Announcements

Today’s material WILL NOT be covered on Exam 3!Material for Exam 3:

Chapters 8, 9, 10

Reminder: Special Homework #7 is due tomorrow.(download and print if you need it)

Friday, November 8, is the last day to withdraw.

Exam 3 is one week from tomorrow. I will need to know by Wednesday of any students who have special needs different than for exam 2.

Today’s agenda:Introduction to Light.You must develop a general understanding of what light is and how it behaves.

Reflection and Refraction (Snell’s Law).You must be able to determine the path of light rays using the laws of reflection and refraction.

Total Internal Reflection and Fiber Optics.You must be able to determine the conditions under which total internal reflection occurs, and apply total internal reflection to fiber optic and similar materials.

Dispersion.You must understand that the index of refraction of a material is wavelength-dependent.

Light

How many physicists does it take to change a light bulb?

Normally, “light” refers to the type of electromagnetic wave that stimulates the retina of our eyes.Light acts like a wave except when it acts like particles.

Light—Waves or Particles?*

http://www.nearingzero.net (quantum007.jpg)

*Light is both! Take Physics 107 for enlightenment!

Light is a type of electromagnetic wave and travels with the speed c = 2.9979x108 m/s in a vacuum. (Just use 3x108!)

The Speed of Light

How many physicists does it take to change a light bulb? Eleven. One to do it and ten to co-author the paper.

Visible light is a small part of the electromagnetic spectrum.

News Flash!

Light slows down when it passes froma vacuum into matter!

Details beginning on slide 16!

Although light is actually an electromagnetic wave, it generally travels in straight lines (like particles do!).We can describe many properties of light by assuming that it travels in straight-line paths in the form of rays. A ray is a straight line along which light is propagated. In other contexts, the definition of ray might be extended to include bent or curved lines.

Geometric Optics

http://www.lab-initio.com (nz341.jpg)

A light ray is an infinitely thin beam of light. Of course, there really isn’t such a thing, but the concept helps us visualize properties of light.

http://www.lab-initio.com (nz342.jpg)

thankfully, there really isn’t such a thing

Light rays from some external source strike an object and reflect off it in all directions.We only see those light rays that reflect in the direction of our eyes.

If you can see something, it must be a source of light!Zillions* of rays are simultaneously reflected in all directions from any point of an object. Later, when we study mirrors and lenses, we won’t try do draw them all! Just enough representative ones to understand what the light is doing.

*one zillion = 10a big number

Today’s agenda:Introduction to Light.You must develop a general understanding of what light is and how it behaves.

Reflection and Refraction (Snell’s Law).You must be able to determine the path of light rays using the laws of reflection and refraction.

Total Internal Reflection and Fiber Optics.You must be able to determine the conditions under which total internal reflection occurs, and apply total internal reflection to fiber optic and similar materials.

Dispersion.You must understand that the index of refraction of a material is wavelength-dependent.

Light striking a surface may be reflected, transmitted, or absorbed. Reflected light leaves the surface at the same angle it was incident on the surface:

i r =

i r

Reflection

Real Important Note: the angles are measured relative to the surface normal.

Possible homework hint: the sum of the angles in a 4-sided polygon is 360.

Reflection from a smooth surface is specular (mirror- like). Reflection from a rough surface is diffuse (not mirror-like).

http://acept.la.asu.edu/PiN/rdg/reflection/reflection.shtml

http://www.mic-d.com/java/specular/

Light travels in a straight line except when it is reflected or when it moves from one medium to another.

Refraction—the “bending” of light rays when light moves from one medium to a different one—takes place because light travels with different speeds in different media.

Refraction

http://id.mind.net/~zona/mstm/physics/light/rayOptics/refraction/refraction1.html

The speed of light in a vacuum is c = 3x108 m/s. The index of refraction of a material is defined by

cn = ,vwhere c is the speed of light in a vacuum and v is the speed of light in the material.

The speed and wavelength of light change when it passes from one medium to another, but not the frequency, so

.n

cv = and = n n

If you study light in advanced classes, you’ll find it is more complex than this.

Because light never travels faster than c, n 1.* For water, n = 1.33 and for glass, n 1.5. Indices of refraction for several materials are listed in your text.

cv = n83×10 m/sv = 2.42

8v = 1.24×10 m/s

Example: calculate the speed of light in diamond (n = 2.42).

*Actually, not true but don’t worry about it unless you take advanced courses in optics.

Because n 1, we see this:

If n < 1, we would see this:

Thanks to Dr. Xiaodong Yang for the images.

When light moves from one medium into another, some is reflected at the boundary, and some is transmitted. “Toy”The transmitted light is refracted (“bent”). a is the angle of incidence, and b is the angle of refraction.

