Reflection and Refraction

Reflection Most objects we see reflect light rather than emit their own light.

Principle of Least Time Fermat's principle - light travels in straight lines and will take the path of least time to strike mirror and reflect from point A to B MIRROR AB Wrong Path True Path

Law of Reflection “The angle of incidence equals the angle of reflection.” This is true for both flat mirrors and curved mirrors.

MIRROR AB Angle of Incidence Angle of Reflection Normal Line =

C F Normal Tangent Incidence Reflection

Types of Reflection Specular Reflection - images seen on smooth surfaces (e.g. plane mirrors) Diffuse Reflection - diffuse light coming from a rough surface (cannot see a reflection of yourself)

Locating the Image for Plane Mirrors 1.Draw the image the same distance behind the mirror as the object is in front. 2.Draw a connector line from each object to each image. 3.If the connector line passes through the mirror, the image will be seen.

A C D E B A E D B C Mirror Images These lines are pointed to the only images that will be seen from each of the original locations (A-E) NOTE: No images will be seen from E

Concave Mirrors

Light from Infinite Distance C F Focuses at the focal point

Two Rules for Locating the Image for Concave Mirrors Any incident ray traveling parallel to the principal axis on the way to the mirror will pass through the focal point upon reflection

C F

Two Rules for Concave Mirrors Any incident ray passing through the focal point on the way to the mirror will travel parallel to the principal axis upon reflection Any incident ray traveling parallel to the principal axis on the way to the mirror will pass through the focal point upon reflection

C F

C F

C F

C F Virtual Image

Mirror Equations

C F

Mirror Equation: d o > C f = 2 cm, C = 4 cm, h o = 2 cm, d o = 5cm, d i = ? 1/f = 1/d o + 1/d i 1/2 = 1/5 + 1/d i 1/d i = 1/2 - 1/5 = 0.5 – 0.2 = 0.3 d i = 3.33 cm M = h i /h o = -d i /d o  (-h o x d i )/ d o = h i h i = (-2 x 3.3)/5 h i = -1.3 cm M = - d i / d o = -0.66

C F

C F

Mirror Equation: C >d o >f f = 2 cm, C = 4 cm, h o = 2 cm, d o = 3 cm, d i = ? 1/f = 1/d o + 1/d i 1/2 = 1/3 + 1/d i 1/d i = 1/2 - 1/3 = 0.5 – = d i = 6.0 cm M = h i /h o = -d i /d o  (-h o x d i )/ d o = h i h i = (-2 x 6)/3 h i = -4.0 M = - d i / d o = -2.0

C F

C F

Mirror Equation: d o = f f = 2 cm, C = 4 cm, h o = 2 cm, d o = 2 cm, d i = ? 1/f = 1/d o + 1/d i 1/2 = 1/2 + 1/d i 1/d i = 1/2 - 1/2 = 0.5 – 0.5 = 0 d i =  no image

C F

C F Virtual Image

Mirror Equation: d o < f f = 2 cm, C = 4 cm, h o = 2 cm, d o = 1 cm, d i = ? 1/f = 1/d o + 1/d i 1/2 = 1/1 + 1/d i 1/d i = 1/2 - 1/1 = 0.5 – 1.0 = -0.5 d i = -2.0 cm M = h i /h o = -d i /d o  (-h o x d i )/ d o = h i h i = (-2 x -2)/1 h i = +4.0 M = - d i / d o = 2.0

C F Virtual Image

Real vs. Virtual Image real imageWhen a real image is formed, it still appears to an observer as though light is diverging from the real image location –only in the case of a real image, light is actually passing through the image location virtual imageLight does not actually pass through the virtual image location –it only appears to an observer as though the light was emanating from the virtual image location

C F Real Image C F Virtual Image

C F Will an image ever focus at a single point with a convex mirror? Therefore, the images you see are virtual!

Refraction Refraction is the bending of light when it passes from one transparent medium to another This bending is caused by differences in the speed of light in the media

NormalLine More Dense Less Dense

WATER AIRNormal Line #1 Slow Fast Light Beam AIR

NormalLine More Dense Less Dense

WATER AIRNormal Line #1 Slow Fast Light Beam Fast AIR Normal Line #2

Refraction Examples Light slows down when it goes from air into water and bends toward the normal. An Analogy: A car slows down when it goes from pavement onto gravel and turns toward the normal. An Illusion : Fish in the water appear closer and nearer the surface.

