1. Physics 1202: Lecture 20 Today’s Agenda
Announcements: Team problems today
Team 14: Gregory Desautels, Benjamin Hallisey, Kyle Mcginnis
Team 15: Austin Dion, Nicholas Gandza, Paul Macgillis-Falcon
Homework #9: due Friday
NO HOMEWORK next week.
Midterm 2: Tuesday April 10: covers Ch
Midterm sample + To-Know sheet on web already
Review session: chapters 24-27 1

2. 24-AC Current L C ~ e R w

3. Suppose:
Phasors for L,C,R i i wt w ß i i wt w i i wt w

4. w - dependence in AC Circuits
The maximum current & voltage are related via the impedence Z
Currents AC-circuits as a function of frequency:

5. 24-5 RLC Circuits Phasor diagram Follow the loop Total V
useful to analyze an RLC circuit
Follow the loop
VR = R Imax (in phase)
VL= XL Imax (leads by 90o)
VC= XC Imax (lags by 90o)
Total V
V= VR + VL+ VC = Z Imax

6. Phasors:LCR f
Imax R
Imax (XL-XC)
Vmax = Imax Z Þ

7. 24-5 RLC Circuits The phase angle for an RLC circuit is:
If XL = XC, the phase angle is zero, and the voltage and current are in phase.
The power factor:

8. Resonance
For fixed R,C,L the current im will be a maximum at the resonant frequency w0 which makes the impedance Z purely resistive.
ie:
reaches a maximum when:
XL=XC
the frequency at which this condition is obtained is given from: Þ
Note that this resonant frequency is identical to the natural frequency of the LC circuit by itself!
At this frequency, the current and the driving voltage are in phase!

9. 24-6 Resonance in Electrical Circuits
In an RLC circuit with an ac power source, the impedance is a minimum at the resonant frequency:
XL=XC

10. Resonance
The current in an LCR circuit depends on the values of the elements and on the driving frequency through the relation
“ Impedance Triangle” Z
|  R
| XL-XC | 1 2 x im
2wo w
R=Ro
m / R0
Suppose you plot the current versus w, the source voltage frequency, you would get:
R=2Ro

11. Power in LCR Circuit The power can be expressed in term of i max: Þ
This result is often rewritten in terms of rms values: Þ
Power delivered depends on the phase, f, the “power factor”
phase depends on the values of L, C, R, and w

12. Chap. 25 f ( x f ( x ) x z y x

13. E & B in Electromagnetic Wave
Plane Harmonic Wave:
where: y x z
Note: the direction of propagation is given by the cross product
where are the unit vectors in the (E,B) directions.
Nothing special about (Ey,Bz); eg could have (Ey,-Bx)
Note cyclical relation:

14. Lecture 14, ACT 1 (a) + z direction (b) -z direction (c) +y direction
Suppose the electric field in an e-m wave is given by:
In what direction is this wave traveling ?
(a) + z direction
(b) -z direction
(c) +y direction
(d) -y direction
To determine the direction, set phase = 0:
Therefore wave moves in + z direction!
Another way:

15. E & B in Electromagnetic Wave
Plane Harmonic Wave:
where: y x z
From general properties of waves : Þ

16. 25-4 Energy and Momentum in Electromagnetic Waves
The energy a wave delivers to a unit area in a unit time is called the intensity.

17. 25-4 Energy and Momentum in Electromagnetic Waves
Substituting for the energy density:
An electromagnetic wave also carries momentum:

18. 25-5 Polarization
Polarized light has its electric fields all in the same direction.
Unpolarized light has its electric fields in random directions.
The polarization of an EM wave refers to the direction of its electric field

19. Polarizers I = I0 cos2q Made of long molecules (polymers)
Block electric field along their length
Electric field perpendicular passes through E
E. H. Land (1909 – 1991): Polaroid E
So Eafter=E cosq
Recall that I ~ E2
I = I0 cos2q

20. 25-5 Polarization For unpolarized light passing through a polarizer
the transmitted intensity is half the initial intensity
A polarizer and an analyzer can be combined

21. 26 R q h h’
o-R
R-i o i

22. 26-1 The Reflection of Light
The law of reflection states that the angle of incidence equals the angle of reflection:
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23. 26-3 Spherical Mirrors: definitions
Spherical mirrors have
a central axis (a radius of the sphere) and a
center of curvature (the center of the sphere)
Concave mirror
Convex mirror
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24. 26-3 Concave Spherical Mirrors
Consider parallel rays
They hit a spherical mirror
They come together at the focal point
This is a ray diagram for finding the focal point of a concave mirror.

