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Unit Ten:Reflection and

Refraction of Light

John Elberfeld

JElberfeld@itt-tech.edu

518 872 2082

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Schedule

• Unit 1 – Measurements and Problem Solving• Unit 2 – Kinematics• Unit 3 – Motion in Two Dimensions• Unit 4 – Force and Motion• Unit 5 – Work and Energy• Unit 6 – Linear Momentum and Collisions• Unit 7 – Solids and Fluids• Unit 8 – Temperature and Kinetic Theory• Unit 9 – Sound• Unit 10 – Reflection and Refraction of Light• Unit 11 – Final

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Chapter 10 Objectives• Define and explain the concept of wave fronts and

rays.• Explain the law of reflection and distinguish

between regular (specular) and irregular (diffuse) reflections.

• Explain refraction in terms of Snell's law and the index of refraction, and give examples of refractive phenomena.

• Describe total internal reflection and understand fiber optic applications.

• Explain dispersion and some of its effects.

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Reading Assignment

• Read and study College Physics, by Wilson and Buffa, Chapter 10, pages 322 to 340

• Week 11 is your scheduled final exam on Chapters 1-10– The final is 40 multiple choice questions

worth 2.5 points each– Questions include problems, definitions

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Written Assignments

• Do the homework on the handout.– You can work on other problems that build up to the

required problems– Answers to odd-numbered problems and Follow-up

Exercises are in the back of your book– The Student Study Guide explains some solutions in

detail

• You must show all your work, and carry through the units in all calculations

• Use the proper number of significant figures and, when reasonable, scientific notation

6 Part 1 : Reflection and Refraction of Light

• We now turn from our study of sound waves to the study of another type of wave, light.

• In contrast to sound, in which the waves consist of pressure or density differences in matter and require matter to propagate, light waves consist of alternating electrical and magnetic fields and need no matter to propagate.

• Therefore, light waves are called electromagnetic radiations.

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Nature of Light

• Light can be thought of as both a wave (electro-magnetic wave) and a particle (photon).

• In this section, we treat light strictly as a wave with a frequency (f), period (t), wavelength (λ) and velocity (v)

• V = f λ f = 1 / t

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Electromagnetic Waves

• Light forms a portion of the electromagnetic spectrum, which includes gamma waves with wavelengths shorter than the size of an atomic nucleus up to radio waves with wavelengths longer than a mile.

• In this week’s lessons, we will be concerned with the visible and near-visible wavelengths of the electromagnetic spectrum.

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Light

• Sound is a mechanical wave and requires a medium to propagate.

• Light, on the other hand, is a wave that propagates in a vacuum and consists of time-varying electric and magnetic fields.

• Light consists of the visible (and near-visible) parts of the electromagnetic spectrum.

10 Wavelengths

• The electromagnetic spectrum includes waves such as radio waves, radar waves, microwaves, and infrared radiation. – These waves have wavelengths longer than visible light.

• It also includes ultraviolet rays, X-rays, and gamma rays that have wavelengths shorter than visible light.

• Infrared waves with wavelengths just longer than visible and ultraviolet waves with wavelengths just shorter are also commonly referred to as "light" even though they are not visible to human eyes.

• Electromagnetic radiation - particularly with wavelengths shorter than visible light - is frequently said to be made up of particles with zero mass, called photons.

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Speed of Light

• All parts of the electromagnetic spectrum travel at 3.00 x 108 m/s in a vacuum and at a lower speed in material.– 299 792 458 m/s is more accurate but

totally unnecessary in your calculations

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Geometric Optics

• When studying light, you can ignore the wave properties of diffraction and interference, and assume that light travels in a straight line.

• You can also ignore the atomic interactions between light and transparent materials, and assume that light travels through transparent materials at reduced speeds.

• These simplifications form the basis of geometric optics, in which phenomena such as the reflection and refraction of light are explained in terms of wave fronts and rays.

