Physics 1230: Light and ColorIvan I. Smalyukh, Instructor

Office: Gamow Tower, F-521Email:

ivan.smalyukh@colorado.edu

Phone: 303-492-7277

Lectures: Tuesdays & Thursdays,

3:30 PM - 4:45 PMOffice hours:

Mondays & Fridays, 3:30 PM – 4:30 PM

TA: Jhih-An Yang jhihan.yang@colorado.edu 

Class # 6

2

Physics 1230: Light and Color

Lecture 6:

Reading: Finish Chapter 2

HW due today;

New HW assigned (due in 2 weeks);

3

Chapter 2 – Geometrical Optics

1. Shadows2. Reflection3. Refraction4. Dispersion

We are

here

Geometrical optics is the theory of RAYS (straight lines) and how they reflect and refract (bend). Lots of similarity to GEOMETRY of lines and triangles.

Main Topics

4

Chapter 2 – Geometrical Optics

1. Shadows2. Reflection

a) Specular or diffuseb) Equal angle rulec) Mirror images, ray tracing

3. Refraction4. Dispersion

a. Point source or diffuse source b. Umbra and penumbra c. How tall is my shadow? d. Pinhole camera

We are

here

What can happen to incoming light

Transmitted

Reflected (including scattering)

absorbed

Or any partial combination of these things

Glass

Silver, water

Black pavement

Specular or diffuse?

Diffuse reflection(paper)

Specular reflection(mirror)

Diffuse transmission(wax paper)

6

Equal angle rule (specular reflection)

7

ri

Normal

Mirror

i = angle of incidence r = angle of reflection

i = r is specular reflection

A normal is a line perpendicular to the surface.

Incident RayReflected Ray

Plasma frequency of silverPlasma frequency of silver

Metals with mobile electrons can cancel out the light field in forward direction - only reflection

• Metals reflect all waves below a certain frequency

• This plasma frequency varies from metal to metal

• Silver reflects light waves at all visible frequencies

• Gold and copper have a yellow-brownish color because they reflect greens, yellows and reds but not blues or violets

Plasma frequency of goldPlasma frequency of gold

Plasma frequency of copperPlasma frequency of copper

What is a mirror?• Since silver is such a good reflector a coating of silver on

glass - a good (common) mirror

• If the silver coating is thin enough the mirror can be made to transmit 50% of the light and to reflect the other 50%

– This is called a half-silvered mirror

– A half-silvered mirror used with proper lighting can show objects on one side or the other of the mirror

Law of specular reflection of a ray from a mirror

Mirror

This angle = this angle

The normal to the mirror is an imaginaryline drawn perpendicular to it from where the incident ray hits the mirror

Normal

• The ray from the light bulb is diffusely reflected off chin. We show one of the many rays coming off his chin hitting a mirror.

• The incident ray undergoes specular reflection off the mirror

– Note the reflected ray

• Draw the normal to the mirror– The angle of incidence = the angle

of reflection

How is an image produced in a mirror?Part 1: Ray-tracing

• To find out how Bob "sees" Alex by looking in the mirror we trace rays which obey the law of reflection

Mirror

AlexBob looks atAlex's image

• We interpret all rays coming into our eye as traveling from a fictitious image in a straight line to our eye even if they are reflected rays!

The psychology of image interpretation

Mirror

Alex Bob looks atAlex's image

• Example: To find the location of his hair in the virtual image we extend any reflected ray from hair backwards

The meaning of a virtual image

• If we trace rays for every ray from every part of Alex which reflects in the mirror– we get a virtual image of the

real Alex behind the mirror.

Virtual image of Alexis behind mirror

Mirror

Alex

– Alex's virtual image is the same size as the real Alex

Bob looks atAlex's image

Bob sees Alex's imagein the same place when

he moves his head

Let’s look at specular reflection

Ray reflection practice

retroreflector

Retroreflectors

• Bike reflectors• Roadside reflectors• Measuring distance to moon?

Half-silvered mirrorIf the silver coating is thin enough the mirror can be made to transmit 50% of the light and to reflect the other 50%

This is called a half-silvered mirror

A half-silvered mirror used with proper lighting can show objects on one side or the other of the mirror

Glass is like a 4% silvered mirror

Image in a mirror1. If a point on the object is distance X in front of the

mirror, the same point in the image appears to be distance X in back of the mirror, or Xobject = Ximage.

2. The image point is on the normal (extended) from the object to the mirror.

18Xobject Ximage

normalextended

Mirror

Ray tracing: Draw the image, then the rays

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Xobject Ximage

Mirror

First: draw rays from image to eyes

Viewed from the side.

Ray tracing: Draw the image, then the rays

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Xobject Ximage

Mirror

First: draw rays from image to eyes Second: draw rays from mirror to object

i = r happens automatically using this method. Demo on board

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Xobject Ximage

Mirror

The top ray goes to the top of the bottle.It is right side up.

i = r happens automatically using this method.

Right side up image?

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Xobject

Ximage

Mirror(to do this drawing,

the mirror must be extended)

The top ray goes to the bottom of the bottle.It is upside down.

i = r happens automatically using this method.

Right side up image?

Extension

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Mirror(to do this drawing,

the mirror must be extended)

i = r happens automatically using this method.

Bottle on its sideViewed from the side.

For simple (flat) mirrors the image location is therefore predictable without knowing where the

observer's eye is and without ray-tracing

Mirror

Mirror Mirror

Mirror

Periscope

25

mirror

mirror

The image of the bottle in the lower mirror is:A)InvertedB)Not invertedC)Something else

Original OBJECT

Periscope?

26

extension

Original OBJECT

The first IMAGE

Periscope?