25. 26-3 Convex Spherical Mirrors
Consider parallel rays
They hit a spherical mirror
They appear to have come from the focal point, if the mirror is convex
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26. Diagram: Concave Mirror, o > R
Active Figure Ray diagrams for spherical mirrors, along with corresponding photographs of the images of candles. (a) When the object is located so that the center of curvature lies between the object and a concave mirror surface, the image is real, inverted, and reduced in size.
The object is outside the center of curvature of the mirror
The image is real
The image is inverted
The image is smaller than the object

27. Diagram: Concave Mirror, o < f
Active Figure Ray diagrams for spherical mirrors, along with corresponding photographs of the images of candles. (a) When the object is located so that the center of curvature lies between the object and a concave mirror surface, the image is real, inverted, and reduced in size.
The object is between the mirror and the focal point
The image is virtual
The image is upright
The image is larger than the object

28. Diagram: Convex Mirror
Active Figure Ray diagrams for spherical mirrors, along with corresponding photographs of the images of candles. (a) When the object is located so that the center of curvature lies between the object and a concave mirror surface, the image is real, inverted, and reduced in size.
The object is in front of a convex mirror
The image is virtual
The image is upright
The image is smaller than the object

29. Mirror – Lens Definitions
Some important terminology we introduced last class,
o = distance from object to mirror (or lens)
i = distance from mirror to image
o positive, i positive if on same side of mirror as o.
R = radius of curvature of spherical mirror
f = focal length, = R/2 for spherical mirrors.
Concave, Convex, and Spherical mirrors.
M = magnification, (size of image) / (size of object)
negative means inverted image R g q a
object b h
image o i

30. o i f h’ h
26.5

31. EM wave at an interface
What happens when light hits a surface of a material?
Three Possibilities
Reflected
Refracted (transmitted)
Absorbed
incident
ray
reflected
ray
MATERIAL 1
MATERIAL 2
refracted
ray

32. 25-6: Index of Refraction
The wave incident on an interface can not only reflect, but it can also propagate into the second material.
Claim the speed of an electromagnetic wave is different in matter than it is in vacuum.
Recall, from Maxwell’s eqns in vacuum:
How are Maxwell’s eqns in matter different?
e0 ® e , m0 ® m (both increase)
Therefore, the speed of light in matter is smaller and related to the speed of light in vacuum by:
where n = index of refraction of the material:
The index of refraction is frequency dependent: For example
nblue > nred

33. The two triangles above each have hypotenuse L
Snell’s Law l1 l2 L n1 n2 q1 q2
From the last slide: q1 q2
The two triangles above each have hypotenuse L ⇒ \ ⇒
But,

34. 26-5 Refraction: Basic properties
Light may refract into a material where its speed is lower
angle of refraction is less than the angle of incidence
The ray bends toward the normal
Light may refract into a material where its speed is higher
angle of refraction is more than the angle of incidence
The ray bends away from the normal
If n1 = n2 Þ no effect
If light enters normal Þ no effect

35. Total Internal Reflection
Consider light moving from glass (n1=1.5) to air (n2=1.0)
incident
ray
reflected
refracted q2 q1 qr
GLASS
AIR n2 n1
ie light is bent away from the normal.
as q1 gets bigger, q2 gets bigger, but q2 can never get bigger than 90° !!
In general, if sin q1  sin qC  (n2 / n1), we have NO refracted ray;
we have TOTAL INTERNAL REFLECTION.
For example, light in water which is incident on an air surface with angle q1 > qc = sin-1(1.0/1.5) = 41.8° will be totally reflected. This property is the basis for the optical fibers used in communication.

