1
Physics 1230: Light and Color
Chuck Rogers, [email protected] Henley, Valyria McFarland, Peter Siegfried
physicscourses.colorado.edu/phys1230
Exam 2
Scores and solutions are on D2L.
PLEASE PICK UP YOUR EXAM FORM
No Online or Written HW this week.
Project names/ideas by Friday
2
Physics 1230: Light and Color
Chuck Rogers, [email protected] Henley, Valyria McFarland, Peter Siegfried
physicscourses.colorado.edu/phys1230
Exam 2 Questions??
1. Write your question on a separate page.
2. Attach to otherwise untouched exam.
3. Bring it to Prof. Rogers and I will have a look.
4. Try to ask questions by Thurs. next week.
PICK UP YOUR EXAM 2 BOOKLET in front.
3
Physics 1230: Light and Color
Chuck Rogers, [email protected] Henley, Valyria McFarland, Peter Siegfried
physicscourses.colorado.edu/phys1230
Lecture 21:
Compound lenses: Putting lenses
together to make ‘effective’ lenses
No Online or Written HW this week.
Project names/ideas by Friday
Last Time: Activities: The lens equation
FXX IO
111
4
Demo: find focal length of lenses
One group member held the lens.
Another group member held the Maglite.
A third held a paper and found the image.
A group member measured the distances.
You can find the focal length of a
converging lens by measuring object and
image distances.
Last Time: Activities: The lens equation
FXX IO
111
5
Demo: find focal length of lenses
Three geometries are
rather easy to test:
1) Make image and object distances
equal.
Then F=2XO
Last Time: Activities: The lens equation
FXX IO
111
6
Demo: find focal length of lenses
Three geometries are
rather easy to test:
2) Point source placed at F causes
parallel rays on output side of lens
(image at infinite distance).
Last Time: Activities: The lens equation
FXX IO
111
7
Demo: find focal length of lenses
Three geometries are
rather easy to test:
3) Parallel rays in (object far away)
produce a point image at F .
Good place to work with some
lenses!
Please form groups (4 or 5) and
send a delegate down for a
maglite, ruler,
both a BIG and a SMALL lens.
One of each per group.
8
Try to handle it by the edges.
Group Activity, Part 1:
9
Using the techniques you learned
Last Time, determine the focal
length of the BIG lens.
Demo: find focal length of lenses
Please click (A) when your group has
measured the focal length.
10
Using the techniques you learned
Last Time, determine the focal
length of the BIG lens.
Please answer: Our group found F by
A) Equal Xo and Xi
B) Point source at F
C) Distant object for image at F
D) All these
E) Something else
Group Activity, Part 1:
11
Using the techniques you learned
Last Time, determine the focal
length of the BIG lens.
F for the BIG lens is nearest to:
A) 70 cm
B) 35 cm
C) 17.5 cm
D) 3 cm
E) Something else
Group Activity, Part 1:
Good place for questions!
At this point, you are roughly
an expert at finding the focal
length of converging lenses!
What happens if we have
several lenses in a line?
In many situations, we will have more
than just a single lens involved in
forming an image…
For example:
Compound Lenses
• A modern camera lens can have 16 elements or more
• The lenses can move to allow “zoom” changes.
• Can have reduced aberrations.
14
“stop”Reduces aberration
Image
plane
Thin lenses together in pairs
15
Demo: put together some lenses
Together they might still
focus the rays,
SO could behave like a
converging lens
Together they might still
diverge the rays,
SO could behave like a
diverging lens
Thin focusing lenses together
16
Suppose you have two
converging lenses. Each
has its own focal length,
maybe call them F1 and F2.
The diagram shows parallel rays hitting the 1st
lens. It starts to converge the rays. The 2nd
lens converges them even faster. SO:
A) The rays focus closer in than F1
B) The rays focus farther away than F1
C) Could be either for two focusing lenses.
17
Work with a neighboring group.
Figure out how TWO BIG lenses put
close together behave as a pair.
Find Fnew for TWO BIG lens together.
Please click (A) if you think you have it.
Group Activity, Part 2:
18
Work with a neighboring group.
Figure out how TWO BIG lenses
behave as a pair.
