Chapter 22Chapter 22Reflection and RefractionReflection and Refraction

of Lightof Light

Conceptual questions: 9,11,16,17,18 Quick quizzes: 2,3,4Problems: 21,28,49,56

Dual Nature of LightDual Nature of Light

Experiments display either the wave Experiments display either the wave nature or the particle nature of lightnature or the particle nature of light

Nature prevents testing both qualities at Nature prevents testing both qualities at the same timethe same time

““Particles” of light are called Particles” of light are called photonsphotons Each photon has a particular energyEach photon has a particular energy

E = h ƒE = h ƒ h is h is Planck’s constantPlanck’s constant

h = 6.63 x 10h = 6.63 x 10-34-34 J s J s

Geometric Optics – Using Geometric Optics – Using a Ray Approximationa Ray Approximation

Light travels in a straight-line path Light travels in a straight-line path in a homogeneous mediumin a homogeneous medium

The The ray approximationray approximation is used to is used to represent beams of lightrepresent beams of light

A A rayray of light is an imaginary line of light is an imaginary line drawn along the direction of travel drawn along the direction of travel of the light beamsof the light beams

Ray ApproximationRay Approximation

A A wave frontwave front is a is a surface passing surface passing through points of a through points of a wave that have the wave that have the same phase and same phase and amplitudeamplitude

The rays, The rays, corresponding to the corresponding to the direction of the wave direction of the wave motion, are motion, are perpendicular to the perpendicular to the wave frontswave fronts

Reflection of LightReflection of Light

A ray of light, the A ray of light, the incident rayincident ray, , travels in a mediumtravels in a medium

When it encounters a boundary When it encounters a boundary with a second medium, part of the with a second medium, part of the incident ray is incident ray is reflectedreflected back into back into the first mediumthe first medium This means it is directed backward This means it is directed backward

into the first mediuminto the first medium

Specular ReflectionSpecular Reflection

Specular Specular reflectionreflection is is reflection from a reflection from a smooth surfacesmooth surface

The reflected rays The reflected rays are parallel to are parallel to each othereach other

Diffuse ReflectionDiffuse Reflection

Diffuse reflectionDiffuse reflection is is reflection from a reflection from a rough surfacerough surface

The reflected rays The reflected rays travel in a variety travel in a variety of directionsof directions

Diffuse reflection Diffuse reflection makes the road makes the road easy to see at nighteasy to see at night

Law of Law of ReflectionReflection The The normalnormal is a line is a line

perpendicular to the perpendicular to the surfacesurface

The incident ray makes The incident ray makes an angle of an angle of θθ11 with the with the normalnormal

The reflected ray The reflected ray makes an angle of makes an angle of θθ11’’

with the normalwith the normal The angle of reflection The angle of reflection

is equal to the angle of is equal to the angle of incidenceincidence

θθ11= θ= θ11’’

Reflection of light, Reflection of light, quizquiz

Refraction of LightRefraction of Light The incident ray, The incident ray,

the reflected ray, the reflected ray, the refracted ray, the refracted ray, and the normal all and the normal all lie on the same lie on the same planeplane

The angle of The angle of refraction, refraction, θθ22, , depends on the depends on the properties of the properties of the mediummedium

1 2

2 1

sinθ v= =constant

sinθ v

v – speed of light

QUICK QUIZ 22.2

If beam 1 is the incoming beam in the figure below, which of the other four beams are reflected and which are refracted?

Refraction DetailsRefraction Details

vv11>v>v22

The angle of The angle of refraction is less refraction is less than the angle of than the angle of incidenceincidence The ray bends The ray bends

towardtoward the normal the normal

Refraction DetailsRefraction Details

vv11<v<v22

The angle of The angle of refraction is refraction is greater than the greater than the angle of incidenceangle of incidence The ray bends The ray bends

away from away from the the normalnormal

The Index of RefractionThe Index of Refraction

Refraction occurs because the Refraction occurs because the speed of light is different in the speed of light is different in the two mediatwo media

The The index of refraction, n,index of refraction, n, of a of a medium can be definedmedium can be defined

v

c

mediumainlightofspeed

vacuumainlightofspeedn

Frequency Between MediaFrequency Between Media

As light travels As light travels from one medium from one medium to another, to another, its its frequency does frequency does not changenot change Both the wave Both the wave

speed and the speed and the wavelength do wavelength do changechange

Index of Refraction Index of Refraction ExtendedExtended

f = ff = f11 = f = f22

vv11 = ƒ = ƒ λλ11 vv22 = ƒ = ƒ λλ22

The ratio of the indices of refraction of The ratio of the indices of refraction of the two media can be expressed asthe two media can be expressed as

1

2

2

1

2

1

2

1

n

n

ncnc

v

v

Snell’s Law of RefractionSnell’s Law of Refraction

nn11 sin sin θθ11 = = nn22 sin sin θθ22 θθ1 1 is the angle of is the angle of

incidenceincidence 30.0° in this 30.0° in this

diagramdiagram

θθ2 2 is the angle of is the angle of refractionrefraction

Table 22.1Table 22.1

Snell’s Snell’s law,law, illustrationillustration

A material has an index of refraction that increases continuously from top to bottom. Of the three paths shown in the figure below, which path will a light ray follow as it passes through the material?

QUICK QUIZ 22.3

As light travels from vacuum(n = 1) to a medium such as glass (n > 1), which of the following properties remains the same: (a) wavelength, (b) wave speed, or (c) frequency?

QUICK QUIZ 22.4

Problem Problem 22.2122.21

The light shown in the figure makes an angle of 20o with the normal NN’ in the linseed oil (n=1.48). Determine angles and ’.

