April 13 Physics 54 Lecture Professor Henry Greenside.

April 13 Physics 54 LectureProfessor Henry Greenside

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Today’s TopicsChapter 34: “Lenses and Optical Instruments”• Obtaining quantitative details via the thin-lens and

magnification equations; sign conventions for f, di, do, hi, and m.• Optics of the human eye, near and far points, eyeglasses, and

contact lenses.• Magnifying glass.• Microscopes.

Demo: Image of Filament Created by Single Converging Lens

• What happens to image if half the lens is blocked?

• What happens to image if an opaque sheet with a small hole is placed in front of the lens?

• What happens to image if the lens is entirely removed?

• What happens to image if screen is moved closer or further away than the image distance di?

Getting Quantitative: The Thin-Lens and Magnification Equations

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Looks like mirror equation but some sign conventions different: f > 0 for converging lens, f < 0 for diverging lens do > 0 if object on side from which light is coming di > 0 if image on side of lens opposite to object, <0 if not. hi > 0 if image is upright, < 0 if inverted. m > 0 if image is upright, <0 if inverted.

Two Worked Examples of Single Lens:Problems 34-13, 34-14 of Giancoli

PRS Question: Orientation and Length of Image?

Given 2.00 cm arrow on optical axis with midpoint75.0 cm from convex lens with f = 30.0 cm,

1. Image points to right and is longer.2. Image points to right and is shorter.3. Image points to left and is longer.4. Image points to left and is shorter.5. Some other answer.

PRS Question Answer: Orientation and Length of Image?

Given 2.00 cm arrow on optical axis with midpoint75.0 cm from convex lens with f = 30.0 cm,

1. Image points to right and is longer.2. Image points to right and is shorter.3. Image points to left and is longer.4. Image points to left and is shorter.5. Some other answer.

A

PRS Question

F G

If F’ and G’ are images of letters F and G for this diverging lens, then 1. F’ is left of G’ and F’ is bigger than G’.2. F’ is left of G’ and G’ is bigger than F’.3. F’ is right of G’ and F’ is bigger than G’.4. F’ is right of G’ and G’ is bigger than F’.5. Some other answer.

Also to consider: are F’,G’ backwards or upside down compared to F, G?

PRS Answer

F G

If F’ and G’ are images of letters F and G for this diverging lens, then 1. F’ is left of G’ and F’ is bigger than G’.2. F’ is left of G’ and G’ is bigger than F’.3. F’ is right of G’ and F’ is bigger than G’.4. F’ is right of G’ and G’ is bigger than F’.5. Some other answer.

G’F’

Multiple Lens and Mirror Systems

Key trick: the image of the first device becomes the object for the second device, and so on successively.

Total magnification is simply the product of successive magnifications:

mtotal = m1 m2 m3

A new wrinkle: the object distance do can now be negative if image of first device lies beyond position of second device.

f1 = 20.0 cm f2 = 25.0 cm

d1o = 60 cm

Two Worked Examples of Two-Lens System:Example 34-4 and Problem 34-19

a. What is the final location of the image I2?b. What is the final magnification?c. Final image: real/virtual, upright/inverted?d. Problem 34-19: what now if 80 cm separation decreased to 20 cm?

Ray Diagram for Virtual Object of Lens

This figure shows how to draw the ray diagram for a virtual object O1 on far side of a converging lens to get real image I2. Insight is that there are two foci F2 and F’2 and you need to be careful to use the appropriate focus when drawing rays. The thin-lens equation and experiment suggest which focus to use when drawing rays.

PRS: How Does Final Image Change?

As the lens on the right is moved to the left:1. The image I2 will become larger and move to the left.2. The image I2 will become larger and move to the right.3. The image I2 will become smaller and move to the left.4. The image I2 will become smaller and move to the right.5. I don’t know how to solve this.

f1=20 cm, f2=25 cm d1

o=60 cm d2o=50 cm

PRS Question Answer: How Does Final Image Change?

As the lens on the right is moved a little bit to the left:1. The image I2 will become larger and move to the left.2. The image I2 will become larger and move to the right.3. The image I2 will become smaller and move to the left.4. The image I2 will become smaller and move to the right.5. I don’t know how to solve this.

f1=20 cm, f2=25 cm d1

o=60 cm d2o=50 cm

Three-lens System of Copepod Pontella

From “Animal Eyes” by Land and Nilsson, 2002.

The Human Eye

Piece of retina

Why is cornea main source of refraction?!

f=2.4 cmf~8 cm

125,000,000 photoreceptors

1,000,000 axons

Ncornea =1.376

Why Lasik Surgery (Laser Assisted In-Situ Keratomileusis) Works

Vocabulary for the Eye

Accommodation: focusing by changing shape of lens

Near point: closest distance at which eye can focus clearly, about 25 cm for average adult

Far point: furthest distance at which eye can focus clearly, value of infinity for healthy adult, about 10 cm for newborn baby

Nearsightedness, farsightedness, astigmatism.

