Unit 6, Chapter 18

CPO ScienceFoundations of Physics

Unit 6: Light and Optics

18.1 The Electromagnetic Spectrum

18.2 Interference, Diffraction, and

Polarization

18.3 Special Relativity

Chapter 18 Wave Properties of Light

Chapter 18 Objectives

1. Calculate the frequency or wavelength of light when given one of the two.

2. Describe the relationship between frequency, energy, color, and wavelength.

3. Identify at least three different waves of the electromagnetic spectrum and an application of each.

4. Interpret the interference pattern from a diffraction grating.

5. Use the concept of polarization to explain what happens as light passes through two polarizers.

6. Describe at least two implications of special relativity with regards to energy, time, mass, or distance.

Chapter 18 Vocabulary Terms x-ray spectrum microwave index of refraction electromagnetic

wave spectrometer gamma ray radio wave transmission axis diffraction grating special relativity

polarization polarizer rest energy destructive interference ultraviolet time dilation infrared speed of light constructive

interference visible light wavelength

18.1 The Electromagnetic Spectrum

Key Question:

What is the electromagnetic spectrum?

*Students read Section 18.1 BEFORE Investigation 18.1

The energy field created by electricity and magnetism can oscillate and it supports waves that move.

These waves are called electromagnetic waves.

18.1 The Electromagnetic Spectrum

Electromagnetic waves have both an electric part and a magnetic part and the two parts exchange energy back and forth.

A 3-D view of an electromagnetic wave shows the electric and magnetic portions.

18.1 The Electromagnetic Spectrum

The wavelength and amplitude of the waves are labeled λ and A, respectively.

The higher the frequency of the light, the higher the energy of the wave.

Since color is related to energy, there is also a direct relation between color, frequency, and wavelength.

18.1 The Electromagnetic Spectrum

18.1 Speed of Light

c = f

Wavelength (m)

Frequency (Hz)

Speed of light3 x 108 m/sec

18.1 Calculate wavelength

Calculate the wavelength in air of blue-green light that has a frequency of 600 × 1012 Hz.

18.1 Waves of the electromagnetic spectrum

Visible light is a small part of the energy range of electromagnetic waves. The whole range is called the electromagnetic spectrum and visible light

is in the middle of it.

18.1 Waves of the electromagnetic spectrum

— Radio waves are on the low-frequency end of the spectrum.

— Microwaves range in length from approximately 30 cm (about 12 inches) to about 1 mm.

— The infrared (or IR) region of the electromagnetic spectrum lies between microwaves and visible light.

18.1 Waves of the electromagnetic spectrum

— Ultraviolet radiation has a range of wavelengths from 400 down to about 10 nm.

— X-rays are high-frequency waves that have great penetrating power and are used extensively in medical and manufacturing applications.

— Gamma rays are generated in nuclear reactions.

18.2 Interference, Diffraction, and Polarization

Key Question:

What are some ways light behaves like a wave?

*Students read Section 18.2 AFTER Investigation 18.2

18.2 Interference, Diffraction, and Polarization

In 1807, Thomas Young (1773-1829) did the most convincing experiment demonstrating that light is a wave.

A beam of light fell on a pair of parallel, very thin slits in a piece of metal.

After passing through the slits, the light fell on a screen.

A pattern of alternating bright and dark bands formed is called an interference pattern.

18.2 Diffraction gratings A diffraction grating is a precise array of tiny

engraved lines, each of which allows light through. The spectrum produced is a mixture of many

different wavelengths of light.

18.2 How a Diffraction Grating WorksWhen you look at a

diffracted light you see:

— the light straight ahead as if the grating were transparent.

— a "central bright spot".

— the interference of all other light waves from many different grooves produces a scattered pattern called a spectrum.

18.2 Spectrometer

A spectrometer is a device that measures the wavelength of light.

A diffraction grating can be used to make a spectrometer because the wavelength of the light at the first-order bright spot can be expressed in a mathematical relationship.

18.2 Grating Formula

= d sindw

L

distance between grating lines (m)

distance between

screen and glasses

wavelengthof light (nm)

d= 13,500 lines/inch = ? lines/m

distance between

2 first order bright spots

18.2 Polarization Polarization is another wave property of light. The fact that light shows polarization tells us

that light is a transverse wave.

18.2 Polarization

Polarization is a vector.

A wave with polarization at 45 degrees can be represented as the sum of two waves.

Each of the component waves has smaller amplitude.

18.2 Polarization A polarizer is a material that selectively absorbs light

depending on polarization. A polarizer re-emits a fraction of incident light polarized

at an angle to the transmission axis.

18.2 Applications of Polarizers Polarizing sunglasses are

used to reduce the glare of reflected light

The LCD (liquid crystal diode) screen on a laptop computer uses polarized light to make pictures.

18.3 Special Relativity

Key Question:

What are some of the implications of special relativity?

*Students read Section 18.3 AFTER Investigation 18.3

18.3 Special Relativity

The theory of special relativity describes what happens to matter, energy, time, and space at speeds close to the speed of light.

18.3 Special Relativity

These effects are observed in physics labs:1. Time moves more slowly for an object in

motion than it does for objects that are not in motion. This is called time dilation.

2. As objects move faster, their mass increases.

3. The definition of the word “simultaneous” changes.

4. Space itself gets smaller for an observer moving near the speed of light.

18.3 Speed of light paradox

The theory of special relativity comes from thinking about light.

A ball thrown from a moving train approaches you at the speed of the ball relative to the train plus the speed of the train relative to you.

The speed of light appears the same to all observers independent of their relative motion.

18.3 Speed of light paradox If the person on the train were to shine a

flashlight toward you, you would expect the light to approach you faster.

The light should come toward you at 3 × 108 m/sec plus the speed of the train.

But Michelson and Morley found experimentally that the light comes toward you at a speed of 3 × 108 m/sec no matter how fast the train approaches you!

18.3 Consequences of time dilation In the early 1970s an experiment was

performed by synchronizing two precise atomic clocks.

One was put on a plane and flown around the world, the other was left on the ground.

When the flying clock returned home, the clocks were compared.

The clock on the plane measured less time than the clock on the ground. The difference agreed precisely with special relativity.

18.3 Einstein's formula

mc2

Mass (kg)

Energy (J) speed of light

3.0 x108 m/sec

This equation tells us that matter and energy are really two forms of the same thing.

18.3 The equivalence of energy and mass

If a particle of matter is as rest, it has a total amount of energy equal to its rest energy.

If work is done to a particle by applying force, the energy of the particle increases.

At speeds that are far from the speed of light, all the work done increases the kinetic energy of the particle.

It would take an infinite amount of work to accelerate a particle to the speed of light, because at the speed of light the mass of a particle also becomes infinite.

18.3 The equivalence of energy and mass

Einstein’s was able to deduce the equivalent of mass and energy by thinking about the momentum of two particles moving near the speed of light.

Since the speed of light must be the same for all observers regardless of their relative motion and energy and momentum must be conserved, as the speed of an object gets near the speed of light, the increase in mass must come from energy.

18.3 Calculate equivalents

A nuclear reactor converts 0.7% of the mass of uranium to energy.

If the reactor used 100 kg of uranium in a year, how much energy is released?

One gallon of gasoline releases 1.3 × 108 joules.

How many gallons of gasoline does it take to release the same energy as the uranium?

18.3 Simultaneity

The two lightning strikes are simultaneous to the observer at rest, but the observer moving with the train sees the lightning strike the front of the train first.

Application: Holography