Welcome to Physics 7C!Welcome to Physics 7C!

Lecture 10 -- Winter Quarter Review-- 2005

Professor Robin Erbacher

343 Phy/Geo

erbacher@physics.ucdavis.edu

AnnouncementsAnnouncements• Pick up re-graded quizzes this week.

• Review Sessions Thursday-Friday. Check Website.

• Lecture 10 will be a review for the final.

• Final Exam: Saturday March 19, 1:30-3:30 pm. See website for which room you should report to.

• Bring photo ID to exam, arrive ahead of time.

• Check website throughout the week for further announcements.

Disclaimers, exceptions, modifications, allowances, ….

This is not a comprehensive review. You are still responsible for things in the lecture, in the block notes, and in the DL that may not be touched upon here. Understanding the material here will not necessarily mean you will breeze by on the exam. But it will help you.

The final has not yet been “finalized” so please don’t beg for information!

What should you study?DL activity introductions, lectures, block notes, FNT’s, quizzes, practice problems.

This Review SessionThis Review Session

• Light is a transverse electromagnetic wave. •The speed of light varies depending on the medium. How does it vary?

• In optics, what is the angle, , measured with respect to?

• Normal is the imaginary line between two media with different n.

• Total Internal Reflection: Refracted ray angle critical is at least 90o: Find minimum angle such that sin c = n2/n1

Also Know: law of reflection, Snells Law, Magnification, Thin Lens equation, …

Block 15: OpticsBlock 15: Optics

€

n = c/v

Block 15: Optics (cont’d)Block 15: Optics (cont’d)Thin Lenses-- some things to notice:

Thin lenses are thin enough to neglect the double refraction of light rays at the front and back surfaces: we assume light rays bend once. Images produced by lenses can be equivalently analyzed either analytically (thin lens equation) or graphically. Real images result from the intersection of refracted light rays. Real images are on the opposite side of a lens as the object. Real image locations correspond to positive values of i in the thin lens equation. Virtual images are the result of light rays diverging from a common point at which there is no actual intersection of light rays. Virtual images are on the same side of a lens as the object. Virtual image locations correspond to negative values of i from the thin lens equation.

h h

o i

light

lens

o i

3 Ray Traces for Lenses3 Ray Traces for Lenses Converging Lenses: Diverging Lenses:

Double Lens ExampleDouble Lens Example Converging Lens: Diverging Lens:

f1 = 40 cm f2 = - 40 cm

60 cm 160 cm

2 cm

a) Use ray trace or thin lens equation to locate image of lens combination.

b) Is the image real or virtual? Is it upright or inverted?c) Calculate the magnitude of the final image.

Block 11: Oscillatory Motion Block 11: Oscillatory Motion Simple Harmonic MotionPeriod of a Simple Pendulum

Period of a Mass on a Spring T

mg

mgcos

mgsin

€

T = 2πl

g

€

T = 2πm

k

€

y(t) = A sin(2π

Tt +φ) + BA generalized solution

is of the form:

A certain pendulum swings through an arc of one degree in one second from maximum height to equilibrium. Another pendulum with the same length but with a bob of twice the mass is made to swing through an arc of two degrees from maximum height to equilibrium. The time required to swing through the two-degree arc is….a.) One-half second, one second, two seconds, or some other choice. Defend your answer.b) Write the appropriate harmonic oscillator equation for both scenarios. Identify all constants and variables. Plot!

Practice Problem:

Block 11: Harmonic WavesBlock 11: Harmonic WavesCertain independent parameters characterize all waves:Amplitude: Controlled by the magnitude of the forces that started the

waveSpeed: Determined by the properties of the medium.Direction: Determined by the direction of the forces starting the wave Frequency f of oscillations: controlled by forces starting the wave

Wavelength (dependent parameter): vwave/f

€

y(x,t) - y0 = Asin(2π

λx ±

2π

Tt +φ) + BThe most general

solution is of the form:

€

Δy(x,t) = Asin[Φ(x,t)]Think of the sin argument as one

big phase (or angle) Total phase

Block 11: Harmonic WavesBlock 11: Harmonic WavesWave Velocity (hold constant):

€

v = dx

dt= m

λ

T

2

y(x)

2

y(t)

Snapshot: Hold time constant, see where we are in space.

Movie: Go forward in time, see how spatial points move.

