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Class 20
Physics 106
Learning
Outcomes
Optical Systems
Class 20
Optical Devices, Review 2
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Physics 106
Chapter 22
Chapter 23
Chapter 24
Winter 2017
Press CTRL-L to view as a slide show.
Last Time
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
Last time we discussed:
The Test
Chapter 20
I
The Eye
I
Single Slit Diffraction
I
Polarization
Chapter 23
I
Thin Film Examples
Chapter 24
Chapter 21
Chapter 22
Learning Outcomes
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Today’s topics are:
I
Optical systems
I
Test Review
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Optical Systems
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Angular Magnification
Class 20
Physics 106
I
Angular magnification is defined as
Learning
Outcomes
Optical Systems
θ
angle with lens
m=
=
θ0
angle without lens
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Angular Magnification
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
I
For a simple magnifying lens:
Chapter 20
Chapter 21
25cm
m=
f
Chapter 22
Chapter 23
Chapter 24
Compound Microscope
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
I
I
The objective
lens makes a
real image
The eyepiece
is a magnifier
to view details
of the real
image
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Compound Microscope
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
I
I
The objective
lens has a
short focal
length, fo < 1
cm
The eyepiece
has a focal
length fe of a
few cm
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Magnifications of the Compound
Microscope
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
I
I
I
Thelateral magnification of the objective lens is
usually marked on it, e.g., ×30
The angular magnification of the eyepiece is also
marked on it, e.g., ×10
The overall magnification of the microscope is the
product of the individual magnifications, here:
times300
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Telescopes
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Two fundamental types of telescopes:
I
Refracting telescope: has an objective lens
I
Reflecting telescope: has an objective mirror
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Refracting Telescope
Class 20
Physics 106
I
I
I
An objective lens
forms a small real
image
An eyepiece is a
magnifying glass to
view the real image
The focal point of the
eyepiece is placed
near the first image
I
The length of tube is
fo + fe
I
The eyepiece forms
an enlarged,
inverted, virtual
image of the first
image
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Angular Magnification of a Telescope
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
I
The angular magnification depends on the focal
lengths of the objective and eyepiece
fo
θ
=
m=
θ0
fe
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Reflecting Telescope, Newtonian Focus
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
I
I
Incoming rays
reflect and
converge toward
point A
A small flat mirror,
M, reflects the
light to the
eyepiece
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
The Test
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
I
I
19 multiple choice questions + basic test questions
Chapters 20-24
I
Excluding Single Slits and Polarization
I
Look at the chapter reviews
I
Look over quizzes
I
Review these slides
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
The Problems
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
I
Faraday’s Law/Lenz’s Law − 2 problems
The Test
I
Series LRC Circuits − 3 problems
Chapter 20
I
Other Circuits − 3 problems
I
Reflection and Refraction − 2 problems
I
Lenses and Mirrors − 4 problems
I
Wave Optics − 5 problems
Chapter 21
Chapter 22
Chapter 23
Chapter 24
The Problems
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
I
Qualitative − 5 + 2/2 problems
I
Quantitative − 12 + 2/2 problems
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Key Idea
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Faraday’s Law
I
I
When the number of magnetic field lines through a
coil of wire changes, an induced current flows
through the loop
Or . . . Changing magnetic fields produce electric
fields that form loops.
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Key Idea
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Lenz’ Law
I
Induced current flows in the direction that opposes
change in flux.
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Class 20
Equations
Physics 106
Learning
Outcomes
Optical Systems
I
Simple Magifiers
Flux
Microscopes
Telescopes
ΦB = BA cos θ
The Test
Chapter 20
Chapter 21
I
Faradays’ Law
∆ΦB
= −N
∆t
Chapter 22
Chapter 23
Chapter 24
Problem 1
Class 20
Physics 106
Learning
Outcomes
The north pole of a magnet is moving away from a loop of
wire. Which way does the current flow?
