Exam 2 - Physics

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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

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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.

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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

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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.


FXX IO

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Three geometries are

rather easy to test:

1) Make image and object distances

equal.

Then F=2XO


FXX IO

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2) Point source placed at F causes

parallel rays on output side of lens

(image at infinite distance).


FXX IO

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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.

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Try to handle it by the edges.

Group Activity, Part 1:

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Using the techniques you learned

Last Time, determine the focal

length of the BIG lens.


Please click (A) when your group has

measured the focal length.

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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


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F for the BIG lens is nearest to:

A) 70 cm

B) 35 cm

C) 17.5 cm

D) 3 cm

E) Something else


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.

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“stop”Reduces aberration

Image

plane

Thin lenses together in pairs

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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

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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.

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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.


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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


How thin lenses work together

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F1

One lens,

F1


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F2

Another lens with

F2


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F1 F2

The two lenses

close together


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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!!


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For a single lens,

we know that:


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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

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1 1 1 2

totalF F F F

2total

FF OR

This is the same as adding powers:

Dtot = D1 + D2

A Question

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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

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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.

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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.


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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


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.

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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

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Length: ~13.2 m.

Diameter: 2.4 m.

Launched by NASA space shuttle Discovery in 1990.


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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.


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Spherical

aberration

Also relevant for

spherical lenses

Spherical aberration

Dispersion: refraction (bending) of different

colors by different amounts.

Light bulbSpectrum Prism

Review: Dispersion

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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

Documents

Exam 2 - Physics