Snell’s Law

air (na)water (nb)

a

b

nb>na

incident ray

refracted ray

air (nb)water (na)

b

a

na>nb

incident ray

refracted ray

a a b bn sin θ = n sin θ

air (na)water (nb)

a

b

nb>na

incident ray

refracted ray

Light passing from air (n 1) into water (n 1.33).

Light “bends” towards the normal to the surface as it slows down in water.

a b(1) sin θ = (1.33) sin θ

a bθ > θ

a a b bn sin θ = n sin θ

air (nb)water (na)

b

a

na>nb

incident ray

refracted ray

Light passing from water (n 1.33) into air (n 1).

Light “bends” away from the normal to the surface as it speeds up in air.

a b(1.33) sin θ = (1) sin θ

a bθ < θ

a a b bn sin θ = n sin θ

Snell’s law, also called the law of refraction, gives the relationship between angles and indices of refraction:

a a b bn sin θ = n sin θ .

a

b

water (nb)

air (na)

a

b

water (nb)

air (na)

is the angle the ray makes with the normal!

You are free to choose which is “a” and which is “b.”

Interactive applet: Fun with Snell’s Law.

Same applet as slide 20, try glass into water.

Today’s agenda:Introduction to Light.You must develop a general understanding of what light is and how it behaves.

Reflection and Refraction (Snell’s Law).You must be able to determine the path of light rays using the laws of reflection and refraction.

Total Internal Reflection and Fiber Optics.You must be able to determine the conditions under which total internal reflection occurs, and apply total internal reflection to fiber optic and similar materials.

Dispersion.You must understand that the index of refraction of a material is wavelength-dependent.

Suppose n2<n1. The largest possible value of sin(2) is 1 (when 2 = 90). The largest possible value of sin(1) is

1 1 2 2n sin θ = n sin θ

21 2

1

nsin θ = sin θ n

21,max

1

nsin θ = .n

This value of is called the critical angle, C. For any angle of incidence larger than C, all of the light incident at an interface is reflected, and none is transmitted.

Total Internal Reflection; Fiber Optics

For 1 larger than this, Snell’s Law cannot be satisfied!

1 < C 1 close to C

1 > C

1 1

1

n2

n1>n2

Ray incident normal to surface is not “bent.”

Ray incident normal to surface is not “bent.” Some is reflected,Ray incident normal to surface is not “bent.” Some is reflected, some is transmitted.

n2

n1>n2

Increasing angle of incidence…

n2

n1>n2

Increasing angle of incidence…more…

n2

n1>n2

Increasing angle of incidence…more…critical angle reached…Increasing angle of incidence…more…critical angle reached… some of incident energy is reflected, some is “transmitted along the boundary layer.

n2

n1>n2

Light incident at any angle beyond C is totally internally reflected.

application: fiber optics

http://laser.physics.sunysb.edu/~wise/wise187/janfeb2001/reports/andrea/report.html

i

f

ni=1 (air)nf>1

Light is incident at an angle i on a transparent fiber.

The light refracts at an angle f.

i i ffn sin θ = n sin θ

i ffsin θ = n sin θ

Example: determine the incident angle i for which light strikes the inner surface of a fiber optic cable at the critical angle.

i

f90-f

ni=1 (air)nf>1

Light strikes the fiber wall an an angle of90-f normal to the surface.

At the critical angle, instead of exiting the fiber, the refracted light travels along the fiber-air boundary. In this case, 90-f is the critical angle.

ff f c an sin 90-θ =n sin θ =n sin 90 1

ff

1sin 90-θ = n

90

Solve the above for f and use to solve for i.

i ffsin θ = n sin θ

i

f90-f

ni=1 (air)nf>1

Numerical example: what is critical angle if nf=1.4?

f1sin 90-θ = 1.4

90

f90-θ =45.58 fθ =44.41

i f1 sin θ = 1.4 sin θ = 1.4 sin 44.41 =0.980iθ =78.5

This is a very large angle of incidence! If you want the incident light to be nearly parallel to the fiber axis, you must surround the fiber with a coating with noutside<ncoating<nfiber.

application: swimming underwater

If you are looking up from underwater, if your angle of sight (relative to the normal to the surface) is too large, you see an underwater reflection instead of what’s above the water.

application: perfect mirrors

(used in binoculars)

application: diamonds

Today’s agenda:Introduction to Light.You must develop a general understanding of what light is and how it behaves.

Reflection and Refraction (Snell’s Law).You must be able to determine the path of light rays using the laws of reflection and refraction.

Total Internal Reflection and Fiber Optics.You must be able to determine the conditions under which total internal reflection occurs, and apply total internal reflection to fiber optic and similar materials.

Dispersion.You must understand that the index of refraction of a material is wavelength-dependent.

Dispersion

We’ve treated the index of refraction of a material as if it had a single value for all wavelengths of light.

In fact, the index of refraction is generally wavelength- (or color-) dependent.

Picture from the Exploratorium (http://www.exploratorium.edu/).