Refraction WATER AIR Observer True Fish False Fish

Atmospheric Refraction Our atmosphere can bend light and create distorted images called mirages.

Index of Refraction Equations n = c/v = speed of light in a vacuumn = c/v = speed of light in a vacuum speed of light in medium speed of light in medium

Index of Refraction Problem What is the speed of light in water, which has an index of refraction of 1.33? n = c/v  v = c/n v = (2.998 x 10 8 m/s) / 1.33 V = 2.25 x 10 8 m/s

Index of Refraction Equations n = c/v = speed of light in a vacuum speed of light in medium n = sin i/sin rn = sin i/sin r

Index of Refraction Problem A ray of light enters a piece of crown glass at an angle of 57 o and is refracted to 31 o inside the glass. What is the index of refraction? n = sin i/sin r = sin 57 o / sin 31 o = 1.63

Index of Refraction Equations n = c/v = speed of light in a vacuum speed of light in medium n = sin i/sin r sin  A / sin  B = n B / n Asin  A / sin  B = n B / n A

Index of Refraction Problem A diamond (n = 2.42) is in water (n = 1.33) and a ray of light shines on it making an angle of incidence of 55 o. What is the angle of refraction inside the diamond? sin  A / sin  B = n B / n A sin 55 o / sin  B = 2.42/1.33  B = 27 o

Lenses Work due to change of direction of light due to refraction Diverging Lens A lens that is thinner in the middle than at the edges, causing parallel light rays to diverge. Converging Lens A lens that is thicker in the middle and refracts parallel light rays passing through to a focus.

C F C F Diverging or Concave Lens

C F C F Converging or Convex Lens

C F C F

C F C F

C F C F

Lens Equation: d o > C f = 2 cm, C = 4 cm, h o = 2 cm, d o = 5cm, d i = ? 1/f = 1/d o + 1/d i 1/2 = 1/5 + 1/d i 1/d i = 1/2 - 1/5 = 0.5 – 0.2 = 0.3 d i = 3.33 cm M = h i /h o = -d i /d o  (-h o x d i )/ d o = h i h i = (-2 x 3.3)/5 h i = -1.3 cm

C F C F Converging or Convex Lens

C F C F

C F C F

C F C F

C F C F

Mirror Equation: d o < f f = 2 cm, C = 4 cm, h o = 2 cm, d o = 0.5 cm, d i = ? 1/f = 1/d o + 1/d i 1/2 = 1/1 + 1/d i 1/d i = 1/2 - 1/0.5 = 0.5 – 2.0 = -1.5 d i = -.67 cm M = h i /h o = -d i /d o  (-h o x d i )/ d o = h i h i = (-2 x -.67)/0.5 h i = +8/3 = M = - d i / d o = +1.33

C F C F Converging or Convex Lens

Total Internal Reflection... …is the total reflection of light traveling in a medium when it strikes a surface of a less dense medium sin θ = n 2 /n 1

Air – Water Interface sin θ = n 2 /n 1 Air n air = 1 and Water n 2 = 1.33 sin θ = 1.00/1.33 = sin θ = θ = sin θ = 49 o

WATER AIR LightSource Critical Angle TotalInternalReflection Refraction 49

What Is Fiber Optics ? Transmitting communications signals over hair thin strands of glass or plasticTransmitting communications signals over hair thin strands of glass or plastic Not a "new" technologyNot a "new" technology Concept a century oldConcept a century old Used commercially for last 25 yearsUsed commercially for last 25 years Fiber Optics Association

Fiber Has More Capacity This single fiber can carry more communications than the giant copper cable! This single fiber can carry more communications than the giant copper cable! Fiber Optics Association

Fiber Optic Communications Applications includeApplications include –Telephones –Internet –LANs - local area networks –CATV - for video, voice and Internet connections –Utilities - management of power grid –Security - closed-circuit TV and intrusion sensors –Military - everywhere! Fiber Optics Association

Why Use Fiber Optics? EconomicsEconomics SpeedSpeed DistanceDistance Weight/sizeWeight/size Freedom from interferenceFreedom from interference Electrical isolationElectrical isolation SecuritySecurity Fiber Optics Association

