Physics 102: Lecture 19, Slide 1 Physics 102: Lecture 19 Lenses and your EYE Ciliary Muscles
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Dec 19, 2014

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Physics 102: Lecture 19, Slide 1

Physics 102: Lecture 19Lenses and your EYE

Ciliary Muscles

Physics 102: Lecture 19, Slide 2

3 Cases for Converging Lenses

Image Object

UprightEnlargedVirtual

Inside F

ImageObject

InvertedEnlargedReal

BetweenF & 2F

Object

Image

InvertedReducedReal

Past 2F

Physics 102: Lecture 19, Slide 3

Only 1 Case for Diverging Lenses

F

F

Object

P.A.

Image is always virtual, upright, and reduced.

Image

Physics 102: Lecture 19, Slide 4

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.

Physics 102: Lecture 19, Slide 5

Lens EquationSame as mirror 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

Physics 102: Lecture 19, Slide 6

Multiple LensesImage from lens 1 becomes object for lens 2 1

f1 f2

2

Lens 1 creates a real, inverted and enlarged image of the object.

Lens 2 creates a real, inverted and reduced image of the image from lens 1.

The combination gives a real, upright, enlarged image of the object.

Physics 102: Lecture 19, Slide 7

f1 f2

First find image from lens 1.

cm 1011

cm 151

idcm 30id

do = 15 cm

f1 = 10 cm

di = 30 cm

f2 = 5 cm

1 2

Multiple Lenses: Image 1

Physics 102: Lecture 19, Slide 8

f1 f2

Now find image from lens 2.

cm 511

cm 121

idcm 6.8id

do = 15 cm

f1 = 10 cm

di = 30 cm

f2 = 5 cm

L = 42 cm

do=12 cm

di = 8.6 cm

Notice that do could be negative for second lens!

1 2

Multiple Lenses: Image 2

Physics 102: Lecture 19, Slide 9

f1 f2

do = 15 cm

f1 = 10 cm

di = 30 cm

f2 = 5 cm

L = 42 cm

do=12 cm

di = 8.6 cm

21530

1 m 72.12

6.82 m

43.121 mmmnet

1 2

Net magnification:mnet = m1 m2

Multiple Lenses: Magnification

Physics 102: Lecture 19, Slide 10

The Eye• One of first organs to develop.• ~100 million Receptors • ~200,000 /mm2

• Sensitive to single photon!• Candle from 12 miles

Ciliary Muscles

Physics 102: Lecture 19, Slide 11

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

Physics 102: Lecture 19, Slide 12

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:

Physics 102: Lecture 19, Slide 13

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:

Physics 102: Lecture 19, Slide 14

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

– Object at any do should 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)

Physics 102: Lecture 19, Slide 15

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

Physics 102: Lecture 19, Slide 16

If you are nearsighted...

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

1do

1

dfar

1

flens

1

1

dfar

1

flens

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 = - dfar

Physics 102: Lecture 19, Slide 17

Refractive Power of Lens

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

meters.Example: • My prescription reads -6.5 diopters• flens = -1/6.5 = -0.154 m = -15.4 cm (a diverging lens)• dfar = 15.4 cm (!)

flens = - dfar

Physics 102: Lecture 19, Slide 18

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

Far-sighted eye can focus on this!

do

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

dnear

(near point is too far)

1do

1

dnear

1

flens

f1

cm 501

cm 251

Physics 102: Lecture 19, Slide 19

Farsightedness

• Near point dnear > 25 cm

• To correct, produce virtual image of object at d0 = 25 cm to the near point (di = dnear)

1 1 1

o i lensd d f

1 1 1

o near lensd d f

1 1 1

25 near lensd f

Example: • My near prescription reads +2.5 diopters• flens = +1/2.5 = 0.4 m = 40 cm• therefore dnear = 67 cm (with my far correction)

Physics 102: Lecture 19, Slide 20

ACT/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?

1. nearsighted2. farsighted

Physics 102: Lecture 19, Slide 21

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.

Physics 102: Lecture 19, Slide 22

Angular size: Unaided Eye

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

How big the object looks with unaided eye.

**If is small and expressed in radians.

o

near

h

d tan( ) o

near

h

d

object

dnear

h0

Physics 102: Lecture 19, Slide 23

/

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: :

0

near

h

d

Ratio of the two angles is the angular magnification M: o o near

o near o

h d dM

h d d

Magnifying Glass

/object

virtual image

hi ho

di

do

magnifying glass

Physics 102: Lecture 19, Slide 24

M = dnear /d0 = dnear/f +1

1 1 1

o neard f d

For max. magnification, put image at dnear:

so set di = -dnear:

Angular Magnification

/object

virtual image

hiho

do

magnifying glass

(dnear = near point distance from eye.)

di

Smaller f means larger magnification

o o near

o near o

h d dM

h d d

For thelens: 1

do 1

di1

f 1

do1

f 1di

Physics 102: Lecture 19, Slide 25

Summary

• Lenses– Lens equation & magnification

– Multiple lenses

• The eye– Near & far point

– Nearsightedness & farsightedness & corrective lenses

– Angular magnification

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