Lab 9: Polarization Phy208 Spring 2008

Transcription

1 Lab 9: Polarization Ph208 Spring 2008 Name Section This sheet is the lab document our TA will use to score our lab. It is to be turned in at the end of lab. To receive full credit ou must use complete sentences and eplain our reasoning clearl. What s this lab about? In this lab ou investigate effects arising when using polarized light. There are four parts to the lab: PART A Use a polarizer to eplore common eamples of polarized light PART B Use a polariscope to understand how polarized light waves can be superposed or broken into components. PART C Create and investigate circular polarization. PART D Use the ideas of circular polarization to see how polarized light interacts with biological sugar molecules. Wh are we doing this? Understanding polarized light is important applications such as microscop, as well as in understanding the properties of electromagnetic waves.. What should I be thinking about before I start this lab? Suppose an electromagnetic wave is propagating through our area at the speed of light. If ou could take a snapshot, ou could freeze the electric and magnetic fields at a particular instant in time so that ou could look at them. At each point in space around ou, and at each instant in time, ou would see electric and magnetic fields with these properties: i) E r and B r are alwas perpendicular to each other, and also to the wave propagation direction (such that E r " B r is in the propagation direction) ii) The magnitudes E r " E and B r " B are related as B( o, o,z o,t o ) = ( 1/c)E( o, o,z o,t o ). iii) r E and r B both oscillate in time with a frequenc f = v /" (v is the propagation speed) iv) In takes a time T=1/f (the period) for the fields to complete one complete ccle at a fied point in space, and a distance λ (the wavelength) to complete one complete ccle at a fied time.

2 A. Making and detecting polarized electromagnetic waves In a linearl polarized electromagnetic wave, the electric field varies in time and space, but it alwas lies in a plane of polarization. Since the associated magnetic field is alwas perpendicular to this, we can describe the polarization completel b describing the orientation of the electric field. Light doesn t often look like this unless it is speciall prepared. It is usuall a superposition of all possible polarizations, which we call unpolarized light. A linear polarizer can be used to investigate the polarization state. It completel transmits linearl polarized light aligned with its transmission ais, and completel absorbs light linearl polarized perpendicular to its transmission ais. 1. Polarization b reflection. Light is partiall polarized whenever it is reflected. You can check this b using the linear polarizer from the polarization kit on the lab table. The transmission ais is marked b raised lines on the black plastic disc that holds the polarizing material. i) First look through the polarizer directl at the black gooseneck lab table lamp. Is this light polarized? How did ou tell? ii) Now aim the gooseneck lamp at about a 30 to 45 angle (from the horizontal) at the lab bench, and look through the polarizer at the reflection of the bulb. Is this light polarized? In what direction is the plane of polarization? iii) Polaroid sunglasses operate on the same principle as our kit polarizer. In what direction is the transmission ais of Polaroid sunglasses? Eplain. iv) Use our polarizer to look at our cell-phone displa or a computer LCD monitor. Describe the light emitted b these. 2

3 The polariscope Your polariscope has two polarizers (even though one is called an analzer!): The bottom one sits directl over the (unpolarized) incandescent bulb, and is fied in place. In a twopolarizer sstem, it is usuall called the polarizer, since it produces linear polarized light from an unpolarized source. The top one can rotate. It is usuall in-line with the bottom polarizer, but can also be swung to the side. In a twopolarizer sstem, it is usuall called the analzer, since it analzes whether a sample placed above the bottom polarizer has altered the polarization. Analzer Polarizer Unpolaized light 1. Turn on our polariscope and look down into the top polarizer. Describe the intensit variations while rotating the top polarizer through Find the transmission ais of the bottom polarizer with the small polarizer (mounted in a black plastic ring) from our bo. This one has its transmission ais marked with two ridges in the plastic. Eplain our procedure and use a piece of masking tape to mark it on the rim of the polariscope. Find the transmission ais of the top polarizer and mark it also. 3. What angle is between the transmission aes of the two polarizers when there is: Maimum transmission? What about no transmission? 3

