light and geometric optics

Light and Geometric Optics

Some info on Light

• Visible light is part of the electromagnetic spectrum of waves.

• Electromagnetic waves are transverse and have a constant speed in space (speed of light)

• Light exhibits all the characteristic and properties of all periodic waves– Reflection, refraction, interference, and

diffraction– Also exhibits the Doppler Effect

The Electromagnetic Spectrum

• The electromagnetic spectrum is the complete spectrum or continuum of light including radio waves, infrared, visible light, ultraviolet light, X-rays and gamma rays

• An electromagnetic wave consists of electric and magnetic fields which vibrates thus making waves.

• All electromagnetic waves are produced by accelerating charged particles.

Wavelength, Frequency and Energy

• Since all electromagnetic waves travel at the same speed, wavelength and frequency have an indirect relationship.

• EM waves with a short wavelength will have a high frequency and high energy.

• EM waves with a long wavelength will have a low frequency and low energy.

The Electromagnetic Spectrum EM waves differ in their frequency and in the sources used to produce them

RADIO WAVES• Have the longest wavelengths and lowest frequencies

of all the electromagnetic waves.• A radio picks up radio waves through an antenna and

converts it to sound waves.• Each radio station in an area broadcasts at a different

frequency. # on radio dial tells frequency.• MRI (MAGNETIC RESONACE IMAGING)– Uses Short wave radio waves with a magnet to create an

image• DO NOT CONFUSE EM RADIO WAVES WITH

LONGITUDINAL SOUND WAVES.

Bands of Radio/TV/Microwaves

Microwaves• Shorter than radio, longer than

light and infrared• Wavelength 1 x 10 - 4 m to 1 x 10-

1 m • Used in radar, air – traffic

control, long distance telephone communication, medicine and to cook food.

• The frequency of microwaves in a microwave oven is the same as the natural rotational frequency of water molecules. Resonance is what causes food to get cooked

Infrared waves

• Invisible electromagnetic waves that are detected as heat

• Can be detected with special devices such as night goggles

• Used in heat lamps, and infrared photography.

• Higher energy than microwaves but lower than visible light

Visible Light

• The portion of the electromagnetic spectrum that human eyes can detect

• Approximately one percent of the EM spectrum• The wavelengths that the human eye can detect are

approximately 400 to 700 nanometers.• ROY G BIV (red, orange, yellow, green, blue, indigo,

violet)• Red is the lowest frequency and violet is the highest

frequency

Ultraviolet waves

• The part of sunlight that causes sunburn• Higher energy than light waves• Can cause skin cancer and blindness in

humans• Used in tanning beds and sterilizing

equipment

X-Rays

• High energy waves• First discovered by

Roentgen • Used in medicine, industry

and astronomy• Can cause cancer

GAMMA RAYS• Shorter wavelength and higher frequency than X-

rays• Emitted by radioactive nuclei.• Carry the greatest amount of energy and

penetrate the most.• Used in radiation treatment to kill cancer cells.• Can be very harmful if not used correctly.

Speed of Light• In 1675 Dutch astronomer, Olaus Roemer, used

his observations of Jupiter and the eclipse of one of its moons to measure the speed of light.

• In the nineteenth century the American physicist Albert Michaelson used sunlight and rotating mirrors to obtain more precise measurements.

• Due to Einstein’s theory of relativity , the speed of light has been set to 2.99792458x108 m/s (approximately 186,000 mi/s) in a vacuum.

Visible LightWavelengths of Light in a Vacuum

Violet 4.0 – 4.2 x 10-7mBlue 4.2 – 4.9 x 10-7mGreen 4.9 – 5.7 x 10-7mYellow 5.7 – 5.9 x 10-7mOrange 5.9 – 6.5 x 10-7mRed 6.5 – 7.0 x 10-7m

Monochromatic light consists of light of a single wavelength (or frequency).White light is all the colors of visible light mixed togetherBlack is the complete absence of visible light.

Review Videos

• http://www.montereyinstitute.org/courses/AP%20Physics%20B%20II/course%20files/multimedia/lesson47/lessonp.html

• Electromagnetic Spectrum

REFLECTION

http://www.montereyinstitute.org/courses/AP%20Physics%20B%20II/course%20files/multimedia/lesson48/lessonp.html

Law of Reflection• “the angle that the incident ray makes with the

normal to the surface is equal to the angle that the reflected ray makes with the normal to the surface.”

• θ1 = θ2 or θi = θr

Types of reflection• Polished surfaces such as plane mirrors produce regular or

specular reflection.• An irregular surface such as a windblown water surface causes a

diffuse reflection.

http://www.stmary.ws/highschool/physics/home/animations3/waves/reflectionInt.swf

• Remember ... reflection always makes a V• What is the smallest mirror

you need to see your whole body?

