physics 1c · 2011-11-30 · sound waves are longitudinal waves traveling through a medium. ......

Physics 1C Class Review

"All good things must come to an end.”

--Proverb

Outline

CAPE evaluations

Give an Overview of the topics

covered

Try to give some examples

Things We Have Learned 1) Simple Harmonic Motion:

For a mass on a spring, the force on the mass will

be given by:

In general, anything that exhibited simple harmonic

motion:

F F restoring constant displacement

The periods of SHM

can be:

Tspring 2m

k

Tpend 2L

g

Problem

A spring stretches 0.300m when a 0.300kg mass

is hung from it. Determine the spring constant.

Draw a force diagram for the mass when it is first hung on

the spring:

mass Fgravity, Earth on mass

Frestoring, spring on mass

Since the mass is in equilibrium:

Frestoring Fg

+y

kx = mg

k = mg/x = .300kg*9.8m/s2/.150m = 9.8kg/s2

Things We Have Learned 2) Waves:

Waves were a disturbance in a medium created by

a source.

We represent a traveling wave with a sine wave.

vwave

T fWe could relate wavelength

and frequency by:

Things We Have Learned 3) Sound:

Sound waves are longitudinal waves traveling

through a medium.

Sound waves interfere (here k, w, and A are the

same): y1+y2 = 2A cos (f/2) sin (kx - wt + f/2)

fo f s

vsound vo

vsound vs

When the source or the observer is

moving, the frequency will change:

Standing waves occur under wave

reflection such that nodes and anti-

nodes are created:

Things We Have Learned 4) Reflection and Refraction:

When light moves between two

different media, the light will be

refracted at an angle given by:

1 1

When light is reflected off of a

surface it will be reflected at an

angle given by:

Remember that all angles are

measured with respect to the normal!

n1 sin1 n2 sin2

Refraction Example

Light travels from air (n=1.0) to a glass with

n=1.3 and then to a plastic with n=1.5.

Describe the path of the ray as it changes

from one medium to the next.

Answer

Draw schematic

Consider each interface

separately

1

2

3

n = 1.0

n = 1.3

n = 1.5

First Interface Light travels from air (n=1.0) to a glass with

n=1.3. Which way will light bend? By how

much if the angle of incidence is 45?

Snell’s law :

n1 sin 1 = n2 sin 2

2 = sin-1 [(n1 /n2) sin 1]

2 = 33

1

n = 1.0

n = 1.3 2 Any reflection? What is

angle of reflection? Any

phase change?

Does wavelength change?

1'

Second Interface Input to second interface is the output from

the first. What is appropriate angle of

incidence?

2

3

n = 1.3

n = 1.5

2 = 33

Snell’s law :

n2 sin 2 = n3 sin 3

3 = sin-1 [(n2 /n3) sin 2]

3 = 28

Any reflection? What

happens?

Does wavelength change?

Thin Films Light travels from air (n=1.0) to a glass with

n=1.3 and then to a plastic with n=1.5. Do the

reflected rays interfere constructively?

1

2

1' Consider each interface

What leads to constructive

interference?

Phase shift at first

interface?

Phase shift at second

interface?

Path length difference?

2t = n’

n = 1.0

n = 1.3

n = 1.5

t

Things We Have Learned 5) Mirrors and Lenses:

Mirrors use the reflection of light

to divert the light rays.

Lenses use the refraction of

light to divert the light rays.

1

p

1

q

1

f

M h

h

q

p

Ray diagrams

may be useful:

Sign conventions

are important

Thin Lens Equation Example

An object is placed 15cm to the left of a

diverging lens that has a focal length of 10cm.

Describe what the resulting image will look

like (i.e. image

distance,

magnification...).

Answer

The coordinate system

defined.

The center of the lens

is the origin.

Object

N F

Image

Thin Lens Equation Answer

First, turn to the thin lens equation:

where the negative sign means that the

image is on the same side of the lens as the

object (i.e. the left side of the lens).

The magnification of the object will be:

1

p

1

q

1

f

Thin Lens Equation Image is: diminished (|M| = 0.40 < 1).

Upright (M = +0.40 > 0).

Virtual (q = –6.0cm < 0; same side as

object).

Located about

halfway between the

near focal point and

the lens (q = –6.0cm,

f = –10cm).

Object

N F

Image

Things We Have Learned 6) Wave Interference:

The wave nature of light leads to interference effects.

These can be caused by a path length difference or a

phase shift.

Double slit interference was due

to a path length difference.

m dsinThin film interference was due to

both:

2nt m1

2 Con. for 1

phase change

Des. for 1

phase change For m = 0, 1, 2...

Things We Have Learned 7) Electromagnetic Waves:

Electromagnetic waves are transverse waves with

electric and magnetic fields

perpendicular to the

direction of motion.

They carry energy and

momentum.

E = hf

p = E/c Polarization.

I Io cos2

Things We Have Learned 8) Quantum Physics:

Light exhibits wave-particle duality.

Experiments such as the photoelectric effect and the

Compton effect demonstrate the particle nature of

light.

Experiments like double-slit interference and Bragg’s

X-ray scattering demonstrate the wave nature of light.

En nhf

deBroglie hypothesized that all matter

also could have wave properties.

Light is also quantized into

discrete units known as photons.

h

p

h

mv

Clicker Question CR-1 • A star in the sky appears to be blue. The

temperature of this star must be:

A) higher than that of the sun.

B) lower than that of the sun

C) equal to that of the sun.

D) about that of the earth.

Things We Have Learned 9) Atomic Physics:

Emission spectral lines were always at particular

wavelengths for certain elements.

Bohr took this information and decided the atom must be

quantized (just about everything in it was).

rn n2 2

mekee2

2

i

2

f

Hn

1

n

1R

1

E tot 1

2ke

e2

n2ao

13.6 eV

n2

Quantum mechanics starts with the principal quantum

number, n, but also includes other quantum numbers (ℓ,

mℓ, ms).

Things We Have Learned 10) Nuclear Physics:

Rutherford’s thin-foil experiment demonstrated that

the nucleus is small and dense.

Stable nuclei can be categorized by the amount of

binding energy per nucleon they have.

Q m c2 minitial m final c2

Sunset pictures courtesy David Vier

Clicker Question CR-2 In a single-slit diffraction experiment, as the width of

the slit is made smaller, the width of the central

maximum of the diffraction pattern:

A) becomes smaller.

B) becomes wider.

C) remains the same.

D) There will be no

diffraction pattern on the

screen since the

apparatus and screen

distance are set up for a

particular width.

Finals Week Information

Clicker points will be posted online (hopefully) by

Monday.

Recall that clicker points are awarded by

answering questions (1 pt per question) and by

answering correctly (1 additional pt per question).

Clicker questions are worth up to 5 % (extra)

So there are two possible points per clicker

question.

Rainbow pictures courtesy David Vier

ALMOST THE END

Final is Monday, 8am – 11am in this room (2722 York).

There will be 27 questions with 3 extra credit problems.

Bring a Scantron, your ID, and write your proper quiz code number on your form.

For the most part, every chapter will be represented on the final.

Forrest will be holding a problem session during the Friday lecture time.

Sunset pictures courtesy David Vier

THE END

“Go forth and slay dragons.”

--Roderick Reid

Thank you for your

attention

Sunset pictures courtesy David Vier