4 B. Transmission through a polarizer: In the previous section, ou found that a linear polarizer will transmit a light wave whose electric field vector is parallel to the transmission ais, and blocks (absorbs) one with electric field vector perpendicular to that direction. For angles not 0º or 90º with respect to the transmission ais the polarizer transmits the component of the E-field along the transmission ais and absorbs the rest.. 1. Below are the electric fields of two linearl-polarized electromagnetic waves shown at various times throughout their period T. One is polarized along the -ais and the other along the -ais. Add these components together in each drawing and draw the electric field vector of the combined electromagnetic wave. -component -component t=0 t=t/6 t=2t/6 t=3t/6 t=4t/6 t=5t/6 What angle does the plane of polarization make with the -ais? t=6t/6 4

5 2. Now suppose a wave with electric field amplitude E o is linearl polarized at an angle of 30 with respect to the transmission ais of the analzer. What are the amplitudes of the components parallel and perpendicular to the transmission ais? 3. Write down the amplitude of the E-field of the wave transmitted b the analzer. What is the polarization angle of this transmitted wave with respect to the analzer s transmission ais? 4. What is the ratio of the amplitude of the E-field of the EM wave transmitted b the analzer to the amplitude of the E-field of the incident EM wave? 5. What is the ratio of the intensit after the analzer to the intensit before the analzer? 6. Put our pencils down, and set the analzer on our polariscope so that no light is transmitted. Now insert the small round polarizer from our kit between them and rotate it. Wh does light now get through at some angles? 5

6 C. Circular Polarization: An important tpe of polarization occurs when the horizontal component is time-delaed, b one quarter of a period (a 90 phase shift). That is, the horizontal component starts later in time as illustrated b the 3D diagram below. Let both amplitudes be E o t o t1 t2 t3 t4 1. The graphs below show the linearl-polarized - and -the components at various times. The -component starts later in time. Draw the vector sum on each ais. t 5 t=0 t=t/8 t=2t/8 t=3t/8 t=4t/8 t=5t/8 t=6t/6 t=7t/8 t=t 6

7 2. Describe the time-dependence of the total E-field (direction and magnitude). Does the magnitude oscillate? Does the direction change? When the horizontal component starts ¼ period earlier (-90 phase shift) rather than later, the electric field vector rotates in the opposite direction. These two polarization states are right and left circular. Making circularl polarized light. As ou showed above, ou can make circularl polarized light b combining two linearl polarized waves, with their plane of polarizations at right angles, and with a relative dela of ¼ wavelength. There is a ver eas wa to do this. Certain materials are opticall anisotropic, meaning that light waves polarized along different directions travel at different speeds. This means that the slower one is time-delaed relative to the faster one. You have two of these in our plastic bo. The fast ais is marked b a scratch in the brass holder. The thickness of the plate is such that the time dela is ¼ of the wave period, and the corresponding phase-dela is ¼ wavelength. These are called ¼ wave plates. 3. The thickness of our quartz ¼ wave plate is mm. Suppose that it gives eactl ¼ wavelength dela between the fast and slow aes for 540 nm wavelength light. What is the difference in the speed of light along the fast and slow aes? Fast ais Slow ais 7

8 Analzing circular polarization: Set the ¼ wave plate on the lower polarizer of the polariscope. Align the wave plate so that the linearl polarized light enters with its plane of polarization halfwa between the fast and slow aes of the ¼ wave plate. Now - and -components of the linearl polarized light have equal amplitude, and are aligned with the fast and slow aes of the ¼ wave plate. Fast ais Transmission ais ¼ wave plate Slow ais 4. Eplain wh this should produce circularlpolarized light. Linear polarizer 5. Now rotate the top polarizer. The intensit of the light transmitted through the wave plate remains almost constant as ou rotate the analzer (top polarizer) [ou ma need to slightl adjust the wave-plate angle]. Eplain wh this happens. 8