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Wave Fronts

• In geometric optics, you assume that light emanates from a point source in a spherical wave.

• A wave front is an imaginary line showing the location of the crest of the wave.

• To be more precise, it can also be referred to as the line that represents all parts of a wave that are in phase, since you can choose the trough of the wave or any point in between the crest and the trough.

• The distance between the wave fronts is known as the wavelength.

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• If we drop a stone into still water, a circular wavefront travels away from the origin of the disturbance.

• Waves and wave fronts in water are shown below:

• • In the case of light, wave fronts are spherical in

shape.

Wave Nature of Light

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Wave Fronts

• A wave front is defined by adjacent points on a wave that are in phase, such as those along wave crest and troughs

• Near a point source, the waves are circular in three dimensions

• Very far from the point source, the wave fronts are approximately linear or planar.

• A line perpendicular to a wave front in the direction of the wave’s propagation is called a ray.

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Rays

• A ray is an imaginary line emanating from a point source, which indicates the direction that the light wave is moving in.

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Reflection

• Reflection of light is an optical phenomenon of enormous importance.

• If light were not reflected to our eyes by objects around us, we wouldn’t see the objects at all.

• Reflection involves the absorption and reemission of light by means of complex electromagnetic vibrations in the atoms of the reflecting medium.

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Rays

• Thankfully, however, the phenomenon is easily described by using rays.

• A light ray arriving at and hitting a surface is called the incident ray.

• After hitting the surface, the departing ray is called the reflected ray.

Incident ray R eflected ray

N orm al

M irror

i r

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Law of Reflection

• The law of reflection is defined as the principle that when a ray of light, radar pulse, or the like, is reflected from a smooth surface the angle of reflection is equal to the angle of incidence, and the incident ray, the reflected ray, and the normal to the surface at the point of incidence all lie in the same plane.

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Θi = Θr

• This law applies to a single ray that strikes any surface and reflects from it.

• The angle of incidence Θi is the angle an incident ray makes with a line that is perpendicular (normal) to the surface.

• The angle of reflection Θr is the angle the reflected ray makes with the perpendicular (normal) of the surface.

• As shown on the graphic, the angle of incidence is equal to the angle of reflection:

• Θi = Θr

Incident ray R eflected ray

N orm al

M irror

i r

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Specular versus Diffuse Reflection

• While the law of reflection always holds, the reflected angle is not always the same over large areas of a surface because light does not keep a constant angle over large areas. – This results in regular and irregular reflection.

• When light rays are reflected from a smooth surface, the reflected rays will be parallel, the reflection is said to be regular or specular – you can see an image in the reflections.

• When light rays reflect from a rough surface, the reflected rays will not be parallel and no image will be visible in the reflection because the reflected light travels in various directions. – Note that the law of reflection still applies locally to

individual rays and small areas of the surface.

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Specular Reflection

23 Refraction

• Reflection and refraction both occur whenever a wave strikes the boundary between two media.

• We have already discussed reflection; refraction refers to the change in the direction of a wave at a boundary where the wave passes from one transparent medium into another.

• Refraction deals with the portion of the incident beam that penetrates into the second medium from the first.

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Examples

• The graphic on the screen shows how an incident beam of light strikes a prism and forms two beams at the surface: a refracted beam and a reflected beam.

• When the refracted beam strikes the inner surface of the prism, it produces two more beams, a refracted beam, which is parallel to the original incident beam, and a reflected beam.

• The reflected beam strikes the upper inner surface and produces two more beams, a refracted beam parallel to the first reflected beam and a reflected beam that is not visible in the picture.

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Refraction

ΘiΘrefl

Θrefr

Air

Water

Normal

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Spearing a Fish

Θi Θrefl

Θrefr

Air

Water

Normal

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Refraction

• The speed of light in transparent media is generally less for denser media and is always less than it’s speed in vacuum - 3x108 m/s. - for air, only slightly less. – It is something of a misnomer to call the glass

a medium through which light travels, since light travels in a vacuum and does not require a medium.