36. Converging Lens Principal RaysF
Image
P.A.
Object F
1) Rays parallel to principal axis pass through focal point.
2) Rays through center of lens are not refracted.
3) Rays through F emerge parallel to principal axis.
Image is: real, inverted and enlarged (in this case).
Assumptions:
• monochromatic light incident on a thin lens.
• rays are all “near” the principal axis.

37. Diverging Lens Principal RaysF
P.A.
Image
Object F
1) Rays parallel to principal axis pass through focal point.
2) Rays through center of lens are not refracted.
3) Rays toward F emerge parallel to principal axis.
Image is virtual, upright and reduced

38. The Mirror/Lens Equation
We have derived, in the paraxial (and thin lens) approximation, the same equations for mirrors and lenses:
when the following sign conventions are used:
Variable
f > 0
f < 0
o > 0
o < 0
i > 0
i < 0
Mirror
concave
convex
real (front)
virtual (back)
Lens
converging
diverging
real (back)
virtual (front)

39. 3 Cases for Converging Lenses
Object
Image
Past 2F
Inverted
Reduced
Real
This could be used in a camera. Big object on small film
Image
Object
Between
F & 2F
Inverted
Enlarged
Real
This could be used as a projector. Small slide on big screen
Image
Object
Inside F
Upright
Enlarged
Virtual
This is a magnifying glass

40. Lecture 18, ACT 5 (a) left half of image disappears
object
A lens is used to image an object on a screen. The right half of the lens is covered.
What is the nature of the image on the screen?
lens
(a) left half of image disappears
(b) right half of image disappears
screen
(c) entire image reduced in intensity
All rays from the object are brought to a focus at the screen by the lens.
The covering simply blocks half of the rays.
Therefore the intensity is reduced but the image is of the entire object!

41. 26-8 Dispersion and the Rainbow
The index of refraction n varies slightly
with the frequency f of light (or wavelength l) of light
in general, the higher f, the higher the index of refraction n
This means that refracted light is “spread out” in a rainbow of colors
This is known as dispersion

42. Prisms f
The index of refraction for a material usually decreases with increasing wavelength
Violet light refracts more than red light when passing from air into a material

43. 27
Optical
Instruments

44. The
EYE I2 I1
~fo
~fe L
objective
eyepiece

45. 27-1 The Human Eye The ciliary muscles The near point The far point
adjust the shape of the lens to accommodate near and far vision.
The near point
the closest point to the eye that the lens is able to focus
normal vision ~ 25 cm from the eye
it increases with age as the lens becomes less flexible
The far point
farthest point at which the eye can focus
it is infinitely far away, if vision is normal

46. The Lens Equation
Convergent Lens: h i o f h’

47. 27-2 Corrective Optics & Human Eye
A nearsighted person: far point at a finite distance
objects farther away will appear blurry: lens focus too strong
so the image is formed in front of the retina.
Use diverging lens
f chosen for a distant object to form image at the far point
Strength of corrective lenses:
© 2017 Pearson Education, Inc.

48. 27-2 Corrective Optics & Human Eye
A farsighted person: see distant objects clearly
but cannot focus on close objects—the near point is too far away
lens not strong enough: image focus is behind the retina.
Use a converging lens
Augment the converging power of the eye
The final image is past the near point
© 2017 Pearson Education, Inc.

49. 27-3 The Magnifying Glass A simple convex lens
makes objects appear bigger by making them appear closer
Similar to a corrective lens for farsightedness
it brings the near point closer to the eye
Angular size of an object
angle it subtends on the retina, and depends both on the size of the object and its distance from the eye
assuming it is small

50. Recap of Today’s Topic :
Announcements: Team problems today
Team 14: Gregory Desautels, Benjamin Hallisey, Kyle Mcginnis
Team 15: Austin Dion, Nicholas Gandza, Paul Macgillis-Falcon
Homework #9: due Friday
NO HOMEWORK next week.
Midterm 2: Tuesday April 10: covers Ch
Midterm sample + To-Know sheet on web already
Review session: chapters 24-27