Physics 102: Lecture 19, Slide 1 Today’s Lecture will cover textbook sections 23.9, 24.1, 3-4, 6 Physics 102: Lecture 19 Lenses and your EYE Ciliary Muscles

Physics 102: Lecture 19, Slide 1

• Today’s Lecture will cover textbook sections 23.9, 24.1, 3-4, 6

Physics 102: Lecture 19Lenses and your EYE

Ciliary Muscles


Review of LensesPreflight 18.8

P.A.

F

Focal point determined by geometry and Snell’s Law: n1 sin() = n2 sin()

Fat in middle = ConvergingThin in middle = DivergingLarger n2/n1 = more bending, shorter focal length.n1 = n2 => No Bending, f = infinityLens in water has _________ focal length!

n1<n2


Review of LensesPreflight 18.8

P.A.

F

Focal point determined by geometry and Snell’s Law: n1 sin() = n2 sin()

Fat in middle = ConvergingThin in middle = DivergingLarger n2/n1 = more bending, shorter focal length.n1 = n2 => No Bending, f = infinityLens in water has larger focal length!

n1<n2

1) Rays parallel to principal axis pass through focal point.2) Rays through center of lens are not refracted.

3) Rays through F emerge parallel to principal axis.

Assumptions: • monochromatic light incident on a thin lens.

• rays are all “near” the principal axis.

Review: Converging Lens Principal Rays

F

F

Object

P.A.

Image is real, inverted and enlarged

Image


Preflight 19.1A converging lens is used to project a real image

onto a screen. A piece of black tape is then placed over the upper half of the lens.

How much of the image appears on the screen?


Preflight 19.1

Java

A converging lens is used to project a real image onto a screen. A piece of black tape is then placed over the upper half of the lens.

http://www.lightlink.com/sergey/java/java/clens/index.html


Java

Preflight 19.1Still see entire image (but dimmer)!

http://www.lightlink.com/sergey/java/java/clens/index.html

Lens Equation

cm 1011

cm 151

id

F

F

Object

P.A.

do

di

f

Image

1do

1di

1f

• do = distance object is from lens:

• Positive: object __________ lens

• Negative: object __________ lens

• di = distance image is from lens:

• Positive: ________ image (behind lens)

• Negative: ________ image (in front of lens)

• f = focal length lens:• Positive: ___________ lens

• Negative: ___________ lens

di =

m =

Lens Equation

cm 1011

cm 151

id

cm 30id

o

i

dd

m 2

F

F

Object

P.A.

do

di

f

Image

1do

1di

1f

• do = distance object is from lens:

• Positive: object in front of lens

• Negative: object behind lens

• di = distance image is from lens:

• Positive: real image (behind lens)

• Negative: virtual image (in front of lens)

• f = focal length lens:• Positive: converging lens

• Negative: diverging lens


Amazing Eye• One of first organs to develop.

• 100 million Receptors 4 million – 200,000 /mm2 2,500 /mm2

– Sensitive to single photons!

• Candle from 12 miles

Ciliary Muscles


ACT: Focusing and the Eye

Cornea n= 1.38

Lens n = 1.4

Vitreous n = 1.33

Which part of the eye does most of the light bending?

1) Lens 2) Cornea 3) Retina 4) Cones

Ciliary Muscles

ACT: Focusing and the Eye

Cornea n= 1.38

Lens n = 1.4

Vitreous n = 1.33

Which part of the eye does most of the light bending?

1) Lens 2) Cornea 3) Retina 4) ConesLens and cornea have similar shape, and index of refraction. Cornea has air/cornea interface 1.38/1, 70% of bending. Lens has Lens/Vitreous interface 1.4/1.33. Lens is important because it can change shape.Laser eye surgery changes Cornea

Ciliary Muscles


Eye (Relaxed)25 mm

Determine the focal length of your eye when looking at an object far away.

relaxedf

odObject is far away:

idWant image at retina:


Eye (Relaxed)25 mm

Determine the focal length of your eye when looking at an object far away.

f

1

mm 25

11

mm 25relaxedf

odObject is far away:

mmdi 25Want image at retina:


Eye (Tensed)25 mm

Determine the focal length of your eye when looking at an object up close (25 cm).

tensef

250 mm

odObject is up close:

idWant image at retina:


Eye (Tensed)25 mm

Determine the focal length of your eye when looking at an object up close (25 cm).

f1

mm 251

mm 2501

mm 7.22tensef

250 mm

mm 25relaxedf

mmcmdo 25025 Object is up close:

mmdi 25Want image at retina:


A person with normal vision (near point at 26 cm) is standing in front of a plane mirror.