Correcting Vision with Converging and Diverging Lenses

PRS Question: Underwater Vision

If a person swims underwater without goggles or a mask, that person’s vision

1. becomes more near-sighted.2. becomes more far-sighted.3. does not change substantially.

And what about a fish out of water?

Correcting Nearsighted Eye

Nearsighted eye has near and far points of 12 cm and 17 cm.

(a) What focal length is needed for person to see distant objects clearly?

(b) What is the new near point?

(c) How do answers change if person wears contact lens instead?

Cameras and the Octopus/Fish Eye

PRS: Focusing on a Tasty Crab

If a tasty NC blue crab moves away from an octopus, then to keep the crab in sharp focus on its retina without moving its body, the octopus should

1. move its lens to the left, closer to its retina.2. move its lens to the right, further from its retina.3. keep its lens in the same place.

PRS Answer: Focusing on a Tasty Crab

If a tasty NC blue crab moves away from an octopus to the right, then to keep the crab in sharp focus on its retinawithout moving its body, the octopus should

1. move its lens to the left, closer to its retina.2. move its lens to the right, further from its retina.3. keep its lens in the same place.

Magnifying Glasses

Magnifying glass useful in its own right but also used at output end of various optical devices such as telescopes and microscopes.

Perception of size depends on how big image is on retina, which in turn depends on angle subtended by object.

Magnifying Glass and Angular Magnification

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Image distance di has to exceed near point NObject has to be closer than f to lens.

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Worked Example of Magnifying Glass:Problem 34-52 of Giancoli

Microscope

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Strategy: Put object O close to focus Fo of strong objective, arrange image I1 to be close to focus Fe of strong eyepiece.

Worked Microscope Example

A compound microscope consists of a 10x eyepiece and 50x objective 17.0 cm apart, observer has near point N=25 cm. Determine:

1. The overall magnification. Answer: 10 x 50 = 500.

2. The eyepiece focal length. Answer: Me=N/fe so fe=25/10=2.5 cm.

3. Position of object do when final image is in focus with relaxed eye. Answer: Use mo=di/do=(L-fe)/do to get do=(17-2.5)/50=0.29 cm. But then this is almost same as focal length of objective lens, fo~0.29 cm.

Quality Microscopes Have Many Lenses

Slides After This One Are Optional

I won’t have time to discuss these slides in lecture but I include them to suggest possible lines of thought to pursue or think about. I will be glad to discuss these slides with you after lecture or in my office.

Human Versus Octopus Eyes: Convergent Evolution

Eyes develop from brain tissue. Eyes develop from skin.

Lens can change shape. Lens is rigid, moves back and forth to focus (no accommodation!)

Photoreceptors point backward (dumb). Photoreceptors face forward (smart).

Can not see polarized light.

Color vision, complex retina.

Can see polarized light.

No color vision, simpler retina

Spherical and Chromatic Aberrations

Thin-lens approximation fails, get blurred image.

Dispersion causes different wavelengths to converge at different focal points, get blurring. Title of this slide will have red word Chromatic looking deeper into page than blue words “Spherical and …”.

Solution to Chromatic Aberration

Use adjacent lenses of different indices of refraction!

This elegant and simple insight was missed by Isaac Newton, who stated his opinion that it was not possible to solve the problem of chromatic aberration.

Trilobite Solution to Spherical Aberration

Huygens’ 1690 AD solution

Trilobite solution 400,000,000 BC

PRS Question: Chromatic Aberration of Mirrors

Which one of the following statements is true:1. A concave mirror will have less chromatic aberration than

a convex mirror.2. A convex mirror will have less chromatic aberration than a

concave mirror.3. A concave and convex mirror of equal focal length will

have comparable chromatic aberration.4. Neither a concave nor convex mirror will have chromatic

aberration.

Were Eyes Designed by an Intelligence?

Many people have pointed to the amazing complexity and quality of animal eyes as proof that there was a divine creation. See the website “The Eye Design Book”, http://www.eyedesignbook.com/, by Curt Deckart.

Argument is not convincing, ignorance of origin is not proof!

1. How well eyes and brains adapted for given animal and environment difficult to quantify. Many non-scientists too quick to accept conjectures that eyes are optimal in some absolute sense.

2. Biologists know of many examples of lousy eyes or eyes that were lost over time, e.g., nautilus and sunflower have primitive pin hole eyes, some animals have become blind over generations.

3. Many humans need eyeglasses, even during childhood (caused by reading as a child!)4. Genomics rather than physics will likely settle the issue by showing how genes work

together to determine properties of eyes. Much interesting science here to discover, e.g., how many genes need to change to alter shape or properties of an eye, speed of change, etc. See the paper “A pessimistic estimate of the time required for an eye to evolve”, Proceedings of the Royal Society of London B 256:53-8 (1994).