Fnew for TWO lens together is nearest:
A) 70 cm
B) 35 cm
C) 17.5 cm
D) 3 cm
E) Something else
Group Activity, Part 2:
How thin lenses work together
19
F1
One lens,
F1
How thin lenses work together
20
F2
Another lens with
F2
How thin lenses work together
21
F1 F2
The two lenses
close together
How thin lenses work together
22
F1 F2
The two lenses
close together
Have you every seen a lens take rays from some point, F1
away, and image them on the other side at a point F2 away?
A) NEVER B) Maybe… C) OF COURSE, and I can describe it.
Behaves like a single lens making an image!!
Last Time: Activities: The lens equation
FXX IO
111
23
Demo: find focal length of lenses
For a single lens,
we know that:
How thin lenses work together
24
F1 F2
The two lenses
close together
For a lens pair, we
must have that:
1 1 1
1 2 PAIRF F F
How thin lenses addFtot = final focal length
F1 = focal length lens 1
F2 = focal length lens 2
Diverging lenses (concave) have negative focal lengths
25
1 1 1 2
totalF F F F
2total
FF OR
This is the same as adding powers:
Dtot = D1 + D2
A Question
26
You have two focusing lenses, each with a focal
length of F. You put them close together to make
them behave as a single lens. The new ‘doublet
lens’ has a focal length of:
A) 2*F because the diopters add.
B) F/2 because the diopters add.
C) Still F for this special case.
D) Something else happens.
You know this because there
was an experiment you tried.
A Question
27
You have two focusing lenses, each with a focal
length of F. You put them close together to make
them behave as a single lens. The new ‘doublet
lens’ has a focal length of:
A) 2*F because the diopters add.
B) F/2 because the diopters add.
C) Still F for this special case.
D) Something else happens.
Physics is always based
on the experiment!!
You know this because there
was an experiment you tried.
28
Work with a neighboring group if you
need a small lens, figure out how a
BIG lens and a small lens put close
together behave as a pair.
Find Fnew for lens pair together.
Please click (A) if you think you have it.
Group Activity, Part 3:
29
The lens pair (BIG+small) has a
focal length that is:
A) Nearly the BIG lens value
B) Nearly the small lens value
C) Half way between them
D) Something else
Group Activity, Part 3:
1 1 1
1 2 PAIRF F F
OK, perhaps time for a breather!
Now you know loads about lenses,
how they produce images, and at least
a few non-ideal properties that cause
images to be not perfect.
All these things and more have impact on the
important artistic pursuit of photography, through
the artist’s main tool: Cameras!
Good place for a break!
Please drop off the lenses in
front.
Enjoy your day.
31
Aberrations
What are aberrations?
Examples:
Mis-shaped or damaged lens or mirror, Spherical aberrations: For spherical mirror - go far enough out on the circle – no single focus pointChromatic aberrations: different focal length for diff colors.
And others…
Anything that makes the image less than perfect is an aberration.
Called Spherical
Aberration
Actually, the light rays from a spherical mirror that come from the edge focus closer to the mirror
Spherical aberration
Fix by using a parabola
shape rather than sphere
OR
Don’t use the edges…
American Astronomer:
Edwin Hubble
A picture from HST:
stars born out of
nebula
Spherical aberration: Hubble space telescope
35
Length: ~13.2 m.
Diameter: 2.4 m.
Launched by NASA space shuttle Discovery in 1990.
Spherical aberration: Hubble space telescope
36
A blurry image caused by
aberration problem: mirror’s
edge was a bit too flat (by
~2 micrometers).
The clear image after installation of
corrective mirrors by astronauts in
1993.
Spherical aberration: Hubble space telescope
37
Spherical aberration: Hubble space telescope
Spherical
aberration
Also relevant for
spherical lenses
Spherical aberration
Dispersion: refraction (bending) of different
colors by different amounts.
Light bulbSpectrum Prism
Review: Dispersion
40
wavelength n (index of refraction)
300 nm (UV) 1.486 (bent more)
500 nm 1.462
700 nm (deep red) 1.455 (bent less)
Quartz glass
Review: Dispersion
Chromatic aberration