Chapter 35
I am Watching YOU!!
Human Retina Sharp Spot: Fovea Blind Spot: Optic Nerve
Human Vision An optical Tuning Fork
Optical Antennae: Rods & Cones Rods: Intensity Cones: Color
Where does light actually come from? Light comes from the acceleration of charges.
Light is emitted when an electron in an atom jumps between energy levels either by excitation or collisions.
Atoms are EM Tuning Forks They are tuned to particular frequencies of light energy.
Atomic Emission of Light Each chemical element produces its own unique set of spectral lines when it burns
Hydrogen Spectra
Light Emission
Incandescent Light Bulb Full Spectrum of Light All frequencies excited!
Light Waves E = Emax cos (kx ωt) B = Bmax cos (kx ωt) E c = = B 1 v= c/ n 0 0 Speed of Light in a vacuum: 186,000 miles per second 300,000 kilometers per second 3 x 10^8 m/s
The Electromagnetic Spectrum
Visible Light Different wavelengths correspond to different colors The range is from red (λ ~ 7 x 10-7 m) to violet (λ ~4 x 10-7 m)
If you pass white light through a prism, it separates into its component colors. long wavelengths R.O.Y. G. B.I.V spectrum short wavelengths
Radiation of Visible Sunlight
Additive Primary Colors Red, Green, Blue
RGB Color Theory
Additive Complementary Colors Yellow, Cyan, Magenta The color you have to add to get white light. Red + Green = Yellow Blue + Green = Cyan Red + Blue = Magenta Red + Blue + Green = White White light red light =?? White light yellow light =??
FYI: Mixing Colored Pigments Subtractive Colors Pigments subtract colors from white light. Yellow + Cyan = Green Cyan + Magenta = Purple Yellow + Magenta = Red Yellow + Cyan + Magenta = Black
Why are some materials colored?
Why are some materials colored? Colored materials absorb certain colors that resonate with their electron energy levels and reject & reflect those that do not.
Why is the Ocean Cyan? White light minus cyan is red. Ocean water absorbs red.
Why are most materials Opaque? (Opaque Can t see through) They absorb light without re-emitting it. Vibrations given by the light to their atoms and molecules are turned into random kinetic energy they become slightly warmer.
Opacity: Mirrors Free electrons in opaque reflective surfaces can vibrate, absorb & re-emit at any frequency.
Transparency Selective Absorption Glass resonates strongly with UV and infrared, absorbing those frequencies while transmitting visible frequencies.
The heating effect of a medium such as glass or the Earth s atmosphere that is transparent to short wavelengths but opaque to longer wavelengths: Short get in, longer are trapped!
Why is the Sky Blue?
How are Rainbows Formed?
Light Ray Approximatin Geometric Optics
Review Basic Geometry!
Ray Approximation The rays are straight lines perpendicular to the wave fronts With the ray approximation, we assume that a wave moving through a medium travels in a straight line in the direction of its rays
Light Rays: Ignore Diffraction and Interference of waves! Diffraction depends on SLIT WIDTH: the smaller the width, relative to wavelength, the more bending and diffraction. We will assume that λ<<d, where d is the diameter of the opening. This approximation is good for the study of mirrors, lenses, prisms, etc.
Reflection & Refraction θ i = θ r n sinθ = n sinθ 1 1 2 2
Law of Reflection The normal is a line perpendicular to the surface It is at the point where the incident ray strikes the surface The incident ray makes an angle of θ 1 with the normal The reflected ray makes an angle of θ 1 with the normal
Specular Reflection Specular reflection is reflection from a smooth surface The reflected rays are parallel to each other All reflection in this text is assumed to be specular
Diffuse Reflection Diffuse reflection is reflection from a rough surface The reflected rays travel in a variety of directions A surface behaves as a smooth surface as long as the surface variations are much smaller than the wavelength of the light
Law of Reflection θ i = θ r
How many times will the incident beam shown be reflected by each of the parallel mirrors?
What is the smallest mirror that you can see your entire image in? 1. As tall as you 2. Longer than you 3. Shorter than you 4. Depends on distance to the mirror. 5. Depends on where it is hung
How long does a mirror have to be to see your entire image in? Suppose a woman stands in front of a mirror as shown. Her eyes are 1.65 m above the floor, and the top of her head is 0.13 higher. Find the height above the floor of the top and bottom of the smallest mirror in which she can see both the top of her head and her feet. How is the distance related to the woman s height?
A light ray travels from medium 1 to medium 3 as shown. For these media, A. n 3 < n 1. B. n 3 = n 1. C. n 3 > n 1. D. We can t compare n 1 to n 3 without knowing n 2.
A light ray travels from medium 1 to medium 3 as shown. For these media, A. n 3 < n 1. B. n 3 = n 1. C. n 3 > n 1. D. We can t compare n 1 to n 3 without knowing n 2.
Refraction: Bending Light into Focus
Refraction: Bending of Light Transmitted through Materials
Light Bends because it Slows Down.
Atoms are Optical Tuning Forks Light slows down as it travels through glass because it takes time to be absorbed and re-emitted.