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
A. Definitely CW
B. Probably CW
C. Definitely CCW
D. Probably CCW
E. Don’t know
Chapter 22
Chapter 23
Chapter 24
Problem 2
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
The magnetic field through a loop of radius 2.00 cm is
increasing at the rate of 0.30 T/s. What is the EMF
around the loop?
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
A. 0.3 V
B. 0.3 ×π × 0.022 V
C. 2 ×π × 0.32 V
D. Don’t know
Chapter 23
Chapter 24
Problem 2a
If there is a 3 Ω resistor in the circuit, what current flows?
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Key Idea and Equation
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
Motional EMF
I
I
If a wire of length L moves perpendicularly to a
magnetic field, the electric and magnetic forces
balance: qE = qvB, E = /L
= BLv
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Problem 3
Class 20
Physics 106
A wire 3.0 cm long moves through a 0.20 T magnetic field
at a speed of 5.0 m/s. R = 2.0Ω. The current is:
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
A. 15 mA up
B. 15 mA down
C. 0.67 A up
D. 0.67 A down
E. Don’t know
Chapter 22
Chapter 23
Chapter 24
Key Idea
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
Generators
I
If a coil rotates in a magnetic field, a voltage is
induced because the number of field lines passing
through the coil is constantly changing.
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Problem 4
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Which of the following do not increase the voltage across
a generator coil?
Microscopes
Telescopes
The Test
Chapter 20
A. Increasing the number of turns in the coil.
B. Increasing the area of the coil.
C. Increasing the magnetic field through the coil.
D. Increasing the coil’s rate of rotation.
E. All of the above increase the voltage.
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Key Idea and Equation
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Self-Inductance
Microscopes
Telescopes
I
An inductor is a coil of wire placed in a circuit
I
When the current through the inductor changes, the
inductor produces a voltage that opposes the change
The Test
Chapter 20
Chapter 21
Chapter 22
I
Chapter 23
∆I
= −L
∆t
Chapter 24
Problem 5
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
The current through an inductor decreases. The inductor
acts like a battery that pushes charge
Telescopes
The Test
Chapter 20
Chapter 21
A. in the same direction as the current
B. opposite the direction of the current
C. in neither direction
D. I don’t know
Chapter 22
Chapter 23
Chapter 24
Key Ideas and Equations
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Energy and Inductors
Simple Magifiers
Microscopes
Telescopes
I
I
We think of an inductor as storing energy in the
magnetic field
The Test
Chapter 20
Chapter 21
1
U = LI 2
2
Chapter 22
Chapter 23
Chapter 24
LR circuits work a lot like LC circuits
I
The LR time constant is τ = L/R
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 21
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Key Idea and Equation
Class 20
Physics 106
Learning
Outcomes
RMS Voltage and Current
I
I
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The "effective" voltage or current in a circuit is less
than the maximum voltage.
The Test
The effective values are the RMS values:
Chapter 21
1
Vrms = √ Vmax
2
Pave = Irms Vrms
Chapter 20
Chapter 22
Chapter 23
Chapter 24
Key Idea and Equation
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
Resistors in AC
I
Voltage in current
are in phase
The Test
Chapter 20
Chapter 21
Chapter 22
I
VR = IR
Chapter 23
I
Phasor:
Chapter 24
Key Idea and Equation
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Inductors in AC
Telescopes
The Test
I
I
I
Voltage leads
current by 90◦
(ELI)
VL = IXL XL =
2πfL
Phasor:
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Key Idea and Equation
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Capacitors in AC
Telescopes
The Test
I
I
I
Current leads
voltage by 90◦
(ICE)
VC = IXC XC =
1/(2πfC)
Phasor:
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Key Idea
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Adding Voltages in Series
Telescopes
The Test
I
I
The current
phasor is the
same
Voltages phasors
add as vectors
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Key Idea
Class 20
Physics 106
Phase Angle
Learning
Outcomes
The phase angle
fis the angle
between the
current and
another phasor
Optical Systems
Phase angles to
remember:
Chapter 22
I
Inductor ϕ = +90◦
Chapter 24
I
Capacitor
ϕ = −90◦
I
Resistor ϕ = 0◦
I
Power Supply ϕ =
tan−1 (XL − XC )/R
I
I
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 23
Key Idea and Equations
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Series LRC Circuits − Voltage Phasors
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Key Idea and Equations
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Series LRC Circuits − Impedance Phasors
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Problem 6a
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
An AC power supply operates at 120 mV (rms) and 60
Hz. It is connected to a 0.2 Ω resistor, a 3.0 mH inductor
and a 2.0 mF capacitor.