-1

-0.6

-0.2

0.2

0.6

1

0 0.5 1 1.5 2 2.5 3 3.5 4

t (nano-seconds)

Practice Problem:To the right is the time dependence at x=0 of a one-dimensional microwave beam traveling in vacuum in the positive x-direction. The units on the vertical axis are volts/meter.

a) What oscillates in this wave and what is it that propagates?b) What is the frequency in Hz? What is the wavelength in meters?c) What is the the electric field E as a funtion of position and time?

Block 12: Wave SuperpositionBlock 12: Wave SuperpositionWhen two or more waves meet, they interfere with each other.Combining waves by adding them is known as superposition.

In Phase: Δ ni (ni = integer)

(constructive interference)

Out of Phase: Δ nh (nh = half-integer)

(destructive interference)

+

− A

+ A

0 t [ ]s

yy

total

= y

1

Sound Waves:Fbeat = |f1-f2| (amplitude)

Fcarrier = (f1+f2)/2 (pitch)

€

y(x, t) = 2Asin 2πx

λ

⎡ ⎣ ⎢

⎤ ⎦ ⎥cos 2π

t

T

⎡ ⎣ ⎢

⎤ ⎦ ⎥

Nodes

Where two oppositely

traveling waves

always destructively

intefere.

Antinodes

Where two oppositely

traveling waves

always constructively

intefere.

+

=

Standing Waves:

(x = n/2) Nodes!!

Block 12: Wave InterferenceBlock 12: Wave Interference

Practice Problem:Two loudspeakers are 1.8 m apart. They play tones of equal frequency. If you stand 3 m in front of the speakers, and exactly between them, you hear a maximum of intensity. When you stand 3m directly in front of one speaker the sound intensity is a minimum.What is the maximum wavelength of the sound?

Location of Maxima:Path length s = dsin = m

S =

d

L

A

1 cm

Block 12: Interference MaximaBlock 12: Interference Maxima

Practice Problem:A screen is placed 200 cm behind two narrow slits that are separated by 0.320 mm. The figure above shows the light intensity on the screen. a) What is the wavelength of the light? b) What is the pathlength difference from point A to one slit and point A to the other slit? (A is on a maximum.)

Location of Maxima:Path length s = dsin = m

S =

d

L

Block 13: Gravitational, Electric, and Magnetic Fields

Block 13: Gravitational, Electric, and Magnetic Fields

See recent lecture notes for highlights…. Just as in Quiz 6, make sure you know the difference between the E field, B field, and G field.

Problem: Electrostatic InductionTwo uncharged (neutral, “n”) metal balls stand on glass rods in scenario I.

In step II a third ball, carrying a positive charge, is brought near the other two balls.

Then, in III a conducting wire is connected betweens the first two balls.

Finally, in step IV the wire is removed and then the third ball is removed.

When this is all done, what are the charged states, if any, of each ball? Identify the charge of each ball (+, -, or n for neutral) and defend your answer with a succinct response.

+

+

I

II

III

IV

n n

Block 13: Electric and Magnetic Fields

Block 13: Electric and Magnetic Fields

E-Field SuperpositionYou’ve seen this before! (See Lecture 5)

Find the net E field at point P.

x

y

q1 q2

4

3

P

v

x

y

I -Q4

3

P

E-Field, B-Field, Q in motionFind the E field at P, the B field at P, and the force on charge -Q travelingwith velocity v to the right a distance 4 away from the current I.

Don’t forget to study gravity, too: g = GM/R2

Block 13: Magnetic FieldsBlock 13: Magnetic Fields

Problem: Uniform Magnetic FieldsA uniform magnetic field points upward, in the plane of the paper. A wire is perpendicular to the paper. When the wire carries a current, the magnetic field at point 2 is zero.

a) What’s the direction of the current?

b) Point 1 is the same distance from the wire as Point 2. What is the direction of the net B field at Point 1?

c) Point 3 is twice as far from the wire as Point 2. Draw and clearly label the net magnetic field vector at Point 3.

1 cm

1

32

B

Block 14: Beyond the Microscope… subatomic physics and the universeBlock 14: Beyond the Microscope… subatomic physics and the universe

You’ve done this recently!

What do you have to know about Lecture 7 (pre-Block 14 material)?

Be able to explain the idea behind extra-dimensions in the context of string theory.

Just kidding!

Should read through and familiarize yourself with basic ideas, but no memorizing the Standard Model of particles and fields. Concentrate on nuclear reactions and material of Block 14, mainly.