OpticsApril 6-7 2015

Do NowDraw a reflected sound wave, labeling the angle of incidence and the angle of reflection.

How do these angles compare?

Draw the wave fronts of a light wave passing through three different media.

The first medium be medium speedThe second should be faster speedThe should be slow speed

Your picture should show realistic angles of refraction and changes in wave length.

Index of Refraction (n)The index of refraction (n) is a value that describes the relative speed of light in a particular medium

cn =

v

n = index of refraction, has no unitsc = speed of light in a vacuum, 3.00 X 108 m/sv = speed of light in a particular medium

MEDIUM n v (m/s)

Vacuumair

Exactly 11.000293

300,000,000

water 1.33 225,564,000

glass 1.52 197,368,000

diamond 2.42 123,967,000

Since c is the fastest speed of light, n is always greater than 1.

The larger the index the _______________ the speed in that medium .

The greater the difference in n, the ______________________ the angle of refraction.

slower

greater

Index of Refraction (n)Draw a light ray passing from air to water (n=1.3) , and another passing from air to glass (n=1.5). In each case, the incident ray approaches the new medium from a 45o angle. Use Snell’s law to determine the refracted angle.

45o 45o

32o

28o

Waterglass

qc

q2=900 n2

n1

21 nn

Normally, when a wave reaches a new medium, some of the energy is reflected and some is refracted. However, when passing from a fast medium to a slow medium, the angle of refraction is greater than the angle of incidence. At a certain point, the angle of refraction becomes 90o and the light no longer is transmitted to the other medium; instead it is completely reflected back.Critical angle: qc - angle of incidence for which angle of refraction is 900

Total Internal Reflection(n)

A fiber optic cable is a bunch (thousandths) of very fine (less than the diameter of a hair) glass strands clad together made of material with high index of refraction. Critical angle is very small almost everything is totally internally reflected. The light is guided through the cable by successive internal reflections with almost no loss (a little escapes).

Even if the light pipe is bent into a complicated shape (tied into knots), light is transmitted practically undiminished to the other end.

Click me

Application: Fiber Optics

Why use fiber optics? can carry more info with less distortion over long distances One single optical fiber can transmit several TV programs

and tens of thousands of telephone conversations, all at the same time.

takes 300 lbs of copper to carry same info as 1 lb of fiber opticsDownside: expensive

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Application: Fiber Optics

Is the straw really broken?

refracted ray

real straw

incident rayperceived straw

JFF: Optical Illusions Caused by Refraction

mirage, not a puddle!

Where is the fish? Deeper than you think!

Apparent location of the fish

JFF: Optical Illusions Caused by Refraction

DispersionEven though all colors of the visible spectrum travel with the same speed in vacuum, the speed of the colors of the visible spectrum varies when they pass through a transparent medium like glass and water. That is, the refractive index of glass is different for different colors.

Different colors (frequencies) are refracted by different amounts! True for different pitches, as well!

1. When white sunlight enters droplet its component colors are refracted at different angles (dispersion)

Rainbows are caused by dispersion of sunlight by water droplets

3. Second refraction from droplet into air – more dispersion

4. Each droplet produces a complete spectrum, but only one color from each drop is seen by observer – you have your own personal rainbow and I have MINE!

observer is between the Sun and a rain shower.

A smile in the sky

2. These colored lights then undergo total internal reflection.

The spreading of a wave into a region behind an obstruction is called diffraction.

When waves pass through a small opening, or pass the edge of a barrier, they always spread out to some extent into the region that is not directly in the path of the waves.

Diffraction

Water waves diffracting through two different sized openings..

diffraction effects are small when slit is much larger than the incident λ.

The waves are diffracted more through the narrower opening, when wavelength is larger than the opening.

DiffractionDiffraction effects are greater when the wavelength is big relative to the size of the obstruction.

Small obstruction, large wavelength = noticeable diffraction

DiffractionDiffraction explains why we can hear but not see around corners and other obstructions...

Wavelengths of audible sound: 16.7 mm – 16.7mWavelengths of visible light: 400 nm – 700 nm

Audible sound wavelengths are around the same size, or even bigger, than most obstructions (open doorway, side of a building, etc.), so they diffract around the obstructions.

Visible EM wavelengths are much much smaller than these obstructions, and so they reflect backwards, rather than diffracting around the obstruction.

DiffractionTurn and Talk:

Why do dolphins, bats, SONAR, and doctors use ultrasound for localizing objects, instead of lower frequency sounds?

High frequency = short wavelength Little diffraction!

Instead of diffracting around obstructions, ultrasound will reflect back towards the source, allowing the animal / instrument to identify the location of objects in the environment.