Chapter 35

I am Watching YOU!!

Human RetinaSharp Spot: Fovea

Blind Spot: Optic Nerve

Human VisionAn optical Tuning Fork

Optical Antennae: Rods & ConesRods: 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 BulbFull Spectrum of LightAll frequencies excited!

Light Waves

E = Emax cos (kx – ωt) B = Bmax cos (kx – ωt)

…∝= =

0 0

1EcB

Speed of Light in a vacuum:186,000 miles per second300,000 kilometers per second3 x 10^8 m/s

/v c n=

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.

R.O.Y. G. B.I.Vlong wavelengths short wavelengths

spectrum

Radiation of Visible Sunlight

Additive Primary ColorsRed, Green, Blue

RGB Color Theory

Additive Complementary ColorsYellow, Cyan, Magenta

The color you have to add to get white light.

Red + Green = YellowBlue + Green = CyanRed + Blue = Magenta

Red + Blue + Green = White

White light – yellow light = ??

White light – red light = ??

FYI: Mixing Colored PigmentsSubtractive 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: MirrorsFree electrons in opaque reflective surfaces

can vibrate, absorb & re-emit at any frequency.

TransparencySelective 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 opaqueto longer wavelengths: Short get in, longer are trapped!

Why is the Sky Blue?

How are Rainbows Formed?

Light Ray ApproximatinGeometric 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

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.

Light Rays: Ignore Diffraction and Interference of waves!

Reflection & Refraction

i rθ θ= 1 1 2 2sin sinn nθ θ=

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 θ1 with the normal

• The reflected ray makes an angle of θ1’ 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

i rθ θ=

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 you2. Longer than you3. Shorter than you4. 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. n3 < n1.B. n3 = n1.C. n3 > n1. D. We can’t compare n1 to n3 without knowing n2.

A light ray travels from medium 1 to medium 3 as shown. For these media,

A. n3 < n1.B. n3 = n1.C. n3 > n1.D. We can’t compare n1 to n3 without knowing n2.

Refraction:Bending Light into Focus

Refraction: Bending of Light Transmitted through Materials

Light Bends because it Slows Down.

Atoms are Optical Tuning ForksLight slows down as it travels through

glass because it takes time to be absorbed and re-emitted.

Light Slows Down in MaterialsLight 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

cnv

=

Vacuum: 1Water: 1.33Glass: 1.46Diamond: 2.4

1n ≥

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 cnspeed of light in a medium v

≡ =

in vacuumin a mediumn

λ λnλ λ

⎛ ⎞= ⎜ ⎟

⎝ ⎠

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

1 1 2 2sin sinn nθ θ=Angles are always measured from the normal.

Snell’s Law – Example

• Light is refracted into a crown glass slab

• θ1 = 30.0o, θ2 = ?• n1 = 1.00 and n2 = 1.52• θ2 = sin-1(n1 / n2) sin θ1 = 19.2o

• The ray bends toward the normal, as expected

Example 35.4Emerging Beam is Parallel to

Incident Beam but offset distance d

Fig. 35-15, p. 989

You Try Problem

25°

What is the apparent depth of the diver?Assume that the horizontal distance doesn’t change.

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 n1 > n2

Total Internal Reflection

2

1

sin Cnn

θ =

2 90θ = o

1 1 2 2sin sinn nθ θ=

The Critical Angle

Fiber Optics• 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

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 ProblemA 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.

R.O.Y. G. B.I.Vlong wavelengths short wavelengths

The index of refraction depends onWAVELENGTH.

R.O.Y. G. B.I.Vlong wavelengths short wavelengths

The speed and wavelength change butthe FREQUENCY does NOT.

R.O.Y. G. B.I.Vlong wavelengths short wavelengths

FrFrequency depends on the oscillating source!

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 ProblemThe 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

Double Rainbow• 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

Huygens’s Principle Prove the Laws of Reflection & Refraction

Huygens’s PrincipleConstruction 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 Spherical Wave

• 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

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 108 m/s• first successfully determined by

Danish astronomer Ole Roemer in 1675: 2.3 x 108 m/s

• First Terrestrial Measurement by Fizeau in 1849: 2.9979 x 108 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?