• The index of refraction (n) of a medium is the speed of light in a vacuum (c) divided by the speed of light in the medium (v):

• n = c / v

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Index of Refraction

• The index of refraction of various materials is shown in the table on the screen.

• The wavelength is specified because the index of refraction of a material varies with the wavelength.

• n = c/v

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Practice

• Light from a laser with a wavelength of 632.8 nm travels from air into water.

• What are the speed and wavelength of the laser light in water?

• Note: Frequency and period do NOT change

• nwater=1.33 from table

• n = c / v v = f λ f = 1 / t

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Calculations

• nwater = c / vwater

• 1.33 = (3x108m/s) / vwater

• vwater = (3x108m/s) / 1.33 = 2.26x108m/s

• vair = f λair

• 3x108m/s = f x 632.8 nm (n = 10-9)• f = (3x108m/s) / 632.8 x 10-9 m = 4.74x1014 Hz

• vwater = f λwater

• 2.26x108m/s = 4.74x1014 Hz λwater

• λwater = 2.26x108m/s / 4.74x1014 Hz = 4.77x10-7m

• λwater = 477nm

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Refraction

• The diagram shows that when a beam of light or a single ray is incident upon a boundary between two media, the beam or ray changes direction.

• This can be understood from the principle that every point on a wave front can act as a source of new circular waves called wavelets.

• Since the wave front strikes the boundary at an angle, the wavelets enter the new medium at different times and one end of the wave front slows down before the other.

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Snell’s Law

• As a result, the wave changes direction.

• This change in direction can be calculated from Snell's law:

• sinΘ1 / sinΘ2 = n2/n1

• The angles are, as usual, measured from the normal.

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Snell’s Law

• A line of six marching soldiers represents a wave front.

• When the soldiers reach the muddy patch their speed decreases.

• Thus, the distance between the lines of marching soldiers decreases. (v = f λ)

• Since one end slows down before the other, the direction of the marching soldiers changes.

• The angle of change is determined by the ratio of the speed in one medium to the speed in the other medium.

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More Illustrations

• This diagram shows the bending of light as it passes from a less dense medium (like air) into a more dense medium (like glass.)

• n2>n1

• Θ2<Θ1

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Another Illustration

• This diagram shows the bending of light as it passes from a more dense medium (like glass) into a less dense medium (like air.)

• n2<n1

• Θ2>Θ1

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Practice

• A ray of light is incident on a piece of crown glass at an angle of 37.0º relative to the normal. (Going from air into the glass)

• n =1.52 from table

• What is the angle of refraction?

37º

??º

Air

glass

Normal

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Calculations

• sinΘ1 / sinΘ2 = n2/n1

• sin(37º) / sin Θ2 = 1.52 / 1

• sin Θ2 = sin(37º) / 1.52 = .396

• Θ2 = sin-1 (.396)

• Θ2 = 23.3º

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Examples

• The following diagrams show three examples of light rays emitted from three objects under water: a fish, a coin, and a chopstick.

• The fish, chopstick, and coin reflect the light in the room, thus enabling you to see them.

• However, you cannot see the actual location of these objects under water.

• This is because when the light rays hit the surface of the water, they travel from a medium of high refractive index (water) to a medium of low refractive index (air).

• This causes the rays to bend away from the perpendicular direction (normal) and the objects appear to be placed at locations different from their actual ones.

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Fish Example

• The light is refracted, and because we tend to think of light as traveling in straight lines, the fish is NOT where we think it is

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Chopstick

• The chopstick appears bent at the air-water boundary. If the cup is transparent, we see another type of refraction.

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Coin

• Because of refraction, the coin appears to be closer than it actually is

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Practice

• Bob and Bill are 3m from a mirror. Bob shines a flashlight and the reflection hits Bill in the face. The angle the light makes is 67º from the normal to the mirror.

• How far away from Bob is Bill?