Find the impedance of the circuit.
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
XL = 2πfL = 1.13Ω, XC = 1/(2πfC) = 1.33Ω
q
Z = (XL − XC )2 + R 2 = 0.280Ω
Chapter 23
Chapter 24
Class 20
Problem 6b
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
An AC power supply operates at 120 mV (rms) and 60
Hz. It is connected to a 0.2 Ω resistor, a 3.0 mH inductor
and a 2.0 mF capacitor.
Find the current in the circuit.
Irms =
Vrms
0.120
=
A = 429mA
Z
0.280
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Problem 6c
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
An AC power supply operates at 120 mV (rms) and 60
Hz. It is connected to a 0.2 Ω resistor, a 3.0 mH inductor
and a 2.0 mF capacitor.
Find the phase between the current and voltage in the
power supply.
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
XL − XC
= −44.3◦
ϕ = tan−1
R
Chapter 24
Key Idea
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Resonance
I
I
A circuit is at resonance when the frequency is
adjusted to allow the maximum current to flow.
Also, at resonance:
I
I
I
XL = XC
Z =R
ϕ=0
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Class 20
Equation
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
Resonance
I
The Test
Chapter 20
The resonance condition is:
f0 =
Chapter 21
1
√
2π LC
Chapter 22
Chapter 23
Chapter 24
Class 20
Problem 7
Physics 106
Learning
Outcomes
Optical Systems
An AC power supply operates at 120 V (rms). It is
connected to a 0.2 Ω resistor, a 3.0 mH inductor and a
2.0 mF capacitor. What is its resonant frequency?
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
f0 =
1
√
2π LC
Chapter 24
= 65.0Hz
Key Idea and Equation
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Transformers
Microscopes
Telescopes
I
Transformers use induction to transform voltages.
I
A step-up transformer has a larger voltage in the
secondary than in the primary.
I
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
V1
N1
I2
=
≈
V2
N2
I1
Chapter 24
Key Ideas and Equations
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Electromagnetic Waves
Simple Magifiers
Microscopes
Telescopes
I
Electric field is perpendicular to the direction of travel
I
Magnetic field is perpendicular to both the electric
field and the direction of travel
The Test
Chapter 20
Chapter 21
Chapter 22
I
Rotate E into B to get the direction of travel
Chapter 23
I
Travel at the speed of light (in vacuum)
Chapter 24
I
E = cB
c = λf
I
Key Idea
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Spectrum of Electromagnetic Waves
Simple Magifiers
Microscopes
Telescopes
I
radio
The Test
I
microwave
Chapter 20
I
infrared
Chapter 21
I
visible light
I
ultraviolet
I
x rays
I
gamma rays
Chapter 22
Chapter 23
Chapter 24
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 22
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Key Ideas
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
The Nature of Light
Telescopes
The Test
I
particle-like
I
I
I
ray optics
photons: E = hf
wave-like
I
I
wave optics
interference and diffraction
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Key Ideas
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Reflection
Telescopes
The Test
I
Light incident on a surface always reflects
Chapter 20
I
The angle of incidence equals the angle of reflection
Chapter 21
I
Light going from one medium toward a more dense
medium undergoes a phase shift upon reflection (Ch.