• 1/2 your height

Plane Mirrors

• When an object is viewed in a plane mirror, the image that is formed is erect (upright), left-right reversed, and the same size as the object.

• Incident ray, normal line, and reflected rays are all in the same plane

• The distance the object is in front of the mirror equals the distance the image is behind the mirror

Angle of Reflection? (with respect to normal)

60 degrees (Angle from normal)

REFRACTION

http://www.montereyinstitute.org/courses/AP%20Physics%20B%20II/course%20files/multimedia/lesson48/lessonp.html

Refraction

• Refraction – the bending of light that occurs when a light wave passes through a boundary between two media

• Any device with a lens refracts light• http://www.stmary.ws/highschool/physics/ho

me/animations3/waves/refraction2.swf

Speed and Refraction

• The faster the medium, the larger the angle a light ray makes with the normal

(light always crosses over normal)

Velocity of Air > Velocity of Water

If Light goes from fast medium to slow, light bends toward the normal

If θin = 0 degrees,no refraction

(Light must come in at an angle to be refracted)

REFRACTION IS ALWAYS ACCOMPANIED BY REFLECTION

Find the missing ray inthe ray diagram

The reflected ray at theglass/air boundary is missing.

Which ray diagram is correct?

Choice 2 (Angle ray leaves air = Angle ray enters air)

35 degrees

At what angle will the ray reenter the air?

A sunset is an optical illusion

Refraction allows you to see the sun even after it has set.

Bill Nye video

Index of Refraction (n) – a comparison of speed of light in a substance to its speed in a vacuum

n = c/v• c = speed of light in a vacuum

(3.00 x 108 m/s) v = speed of light in a medium• Ex. If a substance has an index of refraction of

2.00 it means light is twice as fast in a vacuum than it is in that medium

• http://www.stmary.ws/highschool/physics/home/review/waves/refractionHarrison.htm

Which substance slows down light the most when light enters from air? Diamond – has the

highest index of refraction

Which slows down the least?

Water – lowest n

Ex 1) Speed of light in alcohol?

• Alcohol: n = 1.36 (Reference Table)

n = c/v

• 1.36 = (3.00 x 108 m/s)/V • V = 2.21 x 108 m/s

c= nv n and v are inversely related

• The more light is slowed down or sped up, the more it changes direction.

Snell's Law

n1sinθ1 = n2sinθ2 • 1 – incident medium• 2 – refractive medium

Ex: Calculate θ2

Air/Lucite

n1sinθ1 = n2sinθ2

1.00 sin53 = (1.50) sinθ2

.798 = 1.50sinθ2 θ2 = 320

n and v and λ

n1v1 = n2v2

1 - incident medium 2 – refractive mediumWhen a light changes media, its wavelength

changes NOT its frequencyn2λ2 = n1λ1

When light refracts it BENDS, CHANGES SPEED and WAVELENGTH

Total internal reflection

• http://video.mit.edu/watch/mit-physics-demo-refraction-a-total-internal-reflection-12044/

sinθc = 1/n1

• Critical Angle θc– angle of incidence for which the angle of refraction equals 900 when light travels inside one medium that borders on air or a vacuum

• Deriving Critical Angle Equation n1sinθ1 = n2 sinθ2

Substitute θc, θ2 = 90, n2 = 1 n1sinθc = 1sin90

n1sinθc = 1 sinθc = 1/n1

Ex) Find θc for Lucite

sin θc = 1/n1

From reference table, n1 = 1.50 sinθc = 1/1.50θc = 41.8

Relationships with θ1 & θc

• When θ1 > θc Total Internal Reflection(Outside Medium Must Be Faster)

• When θ1 = θc θ2 = 900

• When θ1 < θc Refraction

Total internal reflection

θ1 > θc

When θ1 = θc θ2 = 900

Which diagram shows:

a) Total Internal Reflection?Choice 2 (Outside Medium Must be Fast)

b) Refraction? Choice 3

c) Impossible? Choice 1 (Light always crosses over normal)

Dispersion

• Dispersion – separation of polychromatic light into its component wavelengths (colors)

Each Color hasA Different Wavelength

Red – fastest (slowed least), bent least

Violet – slowest (slowed most), bent most

• http://www.stmary.ws/highschool/physics/home/notes/waves/Dispersion.htm

• (youtube video)

DIFFRACTION

http://www.montereyinstitute.org/courses/AP%20Physics%20B%20II/course%20files/multimedia/lesson46/lessonp.html

Diffraction – the spreading out of a wave into the region behind an obstacle

• Amount of Diffraction depends on Wavelength & Size of Slit.

• Diffraction increaseswhen size of the slit approaches wavelength size.

• http://www.stmary.ws/highschool/physics/home/notes/waves/WaveBehavior/diffractionSlitD.swf