9 6. Now superimpose these two right and left circular polarizations. Suppose at t o both have their E-fields pointing along the -ais (i.e. the are in phase with each other). Add them graphicall as ou did the two linear polarizations. t o t 1 t 2 t 3 t 4 t 5 Describe the polarization of the sum of these two circularl polarized waves. 7. If the don t start out in phase, then the sum is still linearl polarized, but at a different angle. Below, the left-handed light is delaed (" left # " right )=90 (1/4 period) relative to the right-handed light. t o t 1 t 2 t 3 t 4 t 5 Describe the polarization of the sum of these two circularl polarized waves. Eplain how ou can see that the phase dela and the polarization angle are related as " pol = # left $ # right ( ) /2. 9

10 D. Chiral molecules and polarized light We discuss circular polarization because man molecules interact differentl with left-handed and than right-handed light due to their molecular chiralit, or handedness. Amino acids (shown at right in both chiralities) and sugars are chiral. Your bod uses and produces onl D-sugars (right-handed) and onl L- amino acids (left-handed). In a (right-handed) biological sugar solution, right and left circularl polarized light propagate at different speeds. The best wa to compare the speeds of right and left circular polarization is to send them through at the same time. As ou saw in C6 and C7, superimposing right and left circular polarization gives back linear polarization. Here ou use our polariscope to look at linearl polarized light propagating through Karo srup. If ou don t know what Karo srup is, call our mother and ask her. She probabl hasn t heard from ou in a while, and would enjo talking with ou. We use Karo because it is a ver concentrated chiral solution of right-handed molecules (sugars) onl. This handedness causes the plane of polarization of linearl polarized light to rotate as it goes through the srup. More srup leads to more rotation. Get a set of four jars of Karo srup (three small and one large, with different heights of srup). Be careful not to tip them as the srup will cling to the side and take time to run back down into the jar. 1. Place the large jar (lid off, open end up) on the polarizer and rotate the analzer while looking through the polarizers and srup. You should see colors in the srup. In what order do the colors appear as ou rotate the analzer clockwise? 2. Since the rotation appears to be different for different colors (wavelengths), place a color filter (colored transparenc) under the srup so ou are onl looking at one color (see spectral transmission below). TRANSMISSION ( % ) Roscolu #122, Green Diffusion WAVELENGTH ( nm ) TRANSMISSION ( % ) Roscolu #124, Red Cc Silk WAVELENGTH ( nm ) 10

11 Rotate the analzer so the light outside the jar but through the filter is etinguished. Then rotate the analzer until the light through the srup is etinguished. The difference of these angles is the angle b which the Karo has rotated the light. What direction (clockwise or counter clockwise, looking from the top) is the plane of polarization rotated? How did ou tell? (Hint: a little bit of Karo rotates the polarization a little bit, and a lot rotates it more). Record the polarization rotation for the red and green filters. Filter color: Relative rotation (deg): 3. Do this for the other jars and record all our data below. Sugar depth Green angle Red angle 4. Plot the data for the two colors on the aes below. Use a reasonable scale on the aes and put each color on the graph. Polarization Rotation Sugar Depth 11

12 Right circularl polarized and left circularl polarized light propagate at different speeds in a chiral solution because the interact differentl with the right-handed sugars. Since the travel at different speeds, the arrive at the top of the Karo at different times. This results in a time dela of one component relative to the other after passing through the solution, and a corresponding phase shift. 5. Suppose that the right-handed component moves at the speed of the lefthanded component (take v left =310 8 m/s). Then the left-handed component arrives at the top of the srup a short time "t before the left-handed component. What is "t after traversing 10 cm of Karo? 6. This time difference corresponds to a phase difference between the right- and lefthanded components, determined b what fraction it is of the oscillation period T. Write a relation between the phase shift φ, the time difference Δt, and the frequenc of the wave f =1/T. 7. The peak wavelength of red light ou used above is 670 nm. What is the phase shift for the time dela calculated in 5? 12

13 8. Using " pol = (# left $ # right ) /2 from C7, what polarization rotation is this? 9. Combining the ideas of 6-8, write the polarization rotation θ in terms of the wavelength and time dela. 10. Eplain whether this describes the sequence of colors ou observed in D1, assuming that the time dela does not depend on wavelength. 11. From our data for red and green polarization rotation, determine the actual speed difference for right- and left-handed light in the Karo srup. 13