein) of the photoelectric effect. 10

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