Light Slows Down in Materials Light Bends Toward the Normal when going from a medium of lower refractive index to one that has a higher refractive index and visa versa. lower n higher n
Index of Refraction n = c v n 1 Vacuum: 1 Water: 1.33 Glass: 1.46 Diamond: 2.4
The Index of Refraction The speed of light in any material is less than its speed in vacuum The index of refraction, n, of a medium can be defined as speed of light in a vacuum c n = speed of light in a medium v n λ λin vacuum = λn λin a medium
Some Indices of Refraction
Frequency Doesn t Change! As light travels from one medium to another, its frequency does not change Both the wave speed and the wavelength do change The wavefronts do not pile up, nor are created or destroyed at the boundary, so ƒ must stay the same
Snell s Law of Refraction Angles are always measured from the normal. n sinθ = n sinθ 1 1 2 2
Snell s Law Example Light is refracted into a crown glass slab θ 1 = 30.0 o, θ 2 =? n 1 = 1.00 and n 2 = 1.52 θ 2 = sin -1 (n 1 / n 2 ) sin θ 1 = 19.2 o The ray bends toward the normal, as expected
Example 35.4 Emerging Beam is Parallel to Incident Beam but offset distance d Fig. 35-15, p. 989
You Try Problem What is the apparent depth of the diver? Assume that the horizontal distance doesn t change. 25
Possible Beam Directions Possible directions of the beam are indicated by rays numbered 1 through 5 The refracted rays are bent away from the normal since n 1 > n 2
Total Internal Reflection θ = 90 o 2 n sinθ = n sinθ 1 1 2 2 sinθ = C n n 2 1 The Critical Angle
An application of internal reflection Plastic or glass rods are used to pipe light from one place to another Applications include: medical use of fiber optic cables for diagnosis and correction of medical problems Telecommunications A flexible light pipe is called an optical fiber A bundle of parallel fibers (shown) can be used to construct an optical transmission line Fiber Optics
Construction of an Optical Fiber The transparent core is surrounded by cladding The cladding has a lower n than the core This allows the light in the core to experience total internal reflection The combination is surrounded by the jacket
Critical Angle Sample Problem A ray of light, emitted by a laser located beneath the surface of an unknown liquid with air above it, undergoes total internal refection as shown. What is the index of refraction for the liquid? Wht is its likely identification?
If you pass white light through a prism, it separates into its component colors. long wavelengths R.O.Y. G. B.I.V short wavelengths
The index of refraction depends on WAVELENGTH. long wavelengths R.O.Y. G. B.I.V short wavelengths
The speed and wavelength change but the FREQUENCY does NOT. Fr Frequency depends on the oscillating source! long wavelengths R.O.Y. G. B.I.V short wavelengths
Why does Violet Light bend more than Red Light? Violet light slows down more because the atoms in the material are tuned to higher frequencies. As the violet light travels through glass it takes more time to be absorbed and re-emitted.
Angle of Deviation The ray emerges refracted from its original direction of travel by an angle δ, called the angle of deviation The angle of deviation depends on the wavelength
Refraction in a Prism Since all the colors have different angles of deviation, white light will spread out into a spectrum Violet deviates the most Red deviates the least The remaining colors are in between
Dispersion For a given material, the index of refraction varies with the wavelength of the light passing through the material This dependence of n on λ is called dispersion Snell s law indicates light of different wavelengths is bent at different angles when incident on a refracting material
Variation of Index of Refraction with Wavelength The index of refraction for a material generally decreases with increasing wavelength Violet light bends more than red light when passing into a refracting material
Dispersion Sample Problem The index of refraction for violet light in silica flint glass is 1.66, and that for red light is 1.62. What is the angular dispersion of visible light passing through a prism of apex angle 60.0 if the angle of incidence is 50.0? red (660 nm) violet (410 nm)
How are Rainbows Formed?
Dispersion: Raindrops Act like Prisms A ray of light strikes a drop of water in the atmosphere It undergoes both reflection and refraction First refraction at the front of the drop Violet light will deviate the most Red light will deviate the least
The Rainbow At the back surface the light is reflected It is refracted again as it returns to the front surface and moves into the air The rays leave the drop at various angles The angle between the white light and the most intense violet ray is 40 The angle between the white light and the most intense red ray is 42
Observing the Rainbow If a raindrop high in the sky is observed, the red ray is seen A drop lower in the sky would direct violet light to the observer The other colors of the spectra lie in between the red and the violet
The secondary rainbow is fainter than the primary The secondary rainbow arises from light that makes two reflections from the interior surface before exiting the raindrop Higher-order rainbows are possible, but their intensity is low Double Rainbow
Huygens s Principle Prove the Laws of Reflection & Refraction
Huygens s Principle Construction for a Plane Wave Huygens assumed that light is a form of wave motion rather than a stream of particles All points on a given wave front are taken as point sources for the production of spherical secondary waves, called wavelets, which propagate outward through a medium with speeds characteristic of waves in that medium After some time has passed, the new position of the wave front is the surface tangent to the wavelets
Huygens s Construction for a The inner arc represents part of the spherical wave The points are representative points where wavelets are propagated The new wavefront is tangent at each point to the wavelet Spherical Wave
Galileo In the early 17th century, many scientists believed that there was no such thing as the "speed of light"; they thought light could travel any distance in no time at all. Galileo disagreed, and he came up with an experiment to measure light's velocity: he and his assistant each took a shuttered lantern, and they stood on hilltops one mile apart. Galileo flashed his lantern, and the assistant was supposed to open the shutter to his own lantern as soon as he saw Galileo's light. Galileo would then time how long it took before he saw the light from the other hilltop. The problem was that the speed of light is simply too fast to be measured this way; light takes such a short time (about 0.000005 seconds, in fact) to travel one mile that there's no way the interval could have been measured using the tools Galileo had.
The Speed of Light? 186,000 miles per second 300,000 kilometers per second 3 x 10 8 m/s first successfully determined by Danish astronomer Ole Roemer in 1675: 2.3 x 10 8 m/s First Terrestrial Measurement by Fizeau in 1849: 2.9979 x 10 8 m/s In 1926, Michelson used a rotating prism to measure the time it took light to make a round trip from Mount Wilson to Mount San Antonio in California, a distance of about 22 miles (36 km). The precise measurements yielded a speed of 186,285 miles per second (299,796 kilometres per second).
Why aren t images of objects produced on the wall without a lens or hole?