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Diagrams

67º

3m

67º

3m

x

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Trig

• TanΘ = x / 3m• x = 3m tan(67º)• x = 7.07 m• The distance is

twice that or 14.14 m

67º

3m

7.07m

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Mirrors

• Two plane mirrors, M1 and M2, are placed together as illustrated in the figure.

• If the angle between the mirrors is 75º and the angle of incidence of a light ray incident on M1 is 35º, what is the angle of reflection from M2?

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Diagrams

• 180º in each triangle

• 90º in a right angle

• 40º final angle ofreflection

35º35º

55º

75º

50º

40º

40º

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Problem

• Find nplastic

50º

35º

Air

Plastic

Normal

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Calculations

• sinΘ1 / sinΘ2 = n2/n1

• sin(50º) / sin(35º) = n2 / 1

• n2 = sin(50º) / sin(35º)

• n2 = 1.33

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Internal Reflection

• When you are under water, have you ever looked up toward the surface and tried to see what was going on above the water surface?

• The view may have surprised you! • It looks like the water surface is a huge rippling

mirror with a hole letting you see through directly above you.

• Now that we have studied the basic laws of geometric optics, let us look at some more concepts related to light.

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Total Internal Reflection

• When an incident light ray strikes a boundary between two media, two rays are created: a refracted ray and a reflected ray.

• Consider the case when an incident ray goes from a medium with a higher refractive index (n1) to a medium with a lower refractive index (n2); that is n1 is greater than n2.

• In this case, the refracted angle is farther from the normal than the incident ray.

Θ1

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Critical Angle

• As the incident angle increases, the angle of refraction increases as well.

• However, there is a limit. • When the angle of incidence becomes larger

than a certain angle known as the critical angle, the refracted angle would be 90º.

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Total Internal Reflection

• At the critical angle and all greater incident angles, no refracted ray is created; all of the light is completely reflected, where the angle of incidence is large, no refracted ray is created.

• This phenomenon is called total internal reflection and can be illustrated as follows:

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Critical Angle

• You can use Snell’s law to calculate the critical angle (Θ1), which is the minimum angle at which total internal reflection occurs by assuming that the angle of refraction is 90º (Θ2). So, you have:

• sinΘ1 / sinΘ2 = n2/n1

• sinΘcritical / sin(90º) = n2/n1 , but sin(90º) = 1

• sinΘcritical = n2/n1

• Θcritical = sin-1 (n2/n1)

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Must go from high n1 to low n2

• When n1 ‹ n2, then n2/n1>1, so we cannot calculate the arcsine of n2/n1.

• Therefore, in the case when n1‹ n2, we cannot get an angle of refraction of 90º.

• Critical angle and so total internal reflection exists only when light is trying to go from a high index of refraction to a low index of refraction

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Calculations

• n1 sin(Θ1) = n2 sin(Θ2)

• sin(Θ2) = 1.33 sin(Θ1) / 1

• sin(Θ2) = 1.33 sin(Θ1)

• WhenΘ1 = 30º , Θ2 = 41.7º

Θ1 = 45º , Θ2 = 70.1º

Θ1 = 48.75º , Θ2 = 90º - Critical Angle!

Θ1 = 55º , Θ2 = “Error” All light is reflected

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Practice

• What is the critical angle for a ray of light traveling in water and incident on a water-air boundary?

Θi

Θrefr

Air n2 = 1

Water

n1 = 1.33

Normal

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Calculations

• sinΘ1 / sinΘ2 = n2/n1

• sinΘcritical / sin(90º) = n2/n1 , but sin(90º) = 1

• sinΘcritical = n2/n1 = 1 / 1.33

• Θcritical = sin-1 (.752)

• Θcritical = 48.8º

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Practical Applications

• The graphic depicts an example of total internal reflection, internal reflection in a prism.

• Because the critical angle of glass is less than 45º, prisms with 45º and 90º angles can be used to reflect light through 180º .

• Internal reflection of light by prisms in binoculars makes this instrument much shorter than a telescope.

