Transcript Please put your box number on your homework from now on. Box

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.
We can use rays of light to
see where images “are” or
where they “appear” to be.
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.)
Why do oddly shaped curved mirrors make distorted
images, rather than no image at all?
It’s certainly true that you can’t trace all the reflected
rays (originating from a nose, for example) back to the
same point!
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
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
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.
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.
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.
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.
Ray tracing: parallel to axis  through focus
MEMORIZE THIS!
Sign conventions for mirrors
Will not be given on eqn sheet… but you don’t need to
memorize if you can ray trace!
Concave R>0 Convex R<0
Real Object or Image s,s’ > 0 Virtual object or image s, s’ < 0
Spherical refracting surface
Derivation - requires paraxial approximation
Sign convention CONVEX = +
NOTE: if s = ∞, then s’ = Rn2/(n2-n1)
if s’ = ∞, then s = Rn1/(n2-n1)
FOCAL LENGTHS ARE DIFFERENT ON DIFFERENT SIDES
WE DON’T USE f FOR SINGLE SURFACES.
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
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
R1=R2=10 cm and is made of glass n=1.5?
a) 5 cm
b) 10 cm
c) 20 cm
d) ∞
What is the focal length in air of this lens?
a) 5 cm
b) 10 cm
c) 20 cm
d) ∞
In air this “symmetric biconvex” lens has f = 10 cm.
What is its focal length in a medium with n = 1.25?
a) 5 cm
b) 10 cm
c) 20 cm
d) ∞
In air this “symmetric biconvex” lens has f = 10 cm.
What is its focal length in a medium with n = 1.25?
a) 5 cm
b) 10 cm
c) 20 cm
d) ∞
In air this “symmetric biconvex” lens has f = 10 cm.
What is its focal length in a medium with n = 2?
a) 5 cm
b) -10 cm
c) -20 cm
d) ∞
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)
a) 5 cm
b) 10 cm
c) 16.6 cm
d) It doesn’t have one focal length
Ray tracing for lenses
Same rule as for mirrors.
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
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
Q34.8
An object PQ is placed
in front of a converging
lens, forming a real
image P´Q´. If you use
black paint to cover the
lower half of the lens,
A. only the object’s upper half will be visible in the image.
B. only the object’s lower half will be visible in the image.
C. only the object’s left-hand half will be visible in the image.
D. only the object’s right-hand half will be visible in the image.
E. the entire object will be visible in the image.
A34.8
An object PQ is placed
in front of a converging
lens, forming a real
image P´Q´. If you use
black paint to cover the
lower half of the lens,
A. only the object’s upper half will be visible in the image.
B. only the object’s lower half will be visible in the image.
C. only the object’s left-hand half will be visible in the image.
D. only the object’s right-hand half will be visible in the image.
E. the entire object will be visible in the image.
An image of an image
• Figure 34.39
Note where rays bend in ray tracing!!
If I move lens B so that it is closer to A than the image formed
by A, then:
a) There will be a virtual final image
b) There will be real final image
c) There will be no final image
How do you trace rays for a virtual
object?
Cameras
• Figure 34.40 below shows the key elements of a
digital camera.
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.
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.
Farsighted correction
• Figure 34.46 below shows how to correct a hyperopic
(farsighted) eye using a converging lens.
The magnifier
• Angular magnification is M = /. See Figure 34.51
below.
• The angular magnification of a simple magnifier is
= / = (25 cm)/f.
M
The microscope
• A compound microscope consists of an objective lens and an
eyepiece. (See Figure 34.52 below.)
The astronomical telescope
• Figure 34.53 below shows the the optical system of an
astronomical refracting telescope.
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.
Chapter 35
Interference
• To consider interference of waves in
Goals
for
Chapter
35
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
– Why do soap bubbles
Introduction
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.
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.
–
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.
Two-source interference of light
• Figure 35.5 below shows Young’s double-slit experiment with
geometric analysis.
representation of a sinsoidal light
wave at a point in space
Works because cosine is the
projection of a radius vector onto
the x-axis.
Interference from two slits
• Figure 35.6 at the right is a
photograph of the interference
fringes from a two-slit
experiment.
Two-slit interference
• What is the wavelength of this light?
Broadcast pattern of a radio
station
• Constructive: crests & troughs line up
• Destructive: crest of S1 is at trough of S2
Intensity in interference patterns
• Find E from Trig
• I is proportional to E2