• textbook sections 27-1 – 27-3

Physics 1161: Lecture 23Lenses and your EYE

Ciliary Muscles

Parts of the Eye

Review of LensesPreflight 23.11

P.A.

F

Focal point determined by geometry and Snell’s Law:

n1 sin(q1) = n2 sin(q2)

Fat in middle = ConvergingThin in middle = DivergingLarger n2/n1 = more bending, shorter focal length.n1 = n2 => No Bending, f = infinity

Lens in water has _________ focal length!

n1<n2

Review of LensesPreflight 23.11

P.A.

F

Focal point determined by geometry and Snell’s Law: n1 sin(q1) = n2 sin(q2)

Fat in middle = ConvergingThin in middle = DivergingLarger n2/n1 = more bending, shorter focal length.n1 = n2 => No Bending, f = infinity

Lens in water has larger focal length!

n1<n2

Preflight 23.7A 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?

1. Only the lower half will show on screen2. Only the upper half will show on screen3. The whole object will still show on screen

48%40%12%

Preflight 23.7A 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.

Preflight 23.7Still see entire image (but dimmer)!

Two very thin converging lenses each with a focal length of 20 cm are are placed in contact. What is the focal length of this compound lens?

1 2 3

44%

38%

19%

1. 10 cm2. 20 cm3. 40 cm

Two very thin converging lenses each with a focal length of 20 cm are are placed in contact. What is the focal length of this compound lens?

1 2 3

94%

0%6%

1. 10 cm2. 20 cm3. 40 cm

Amazing Eye

• One of first organs to develop.• 100 million Receptors

– 200,000 /mm2

– Sensitive to single photons!• http://hyperphysics.phy-astr.gsu.edu/hbase/vision/reti

na.html#c2

Ciliary Muscles

Digital Camera10 million6,500 /mm2

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

1 2 3 4

56%

6%6%

31%

1. Lens2. Cornea3. Retina4. Cones

Ciliary Muscles

Cornea n= 1.38

Lens n = 1.4

Vitreous n = 1.33

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

1 2 3 4

13%6%

19%

63%

1. Lens2. Cornea3. Retina4. Cones

Ciliary Muscles

Cornea n = 1.38

Lens n = 1.4

Vitreous n = 1.33

Lens 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

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 23.9

12%

56%

32%

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 23.9

Image from mirror becomes object for eye!

Multiple LensesImage from lens 1 becomes object for lens 2

1

f1 f2

2

Complete the Rays to locate the final image.

Multiple LensesImage from lens 1 becomes object for lens 2

1

f1 f2

2

Multiple Lenses: Magnification

f1 f2

do = 15 cm

f1 = 10 cm

di = 30 cmf2 = 5 cm

L = 42 cm

do=12 cm

di = 8.6 cm

1i

o

dm

d

2

8.6

12

cmm

cm

1 2 1.4netm mm

1 2

Net magnification: mnet = m1 m2

30

15

cm

cm 2

.717

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)

Preflight 23.10Two 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 68%Nearsighted 32%

Preflight 23.10Two 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 Size

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

qq

qq

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 q is small and expressed in radians.

Nho

Nho)tan(

q

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 q’

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

The focal length of the lens of a simple camera is 40 mm. In what direction must the lens be moved to “change the focus of the camera” from a person 25 m away to a person 4.0 m away? i.e. does the image distance increase or decrease?

1 2

38%

63%

1. Away from the film2. Towards the film

The focal length of the lens of a simple camera is 40 mm. In what direction must the lens be moved to change the focus of the camera from a person 25 m away to a person 4.0 m away? ? i.e. does the image distance increase or decrease?

1 2

63%

38%

1. Away from the film2. Towards the film