What is the closest distance to the mirror where the person can stand and still see himself in focus?

1) 13 cm

2) 26 cm

3) 52 cm

Preflight 19.3


A person with normal vision (near point at 26 cm) is standing in front of a plane mirror.

What is the closest distance to the mirror where the person can stand and still see himself in focus?

1) 13 cm

2) 26 cm

3) 52 cm

26cm

13cm

Preflight 19.3

Image from mirror becomes object for eye!


Multiple LensesImage from lens 1 becomes object for lens 2 1

f1 f2

2

Complete the Rays!!


Multiple Lenses: Magnification

f1 f2

do = 15 cm

f1 = 10 cm

di = 30 cm

f2 = 5 cm

L = 42 cm

do=12 cm

di = 8.6 cm

1m

2m 21mmmnet

1 2

Net magnification:mnet = m1 m2


Near Point, Far Point• Eye’s lens changes shape (changes f )

– Object at any do can have image be at retina (di = approx. 25 mm)

• Can only change shape so much• “Near Point”

– Closest do where image can be at retina

– Normally, ~25 cm (if far-sighted then further)

• “Far Point”– Furthest do where image can be at retina

– Normally, infinity (if near-sighted then closer)


If you are nearsighted...

Want to have (virtual) image of distant object, do = , at the far point, di = -dfar.

Too far for near-sighted eye to focus

dfarNear-sighted eye can focus on this!

Contacts form virtual image at far point – becomes object for eye.

do

(far point is too close)

flens =


Refractive Power of Lens

Diopter = 1/f where f is focal length of lens in

meters.

Person with far point of 5 meters, would need contacts with focal length –5 meters.

Doctor’s prescription reads:

1/(-5m) = –0.20 Diopters

If you are farsighted...

When object is at do, lens must create an (virtual) image at -dnear.

Want the near point to be at do.

Too close for far-sighted eye to focus

dnear

Far-sighted eye can focus on this!

do

Contacts form virtual image at near point – becomes object for eye.

(near point is too far)

flens =

If you are farsighted...

When object is at do, lens must create an (virtual) image at -dnear.

Want the near point to be at do.

cm 50f

Too close for far-sighted eye to focus

dnear

Far-sighted eye can focus on this!

do

Contacts form virtual image at near point – becomes object for eye.

(near point is too far)

1do

1

dnear

1

flens

f1

cm 501

cm 251


Preflight 19.4Two people who wear glasses are camping.

One of them is nearsighted and the other is farsighted. Which person’s glasses will be useful in starting a fire with the sun’s rays?


Preflight 19.4Two people who wear glasses are camping.

One of them is nearsighted and the other is farsighted. Which person’s glasses will be useful in starting a fire with the sun’s rays?

Farsighted person’s glasses are converging – like magnifying glass!


Angular SizePreflight 19.6, 19.7

• Angular size tells you how large the image is on your retina, and how big it appears to be.

• How small of font can you read? Highwire Caramel Apples Rabbits Kindergarten Hello Arboretum Halloween Amazing

Both are same size, but nearer one looks bigger.


Unaided Eye

Bring object as close as possible (to near point N)

How big the object looks with unaided eye.

**If is small and expressed in radians.

Nho

Nho)tan(

object

N

h0


/

hi

di

ho

do

Magnifying glass produces virtual image behind object, allowing you to bring object to a closer do: and larger ’

Compare to unaided eye: :

h0

N

Ratio of the two angles is the angular magnification M:

M

ho do

ho N

Ndo

Magnifying Glass

/object

virtual image

hi ho

di

do

magnifying glass

For thelens:

1do

1di

1f

1do

1f

1di

M lies between

Nf

andNf

1 and the shorter the

focal length, the greater the magnification M.

Angular Magnification M=N/do

M =

/object

virtual image

hiho

do

magnifying glass

(N = near point distance from eye.)

di

For max. magnification, need image at N,so set di = -N:

For thelens:

1do

1di

1f

1do

1f

1di

M lies between

Nf

andNf

1 and the shorter the

focal length, the greater the magnification M.

1f

1do

1f

1N

1do

=For max. magnification, need image at N:

so set di = -N: di < -N

Angular Magnification M=N/do

M = 25/10 + 1 = 3.5

/object

virtual image

hiho

do

magnifying glass

(N = near point distance from eye.)

di


See you next class!

• Read Sections 25.1, 3-4

Documents

Physics 102: Lecture 19, Slide 1 Today’s Lecture will cover textbook sections 23.9, 24.1, 3-4, 6 Physics 102: Lecture 19 Lenses and your EYE Ciliary Muscles