Final Exam (chapters since Exam#2). time: Friday 05/03 3:30 pm- 5:30 pm. Location: room 114 of physics building. If you can not make it, please let me know by Friday 04/26 so that I can arrange a make-up exam. If you have special needs, e.g. exam time extension, and has not contact me before, please bring me the letter from the Office of the Dean of Students before Friday 04/26. No requested will be accepted after that. AOB problems. Prepare your own scratch paper, pencils, erasers, calculators etc. Use only pencil for the answer sheet No cell phones, no text messaging which is considered cheating. No crib sheet of any kind is allowed. Equation sheet will be provided and will also be posted on the web. 1

Different wavelengths of visible light are associated with different colors. Violet is about 3.8 x m. Wavelengths shorter than the violet comprise ultraviolet light. Red is about 7.5 x m. Wavelengths longer than the red comprise infrared light. In between, the colors are red, orange, yellow, green, blue, indigo, and violet. 2

Color Mixing  The process of mixing two different wavelengths of light, such as red and green, to produce a response interpreted as another color, such as yellow, is additive color mixing.  Combining the three primary colors blue, green, and red in different amounts can produce responses in our brains corresponding to all the colors we are used to identifying.  Red and green make yellow, blue and green make cyan, and blue and red make magenta.  Combining all three colors produces white. 3

Color Mixing  The pigments used in paints or dyes work by selective color mixing. They absorb some wavelengths of light more than others.  When light strikes an object, some of the light undergoes specular reflection: all the light is reflected as if by a mirror.  The rest of the light undergoes diffuse reflection: it is reflected in all directions.  Some of the light may be selectively absorbed, affecting the color we see.  If red light is absorbed, we see blue-green. 4

 The white light coming from the sun is actually a mixture of light of different wavelengths (colors).  The shorter wavelengths of blue light are scattered by gas molecules in the atmosphere more than longer wavelengths such as red light.  The blue light enters our eyes after being scattered multiple times, so appears to come from all parts of the sky. Why is the sky blue? 5

Why is the sunset red?  The shorter wavelengths of blue light are scattered by gas molecules in the atmosphere more than longer wavelengths such as red light.  When the sun is low on the horizon, the light must pass through more atmosphere than when the sun is directly above.  By the time the sun’s light reaches our eyes, the shorter wavelengths such as blue and yellow have been removed by scattering, leaving only orange and red light coming straight from the sun. 6

Mirage and Rainbow water droplet rainbow  red is outside.  intensity max at 42  7

8 Thin film interference  Thin film interference occurs when light is reflected from the top surface and the underneath surface.  This provides the two beams of coherent light that interfere.  Since we normally observe this with white light we see colors because the path difference varies depending on the angle of observation  So different wavelengths (colors) have constructive and destructive interference at different places on the film.

9 Coatings for lenses  As light passes from one transparent medium to another a few percent of the light will be reflected.  This is a particular problem in optical systems like lenses where there may be many glass elements.  For example if 96% of the light is transmitted at a surface after 8 surfaces only 72% of the light remains and the other 28% will be scattered everywhere.  Thin coatings are put on glass surfaces so that for particular wavelengths the light reflected from the top surface is exactly cancelled by the light from the bottom surface.  This is only true for a single wavelength and to reduce the reflections for a range of wavelengths requires multiple thin film layers very often just λ/4 thick.

Polarization of Electromagnetic Waves Polarization is a measure of the degree to which the electric field (or the magnetic field) of an electromagnetic wave oscillates preferentially along a particular direction. linearly polarized unpolarized partially polarized Looking at E head-on Linear combination of many linearly polarized rays of random orientations components equal y- and z- amplitudes unequal y- and z- amplitudes 10

Polarizer: polarization by absorption An electric field component parallel to the transmission axis is passed by a polarizer; a component perpendicular to it is absorbed. So if linearly polarized beam with E is incident on a polarizer as shown, Zero if  =  /2, I 0 if  =0 If unpolarized beam is incident instead, The intensity will reduce by a factor of two. The light will become polarized along the transmission axis transmission axis dichroism (tourmaline, polaroid,…) 11

Quiz (Bonus: 20 points)  A beam of un-polarized lights with intensity I is sent through two polarizers with transmission axis perpendicular to each other. What’s the outgoing light intensity? a) ½ I b) 2 I c) 0 d) 1.5 I 12

Example: two polarizers This set of two linear polarizers produces LP (linearly polarized) light. What is the final intensity? P 1 transmits 1/2 of the unpolarized light: I 1 = 1/2 I 0 P 2 projects out the E-field component parallel to x’ axis: = 0 if  =  /2 (i.e., crossed) 13

7B-22 Polarizer Effects 14

Quiz (bonus: 20 points): Unpolarized light of intensity I 0 is sent through 3 polarizers, each of the last two rotated 45  from the previous polarizer so that the last polarizer is perpendicular to the first. What is the intensity transmitted by this system? (hint: sin 2 (45  )=0.5) a) 0.71 I 0 b) 0.50 I 0 c) 0.25 I 0 d) I 0 e) 0 15

Image by Reflection from a Plane Mirror An extended object can be broken into infinite number of point objects. Image has the same height and orientation as the object.  Only small fraction of reflected rays received. extended object  Virtual image at same distance from but on the other side of the mirror as the object it is called a virtual image since no rays actually go through the image, point object 16

7A-05 Candle Illusion 17

“Full Length” Mirror Only half the object (and image) size is needed. 18

Quiz (bonus: 20 points) A person is standing still 2 meters in front of a mirror, then the mirror is moved 1 meter towards him and then stopped. What’s the distance between the person and his image before and after the mirror is moved? a) 2m and 1m b) 3m and 2m c) 4m and 2m d) 5m and 4m 19