24)
Chapter 22
Chapter 23
Chapter 24
Key Idea
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Index of refraction
I
I
I
In a medium, the velocity of light v is less than c, the
velocity of light in vacuum
As light goes from one medium to another, the
frequency remains the same, but the wavelength
changes
The index or refraction is defined by n = c/v
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Key Ideas and Equation
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Refraction
Simple Magifiers
Microscopes
I
Light incident on a surface usually refracts
I
Snell’s Law:
Telescopes
The Test
Chapter 20
Chapter 21
n1 sin θ1 = n2 sin θ2
Chapter 22
Chapter 23
Chapter 24
I
Light going from one medium into another medium
undergoes no phase shift (Ch. 24)
Problem 8
Class 20
Physics 106
Light is incident from air on pane of glass (n=1.55) at an
incident angle of 45◦ . What is the angle between the
reflected and refracted rays?
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
The angle of reflection is
45◦ .
Chapter 24
Problem 8
Class 20
Physics 106
Light is incident from air on pane of glass (n=1.55) at an
incident angle of 45◦ . What is the angle between the
reflected and refracted rays?
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Snell’s law gives:
n1 sin θ1 = n2 sin θ2
sin θ2 =
sin 45◦
1×
= 0.456
1.55
θ2 = 27.1◦
Chapter 22
Chapter 23
Chapter 24
Problem 8
Class 20
Physics 106
Light is incident from air on pane of glass (n=1.55) at an
incident angle of 45◦ . What is the angle between the
reflected and refracted rays?
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Now do a little geometry:
45◦ + 62.9◦ = 107.9◦
Chapter 24
Key Idea
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
Total Internal Reflection
I
When light goes from a more dense medium to a
less dense medium, the angle of refraction can never
get larger than 90◦ .
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
I
All the light then reflects back into the original
medium.
Chapter 24
Class 20
Equation
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Total Internal Reflection
I
Set the angle of reflection to
Chapter 20
90◦ .
n1 sin θc = n2 sin 90◦ = n2
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Problem 9
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
A horizontal pane of glass has a drop of water on its
surface. Is the critical angle larger in the region where
there is air on the surface or in the region where there is
water on the surface?
A. air
B. water
C. same
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Key Idea
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Dispersion
Telescopes
The Test
I
The index of refraction varies with wavelength.
Chapter 20
I
Generally, the index of refraction is larger for blue
light than red light.
Chapter 21
I
Thus blue light bends more. (Blue light also scatters
more.)
Chapter 22
Chapter 23
Chapter 24
Key Idea
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
Huygens’ Principle
I
I
All points on a wavefront are point sources of
spherical wavelets.
The collection of all these wavelets a little late later in
time forms a new wavefront.
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 23
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Key Idea
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Real Images
I
Inverted
I
Light is really there (can see then on a screen)
Microscopes
Telescopes
The Test
Chapter 20
Virtual Images
I
Upright
I
Light is not really there (trace the rays back to see
where the image is located)
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Key Idea
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Sign Conventions
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
+
−
f Converging
Diverging
p Real Object Virtual Object
(almost always)
q Real Image Virtual Image
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Class 20
Equations
Physics 106
I
Learning
Outcomes
Lens/mirror equation:
Optical Systems
1
1 1
= +
f
p q
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
I
Chapter 21
Magnification:
M=−
I
Mirror focal length:
f =
R
2
q
p
Chapter 22
Chapter 23
Chapter 24
Ray Sketches
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Ray Sketches
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Problem 10a
Class 20
Physics 106
Learning
Outcomes
A concave mirror has a radius of curvature of 40 cm. An
object is placed 10 cm from the mirror. Find the image
distance:
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
1
1 1
1
1
1
= − =
−
=−
q
f
p
20 10
20
q = −20cm
Chapter 23
Chapter 24
Problem 10b
Class 20
Physics 106
Learning
Outcomes
A concave mirror has a radius of curvature of 40 cm. An
object is placed 10 cm from the mirror. Find the image
distance:
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
The image is:
Chapter 22
Chapter 23
Chapter 24
A. real and upright
B. real and inverted
C. virtual and upright
D. virtual and inverted
Key Ideas
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
Aberrations
I
I
spherical − rays parallel to the axis don’t converge to
a single point
chromatic − dispersion causes different colors to
focus at different locations
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 24
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Key Ideas
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
Constructive Interference
The Test
Chapter 20
I
Waves in phase, crests on crests
Chapter 21
I
Destructive Interference
Chapter 22
I
Waves out of phase, crests on troughs
Chapter 23
Chapter 24
Key Ideas
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Thin film interference
I
I
I
Phase shifts occur on reflection when light is going
toward a more dense medium
The wavelength in the film is the wavelength in
vacuum divided by n
When reflection is a maximum, transmission is a
minimum and vise versa.
