Please put your box number on your homework from now on. Box numbers are written in orange on the homework I am handing back. They are also posted in the lobby.

1
Please put your box number on your homework from
now on. Box numbers are written in orange on
the homework I am handing back. They are also
posted in the lobby.
2
We can use rays of light to see where images
are or where they appear to be.
3
A planar interface (e.g. between water and air)
can also make an image. The location of the
image depends on the viewing angle (unlike with
mirrors.)
4
Why do oddly shaped curved mirrors make distorted
images, rather than no image at all? Its
certainly true that you cant trace all the
reflected rays (originating from a nose, for
example) back to the same point!
5
Q34.2
A concave mirror with a radius of curvature of 20
cm has a focal length of
A. 40 cm. B. 20 cm. C. 10 cm. D. 5 cm. E. answer
depends on the index of refraction of the air
around the mirror
6
A34.2
A concave mirror with a radius of curvature of 20
cm has a focal length of
A. 40 cm. B. 20 cm. C. 10 cm. D. 5 cm. E. answer
depends on the index of refraction of the air
around the mirror
7
Q34.3
An object is placed 4.0 m away from a concave
mirror of focal length 1.0 m. The image formed
by the mirror is
A. real and larger than the object. B. real and
smaller than the object. C. real and the same
size as the object. D. virtual and larger than
the object. E. virtual and smaller than the
object.
8
A34.3
An object is placed 4.0 m away from a concave
mirror of focal length 1.0 m. The image formed
by the mirror is
A. real and larger than the object. B. real and
smaller than the object. C. real and the same
size as the object. D. virtual and larger than
the object. E. virtual and smaller than the
object.
9
Q34.6
An object is placed 0.5 m away from a concave
mirror of focal length 1.0 m. The image formed
by the mirror is
A. real and larger than the object. B. real and
smaller than the object. C. real and the same
size as the object. D. virtual and larger than
the object. E. virtual and smaller than the
object.
10
A34.6
An object is placed 0.5 m away from a concave
mirror of focal length 1.0 m. The image formed
by the mirror is
A. real and larger than the object. B. real and
smaller than the object. C. real and the same
size as the object. D. virtual and larger than
the object. E. virtual and smaller than the
object.
11
Ray tracing parallel to axis ?? through
focus MEMORIZE THIS! Sign conventions for
mirrors Will not be given on eqn sheet but you
dont need to memorize if you can ray
trace! Concave Rgt0 Convex Rlt0 Real Object or
Image s,s gt 0 Virtual object or image s, s lt 0
12
Spherical refracting surface Derivation -
requires paraxial approximation Sign convention
CONVEX NOTE if s 8, then s
Rn2/(n2-n1) if s 8, then s
Rn1/(n2-n1) FOCAL LENGTHS ARE DIFFERENT ON
DIFFERENT SIDES WE DONT USE f FOR SINGLE
SURFACES.
13
THIN LENSES The image of the first surface is the
object for the second. The object for the 2nd
surface may be a VIRTUAL OBJECT
14

• A thin lens surrounded by the same medium on both
  sides has symmetric imaging properties
  (regardless of whether the surfaces have the same
  R or not!)
• What is the focal length in air of a lens that
  has R1R210 cm and is made of glass n1.5?
• 5 cm
• 10 cm
• 20 cm
• 8

15

• What is the focal length in air of this lens?
• 5 cm
• 10 cm
• 20 cm
• 8

16

• In air this symmetric biconvex lens has f 10
  cm.
• What is its focal length in a medium with n
  1.25?
• 5 cm
• 10 cm
• 20 cm
• 8

17

• In air this symmetric biconvex lens has f 10
  cm.
• What is its focal length in a medium with n
  1.25?
• 5 cm
• 10 cm
• 20 cm
• 8

18

• In air this symmetric biconvex lens has f 10
  cm.
• What is its focal length in a medium with n 2?
• 5 cm
• -10 cm
• -20 cm
• 8

19

• In air this symmetric biconvex lens has f 10
  cm.
• What is its focal length if the right side is in
  water (on the side of a fish tank, for example.
  nw 1.33)
• 5 cm
• 10 cm
• 16.6 cm
• It doesnt have one focal length