27

extension

The second IMAGE

Periscope?

28

The image of the bottle in the lower mirror is:A)InvertedB)Not invertedC)Something else

Mirror

Alex• Question: Where are

the images of Alex in the 2 mirrors?

a) At A onlyb) At B onlyc) At A and B onlyd) At C onlye) At A, B and C

Multiple mirrors - a virtual image can act as a real object and have its own virtual image

Mirror

A C

B

The virtual image at A acts as an object to produce the virtual image of C. It acts as an intermediate image. More precisely it is the red rays which reflect as green rays.

30

Is the writing reversed?

AR

(Two mirrors, viewed from above)

A) YESB) NO

31

Is the writing reversed?

AR

ЯA

32

Is the writing reversed?

AR

ЯA

AR

extension

33

Is the writing reversed?

AR

ЯA

AR

A) YESB) NO

3434

Lec. 6: Ch. 2 - Geometrical Optics

1. Shadows2. Reflection3. Refraction4. Dispersion

We are

here

35

Refraction

1. Index of refraction: n = c / v2. Ray in water is closer to the normal 3. Total internal reflection 4. Mirages

Reflection of waves occurs where the medium of propagation changes abruptly• Part of the wave can be

transmitted into the second medium while part is reflected back– You can hear someone from

outside the pool when you are underwater because sound waves are transmitted from the air through the water (withdifferent speed in each).

• When light waves are incident on a glass slab they are mostly transmitted but partly reflected (about 4%)!

Glass slab

Is the speed of light in the glass slab the same as in the free space???

No.

How can reflection require that the speed of the wave changes? We thought the speed of light was always

c = 3 x 108 m/s!

• The speed of an electromagnetic (EM) wave is constant (for every wavelength) in empty space!

• The speed of light is slower than c in glass, water and other transparent media

– (Einstein showed that light can never travel faster than c)

• The speed of light in a medium is v = c/n, where n is a number larger than one called the index of refraction

• n = 1.5 for glass• n = 1.3 for water• n = 1.5 for vegetable oil

• Light is reflected and transmitted at a boundary because

– When a light wave travels in a medium the electric field of the light jiggles the electrons in the medium.

– This produces new electric fields which can cancel or add to the original light wave both in the forward and backward directions

• These are the transmitted and reflected light waves

Material Refractive Index

Air 1.0008

Water 1.330

Glass 1.5

Diamond 2.417

Ruby 1.760

Oil 1.5

Refractive indices of different materials

Can we see a glass rod immersed into the oil with the same refractive index?

• A. Yes• B. No

Demo

Got to here on Thursday 6/10/2010

Refraction is the bending of a ray after it enters a medium where its speed is different

• A ray going from a fast medium to a slow medium bends towards the normal to the surface of the medium

• A ray going from a slow medium to a fast medium bends away from the normal to the surface of the medium

• The speed of light in a medium is v = c/n, where n is a number larger than one called the index of refraction andc = 3 x 108 m/s• n = 1.3 for glass• n = 1.5 for water

• Hence, a ray going into a medium with a higher index of refraction bends towards the normal and a ray going into a medium with a lower index of refraction bends away from the normal

Air (fast medium)

Glass orwater(slow)

Normal

Glass orwater(slow)

Normal Air (fast medium)

nair < nwater

1.0008 < 1.33

How about light going into a medium with exactly the same index of refraction?

Ray-bending together with our psychological straight-ray interpretation determine the location of images underwater

• The precise amount of bending is determined by the law of refraction (sometimes called Snell's law):

• ni sini = nt sint

• Here,i = angle between incident ray and normal,

• and t = angle between transmitted ray and normal

• ni and nt are the indices of refraction in the medium containing the incident ray and in the medium containing the transmitted ray

• Fig 2.49 Fisherman and fish

incident ray

transmitted ray

normal

image of fish for someone out of water

fish

• In order to observe the fish from outside the water a transmitted ray must enter your eye. • You will think it comes from a point obtained by tracing it backwards,• Extend any 2 of the many many transmitted rays from the fish backwards to find the image of the fish (where they intersect). • The location of that image will be the same for any observer outside of the water.

What we see and how different it can be from what it seems to be

• The woman will see the underwater part of body being

a) Smaller than it really is;b) Much larger than it really is;c) Of natural size;

• The woman will see the underwater part of body being

a) Smaller than it really is;b) Much larger than it really is;c) Of natural size;

What we see and how different it can be from what it seems to be

What we see and how different it can be from what it seems to be

• The boy will see the underwater part of body being

a) Smaller than it really is;b) Much larger than it really is;c) Of natural size;

Total internal reflection is an extreme case of a ray bending away from the normal as it goes from a higher to a lower index of

refraction medium (from a slower to a faster medium)

Glass orwater(slow)

NormalAir (fast medium)

Just below the critical angle for total internal reflection there is a reflected and a transmitted (refracted) ray

Glass orwater(slow)

Normal

Just above the critical angle for total internal reflection there is a reflected ray but no transmitted (refracted) ray

CriticalCriticalangleangle

For the glass-air interface

Total internal reflection

• Show that the internal reflection is a consequence of the Snell’s law

• The precise amount of bending is determined by the law of refraction (sometimes called Snell's law):

• ni sini = nt sint

• Here,i = angle between incident ray and normal,

• and t = angle between transmitted ray and normal

• ni and nt are the indices of refraction in the medium containing the incident ray and in the medium containing the transmitted ray

What we see and how different it can be from what it seems to be

• If the critical angle condition is satisfied, will the boy see the part of body above water:

a) yes;b) No.

• Extra Credit: Refractive index of water is 1.33;

What is the critical angle for the case of air-water interface?