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Class 20
Equations
Physics 106
Learning
Outcomes
Thin film interference:
Optical Systems
Simple Magifiers
Microscopes
Telescopes
m = 0, 1, 2, . . .
1 phase shift
0 or 2 phase shifts
The Test
Chapter 20
Chapter 21
Chapter 22
1 λ
2t =(m+ 2 ) n
constructive
λ
2t = m n
destructive
destructive
Chapter 23
Chapter 24
constructive
Problem 11a
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Light of wavelength 480 nm (in vacuum) is normally
incident on a thin film of oil (n=1.20) on a puddle of water
(n=1.33). A bright reflection is seen.
How many phase shifts are there?
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
A. 0
B. 1
C. 2
D. 3
Chapter 23
Chapter 24
Class 20
Problem 11b
Physics 106
Light of wavelength 480 nm (in vacuum) is normally
incident on a thin film of oil (n=1.20) on a puddle of water
(n=1.33). A bright reflection is seen.
What are the possible thickness of the film?
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
2nt = mλ
Chapter 22
Chapter 23
Chapter 24
mλ
480nm
t=
=m
= 200m nm
2n
2.4
t = 0 nm, 200 nm, 400 nm, . . .
Key Ideas
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Double slit interference
I
If the path difference of the light traveling from the
slits is an integral number of wavelengths, there is
constructive interference.
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Class 20
Equations
Physics 106
Double slit interference
I
Learning
Outcomes
Constructive Interference:
Optical Systems
Simple Magifiers
mλ = d sin θ
Microscopes
Telescopes
The Test
Chapter 20
I
I
Destructive Interference:
1
m+
λ = d sin θ
2
Small Angle: use the substitution
sin θ ≈
ym
L
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Class 20
Problem 12
Physics 106
A screen is located 12.0 m away from double slits
illuminated by light having a wavelength of 500 nm. The
slit separation is d= 0.25 mm. At what distance away
from the central maximum will the third dark band appear
on the screen?
1
λ
d sin θ = m +
2
y
1
d ≈ m+
λ
L
2
y≈
y≈
L
× 2.5λ
d
12
× 2.5 × 500nm ≈ 60mm
0.25 × 10−3
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Key Ideas
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
Diffraction Gratings
I
With many lines very closely spaced, maxima are
spread out to large angles
I
Maxima are very narrow
I
The conditions for maxima are the same as for two
slits
The Test
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Class 20
Equations
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
Diffraction Grating
Chapter 20
I
Constructive Interference;
Chapter 21
Chapter 22
mλ = d sin θ,
m = 0, ±1 ± 2, . . .
Chapter 23
Chapter 24
Problem 13
Class 20
Physics 106
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Which color of light bends the most with a diffraction
grating?
Telescopes
The Test
Chapter 20
A. red
B. orange
C. green
D. blue
E. white
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Class 20
Problem 14
Physics 106
In a diffraction grating, one order of the 400 nm red line
and another order of the 700 nm blue line are seen at the
same point. What is the maximum d for which this is
possible?
Learning
Outcomes
Optical Systems
Simple Magifiers
Microscopes
Telescopes
The Test
d sin θ = m1 λ1 = m2 λ2
Chapter 20
700m1 = 400m2
7
m2
=
m1
4
d sin θ = 2800nm
2800nm
d=
sin θ
dmax = 2800nm
Chapter 22
Chapter 21
Chapter 23
Chapter 24