20
Ray tracing for lenses Same rule as for mirrors.
21
Q34.1
Which of the following changes its focal length
when it is immersed in water?
A. a concave mirror B. a convex mirror C. a
diverging lens D. all of the above E. none of the
above
22
A34.1
Which of the following changes its focal length
when it is immersed in water?
A. a concave mirror B. a convex mirror C. a
diverging lens D. all of the above E. none of the
above
23
Q34.8
An object PQ is placed in front of a converging
lens, forming a real image PQ. If you use black
paint to cover the lower half of the lens,

• A. only the objects upper half will be visible
  in the image.
• B. only the objects lower half will be visible
  in the image.
• C. only the objects left-hand half will be
  visible in the image.
• D. only the objects right-hand half will be
  visible in the image.
• E. the entire object will be visible in the image.

24
A34.8
An object PQ is placed in front of a converging
lens, forming a real image PQ. If you use black
paint to cover the lower half of the lens,

• A. only the objects upper half will be visible
  in the image.
• B. only the objects lower half will be visible
  in the image.
• C. only the objects left-hand half will be
  visible in the image.
• D. only the objects right-hand half will be
  visible in the image.
• E. the entire object will be visible in the image.

25
An image of an image

• Figure 34.39

Note where rays bend in ray tracing!!
26
If I move lens B so that it is closer to A than
the image formed by A, then

• There will be a virtual final image
• There will be real final image
• There will be no final image
• How do you trace rays for a virtual
• object?

27
Cameras

• Figure 34.40 below shows the key elements of a
  digital camera.

28
The eye

• The optical behavior of the eye is similar to
  that of a camera.
• Figure 34.44 below shows the basic structure of
  the eye.

29
Defects of vision

• The near point typically recedes with age, as
  shown in Table 34.1.
• Figure 34.45 (at right) shows a normal, a myopic,
  and a hyperopic eye.

30
Farsighted correction

• Figure 34.46 below shows how to correct a
  hyperopic (farsighted) eye using a converging
  lens.

31
The magnifier

• Angular magnification is M ??/?. See Figure
  34.51 below.
• The angular magnification of a simple magnifier
  is M ??/? (25 cm)/f.

32
The microscope

• A compound microscope consists of an objective
  lens and an eyepiece. (See Figure 34.52 below.)

33
The astronomical telescope

• Figure 34.53 below shows the the optical system
  of an astronomical refracting telescope.

34
The reflecting telescope

• Figure 34.54 below shows three designs for
  reflecting telescopes. Part (d) shows the Gemini
  North telescope, which uses the design in (c)
  with an objective mirror 8 meters in diameter.

35
Chapter 35

• Interference

36
Goals for Chapter 35

• To consider interference of waves in space
• To analyze two-source interference of light -
  using phasors!
• To calculate the intensity of interference
  patterns - using phasors!
• To understand interference in thin films

37
Introduction

• Why do soap bubbles show vibrant color patterns,
  even though soapy water is colorless?
• What causes the multicolored reflections from
  DVDs?
• We will now look at optical effects, such as
  interference, that depend on the wave nature of
  light.

38
Wave fronts from a disturbance

• Figure 35.1 at the right shows a snapshot of
  sinusoidal waves spreading out in all directions
  from a source.
• Superposition principle When two or more waves
  overlap, the resultant displacement at any
  instant is the sum of the displacements of each
  of the individual waves.

39
Constructive and destructive interference

• Figure 35.2 at the right shows two coherent wave
  sources.
• Constructive interference occurs when the path
  difference is an integral number of wavelengths.
• Destructive interference occurs when the path
  difference is a half-integral number of
  wavelengths.

40
Two-source interference of light

• Figure 35.5 below shows Youngs double-slit
  experiment with geometric analysis.

41
Phasors - a graphical representation of a
sinsoidal light wave at a point in spaceWorks
because cosine is the projection of a radius
vector onto the x-axis.
42
Interference from two slits

• Figure 35.6 at the right is a photograph of the
  interference fringes from a two-slit experiment.

43
Two-slit interference

• What is the wavelength of this light?

44
Broadcast pattern of a radio station

• Constructive crests troughs line up
• Destructive crest of S1 is at trough of S2

45
Intensity in interference patterns

• Find E from Trig
• I is proportional to E2