Problem Problem 22.2822.28A cylindrical cistern, constructed below ground level, is 3.0 m in diameter and 2.0 m deep and is filled to the brim with a liquid whose index of refraction is 1.5. A small object rests on the bottom of the cistern at its center. How far from the edge of the cistern can a girl whose eyes are 1.2 m from the ground stand and still see the object?

DispersionDispersion

The dependence The dependence of the index of of the index of refraction on refraction on λ is λ is called called dispersiondispersion

Refraction in a PrismRefraction in a Prism

δδ the angle of the angle of deviationdeviation

n(n() ) Since all the colors Since all the colors

have different angles have different angles of deviation, they will of deviation, they will spread out into a spread out into a spectrumspectrum Violet deviates the Violet deviates the

mostmost Red deviates the leastRed deviates the least

Using Spectra to Identify Using Spectra to Identify GasesGases

All hot, low pressure gases emit their All hot, low pressure gases emit their own characteristic spectraown characteristic spectra

The particular wavelengths emitted The particular wavelengths emitted by a gas serve as “fingerprints” of by a gas serve as “fingerprints” of that gasthat gas

Some uses of spectral analysisSome uses of spectral analysis Identification of moleculesIdentification of molecules Identification of elements in distant starsIdentification of elements in distant stars Identification of mineralsIdentification of minerals

The RainbowThe Rainbow At the back surface the At the back surface the

light is reflected light is reflected It is refracted again as It is refracted again as

it returns to the front it returns to the front surface and moves into surface and moves into the airthe air

The rays leave the drop The rays leave the drop at various anglesat various angles The angle between the The angle between the

white light and the violet white light and the violet ray is 40°ray is 40°

The angle between the The angle between the white light and the red white light and the red ray is 42°ray is 42°

Observing the RainbowObserving the Rainbow

Double rainbowDouble rainbow

Huygen’s PrincipleHuygen’s Principle Huygen assumed that light is Huygen assumed that light is

a form of wave motion rather a form of wave motion rather than a stream of particlesthan a stream of particles

All points on a wave front All points on a wave front produce spherical secondary produce spherical secondary waves, which propagate in waves, which propagate in the forward direction with the forward direction with speeds characteristic of speeds characteristic of waves in that mediumwaves in that medium

Huygen’s Principle and the Huygen’s Principle and the Law of RefractionLaw of Refraction

In time In time Δt, ray 1 Δt, ray 1 moves from A to B moves from A to B and ray 2 moves and ray 2 moves from A’ to Cfrom A’ to C

From triangles From triangles AA’C and ACB, all AA’C and ACB, all the ratios in the the ratios in the Law of Refraction Law of Refraction can be foundcan be found nn11 sin sin θθ11 = = nn22 sin sin θθ22

Total Internal ReflectionTotal Internal Reflection

Total internal Total internal reflectionreflection can can occur when light occur when light attempts to move attempts to move from a medium from a medium with a high index with a high index of refraction to of refraction to one with a lower one with a lower index of refractionindex of refraction Ray 5 shows Ray 5 shows

internal reflectioninternal reflection

Critical AngleCritical Angle

The critical angle The critical angle is an angle of is an angle of incidence that will incidence that will result in an angle result in an angle of refraction of of refraction of 90°90°

21 2

1

sin c

nfor n n

n

Fiber OpticsFiber Optics

Conceptual questionsConceptual questions

18. If a beam of light with a given cross-section 18. If a beam of light with a given cross-section enter a new medium, the cross section of the enter a new medium, the cross section of the refracted beam is refracted beam is a) largera) largerb) smallerb) smallerc) not changedc) not changed

9. In dispersive materials, the angle of refraction 9. In dispersive materials, the angle of refraction for a light ray depends on the wavelength of light. for a light ray depends on the wavelength of light. Does the angle of reflection depend on the Does the angle of reflection depend on the wavelength?wavelength?

11. Explain why a diamond loses most of its sparkle 11. Explain why a diamond loses most of its sparkle when submerged in carbon disulfide.when submerged in carbon disulfide.

16. Explain why an oar partially in water appears to 16. Explain why an oar partially in water appears to be bent.be bent.

17. Why do astronomers looking at distant galaxies 17. Why do astronomers looking at distant galaxies talk about looking backward in time?talk about looking backward in time?

Problem 22.56Problem 22.56

A laser beam strikes one end of a slab of material, as in Figure P22.56. The index of refraction of the slab is 1.48. Determine the number of internal reflections of the beam before it emerges from the opposite end of the slab.

SolutionSolution

Problem 21-49Problem 21-49

As shown in Figure P22.49, a light ray is incident normally on one face of a 30°-60°-90° block of dense flint glass (a prism) that is immersed in water. (a) Determine the exit angle θ4 of the ray. (b) A

substance is dissolved in the water to increase the index of refraction. At what value of n2 does total

internal reflection cease at point P?

Review questionsReview questions

1. Visible light of which color bends 1. Visible light of which color bends the most when changing the most when changing mediums?mediums?

A.A. yellowyellow B.B. greengreen C.C. violetviolet D. D. redred

2. Water has an index of refraction of 1.3. Approximately how fast does light move through the water?

a. 1.0 x 108 m/s b. 2.3 x 108 m/s

c. 3.0 x 108 m/s d. 4.9 x 108 m/s

3. The sky is blue because it

a. Absorbs light at 390 nm

b. Reflects light at 390 nm

c. Absorbs light at 700 nm

d. Reflects light at 700 nm