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Fiber Optics

• Total internal reflection also forms the basis of fiber optics, a fascinating technology in which transparent fibers are used to transmit light.

• Multiple total internal reflections make it possible to “pipe” light along a transparent rod even if the rod is curved.

• Using optical fibers, light can be transmitted over long distances, even in circuitous routes.

• This happens because the light rays reflect internally along the optical path, as shown in the graphic.

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Light Pipe

• Examples of light pipes

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Fiber Optics

• Because visible light has a much higher frequency than radio waves, much more information can be transmitted per second using light, compared to traditional radio waves.

• Fiber optics makes using light for information transmission practical since fiber optic connections do not have to follow a straight line.

• Television cable companies use optical fibers, as do telephone companies and high speed computer networks.

• In medicine, optical fibers enable doctors to view areas of the body that can only be reached with a flexible narrow tube.

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Color

• Color is a sensation that light produces in the brain after stimulating the optic nerve.

• The wavelength of the visible part of the electromagnetic spectrum ranges from 700 nm to 400 nm.

• Light with a wavelength of 700 nm produces the sensation of red and light with a wavelength of 400 nm produces the sensation of violet.

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More on Colors

• White is the sensation produced by a combination of all the wavelengths of light.

• Black is the sensation produced when there is no light striking the retina.

• A human being can distinguish up to 10 million colors.

• All these colors are the result of mixing red, orange, yellow, green, blue, indigo, and violet light (Roy. G. Biv).

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Dispersion

• The light produced by incandescent light bulbs is white, as is the light from the sun and fluorescent light bulbs.

• You can use a prism to separate the different wavelengths of white light, as shown in the graphic.

• A prism disperses white light because the refractive index depends on the wavelength of light being refracted.

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Prisms

• The index of refraction for red light is less than that of blue light.

• Therefore, red light bends less than blue light when refracted.

• The triangular shape of the prism causes a ray of light to undergo two refractions, which augment the separation of the wavelengths.

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Dispersive Medium

• In a dispersive medium, the index of refraction varies slightly with wave length. Red light, longest in wave length, has the smallest index of refraction and is refracted least

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Practical

• The index of refraction of a particular transparent material is 1.4503 for the red end of the visible spectrum and 1.4698 for the blue end.

• If white light is incident upon the material at an angle of 45º with the perpendicular, what is the angular separation between the red and blue light upon refraction?

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Calculations

• sinΘ1 / sinΘ2 = n2/n1

• sin45º / sin(ΘRed) = 1.4503 / 1

• sin(ΘRed) = sin45º / 1.4503

• ΘRed= 29.18º

• sin45º / sin(ΘViolet) = 1.4698 / 1

• sin(Θviolet) = sin45º / 1.4698

• Θviolet= 28.76º

• Angle difference = .42º

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Rainbows

• A rainbow is created by the refraction, dispersion, and internal reflection of the sunlight that enters water droplets

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Practice

• A beam of light with red and blue components of wavelengths 670 nm and 425 nm, respectively, strikes a slab of fused quartz at an incident angle of 50º. (Going from air into quartz)

• On refraction, the different components are separated by an angle of 1.3 X 10-3 rad.

• If the index of refraction of the red light is 1.50, what is the index of refraction of the blue light?

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Calculations

• sinΘ1 / sinΘ2 = n2/n1

• sin50º / sin(ΘRed) = 1.50 / 1

• sin(ΘRed) = sin50º / 1.5

• ΘRed= 30.710º

• Difference is 1.3 X 10-3 rad. (180º / Π)• Difference = .745º so angle = 29.965º

– Angle is smaller for longer wave lengths going from air into quartz

• sin50º / sin(29.965º) = n2blue / 1

• n2blue = 1.5337

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Summary

• What are wave fronts and rays?

• What is the difference between specular and diffuse reflections?

• What is Snell’s law? What are examples of the refraction of light?

• How does fiber optics work?