Fiber Optic Applications Fiber is already used in:Fiber is already used in: –> 90% of all long distance telephony –> 50% of all local telephony –Most CATV networks –Most LAN (computer network) backbones –Many video surveillance links Fiber Optics Association

Fiber Optic Applications Fiber is the least expensive, most reliable method for high speed and/or long distance communicationsFiber is the least expensive, most reliable method for high speed and/or long distance communications While we already transmit signals at Gigabits per second speeds, we have only started to utilize the potential bandwidth of fiberWhile we already transmit signals at Gigabits per second speeds, we have only started to utilize the potential bandwidth of fiber Fiber Optics Association

Fiber Technology Fiber Optics Association

Fiber Technology Fiber Optics Association

Fiber Optic Data Links Fiber Optics Association

Light Used In Fiber Optics Fiber optic systems transmit using infrared light, invisible to the human eye, because it goes further in the optical fiber at those wavelengths. Fiber Optics Association

Wavelength-Division Multiplexing Fiber Optics Association

Fiber Optic Cable Protects the fibers wherever they are installedProtects the fibers wherever they are installed May have 1 to over 1000 fibersMay have 1 to over 1000 fibers Fiber Optics Association

Fiber Optic Connectors Terminates the fibersTerminates the fibers Connects to other fibers or transmission equipmentConnects to other fibers or transmission equipment

Medical Fiberscopes Electromagnetic radiation has played a role in medicine for decades Particularly interesting is the ability to gain information without invasive procedures Using fiber optics in medicine has opened up new uses for lasers

Fiberscope Construction Fiberscopes were the first use of optical fibers in medicine Invented in 1957 The objective lens forms a real image on the end of the bundle of fiber optics This image is carried to the other end of the bundle where an eyepiece is used to magnify the image

Endoscopes An endoscope is a fiberscope with additional channels besides those for illuminating and viewing fibers The uses of these extra channels may include –Introducing or withdrawing fluids –Vacuum suction –Scalpels for cutter or lasers for surgical applications

Air – Diamond Interface sin θ = n 2 /n 1 Air n air = 1 and Diamond n 2 = 2.42 sin θ = 1.00/2.42 = sin θ = θ = sin θ = 24 o

Dispersion... …is the separation of white light into pure colors (ROY G. BIV). The index of refraction is higher for higher frequencies, so violet is bent the most Dispersion Examples: Prisms Diffraction Gratings CD’s Raindrops

Rainbows Raindrops refract, reflect and disperse sunlight. Rainbows will always appear opposite of the Sun in the sky. You cannot run from or run to a rainbow!

Polarization Unpolarized light has random directions of the electric field vector Light can be polarized by: –(1) passing light though a polarizer material or –(2) reflecting light off of a solid or liquid surface. For example, reflected light from a lake is mostly horizontally polarized.

Polarization of Light Waves Each atom produces a wave with its own orientation of All directions of the electric field vector are equally possible and lie in a plane perpendicular to the direction of propagation This is an unpolarized wave General Physics

Polarization of Light, cont A wave is said to be linearly polarized if the resultant electric field vibrates in the same direction at all times at a particular point Polarization can be obtained from an unpolarized beam by –Selective absorption –Reflection –Scattering General Physics

E. H. Land discovered a material that polarizes light through selective absorption –He called the material Polaroid –The molecules readily absorb light whose electric field vector is parallel to their lengths and transmit light whose electric field vector is perpendicular to their lengths Polarization by Selective Absorption General Physics

The most common technique for polarizing light Uses a material that transmits waves whose electric field vectors in the plane are parallel to a certain direction and absorbs waves whose electric field vectors are perpendicular to that direction Selective Absorption, cont General Physics

Polarization by Reflection When an unpolarized light beam is reflected from a surface, the reflected light is –Completely polarized –Partially polarized –Unpolarized It depends on the angle of incidence –If the angle is 0° or 90°, the reflected beam is unpolarized –For angles between this, there is some degree of polarization –For one particular angle, the beam is completely polarized General Physics

Polarization by Reflection, cont The angle of incidence for which the reflected beam is completely polarized is called the polarizing angle, θ p Brewster’s Law relates the polarizing angle to the index of refraction for the material θ p may also be called Brewster’s Angle General Physics