PH 222-2C Fall 2012

ImagesLectures 24-25

Chapter 34(Halliday/Resnick/Walker, Fundamentals of Physics 8th edition)

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Chapter 34

Images

One of the most important uses of the basic laws governing light is the production of images. Images are critical to a variety of fields and industries ranging from entertainment, to security, to medicine.

In this chapter we define and classify images, and then classify several basic ways in which they can be produced.

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Image: A reproduction derived from light.

Real Image: Light rays actually pass through image, really exist in space (or on a screen for example) whether you are looking or not.

Virtual Image: No light rays actually pass through image. Only appear to be coming from image. Image only exists when rays are traced back to perceived location of source.

Two Types of Images

object lensreal image

object mirror virtual image

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Light travels faster through warm air warmer air has smaller index of refraction than colder air refraction of light near hot surfaces.

For observer in car, light appears to be coming from the road top ahead, but is really coming from the sky.

A Common Mirage

Fig. 34-1

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Plane mirror is a flat reflecting surface.

Plane Mirrors, Point Object

Fig. 34-2

Fig. 34-3

Ib Ob

Identical triangles

Plane Mirror: i p Since I is a virtual image, i < 0. 5

Each point source of light in the extended object is mapped to a point in the image.

Plane Mirrors, Extended Object

Fig. 34-4 Fig. 34-5

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Your eye traces incoming rays straight back, and cannot know that the rays may have actually been reflected many times.

Plane Mirrors, Mirror Maze

Fig. 34-6

1

23

456

78

9

12

34

56

78

9

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Plane mirror concave mirror1. Center of curvature C:

in front at infinity in front but closer2. Field of view - the extent of the scene that is reflected to observer

wide smaller3. Image

i=p |i|>p 4. Image height

image height = object height image height > object height

Fig. 34-7

Plane mirror convex mirror1. Center of curvature C:

in front at infinity behind mirror and closer2. Field of view

wide larger3. Image

i=p |i|<p 4. Image height

image height = object height image height < object height

Spherical Mirrors, Making a Spherical Mirror

concave

plane

convex

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Spherical Mirrors, Focal Points of Spherical Mirrors

Fig. 34-8

concave convex

Spherical Mirror:12

f r

r > 0 for concave (real focal point)r < 0 for convex (virtual focal point) 9

Start with rays leaving a point on object, where they intersect, or appear to intersect, marks the corresponding point on the image.

Images from Spherical Mirrors

Fig. 34-9

Real images form on the side where the object is located (side to which light is going). Virtual images form on the opposite side.

Spherical Mirror:1 1 1p i f Lateral Magnification:

'hmh

Lateral Magnification:imp

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Locating Images by Drawing Rays

Fig. 34-10

1. A ray that is parallel to central axis reflects through F.2. A ray that reflects from mirror after passing through F emerges parallel to central axis.3. A ray that reflects from mirror after passing through C returns along itself.4. A ray that reflects from mirror after passing through c is reflected symmetrically about the

central axis. 11

Proof of the Magnification Equation

Fig. 34-10

Similar triangles (are angles same?)

, ,

(magnification)

de cd decd i ca p mab ca ab

imp

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Spherical Refracting Surfaces

Fig. 34-11

Real images form on the side of a refracting surface that is opposite the object (side to which light is going). Virtual images form on the same side as the object.

Spherical Refracting Surface: 1 2 2 1n n n np i r

When object faces a convex refracting surface r is positive. When it faces a concave surface, r is negative. CAUTION: This is reverse of mirror sign convention! 13

Fig. 34-13

Converging lens

Diverging lens

Thin Lens:1 1 1f p i Thin Lens in Air:

1 2

1 1 11nf r r

Lens only can function if the index of the lens is different from that of its surrounding medium.

Thin Lenses

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Images from Thin Lenses

Fig. 34-14

Real images form on the side of a lens that is opposite the object (side to which light is going). Virtual images form on the same side as the object.

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1. A ray initially parallel to central axis will pass through F2.2. A ray that initially passes through F1, will emerge parallel to central axis.3. A ray that initially is directed toward the center of the lens will emerge from the lens

with no change in its direction (the two sides of the lens at the center are almost parallel).

Locating Images of Extended Objects by Drawing Rays

Fig. 34-15

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Image formation by a converging lens

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19

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Two-Lens System

1. Let p1 be the distance of object O from Lens 1. Use equation and/or principle rays to determine the distance to the image of Lens 1, i1.

2. Ignore Lens 1, and use I1 as the object O2. If O2 is located beyond Lens 2, then use a negative object distance p1. Determine i2 using the equation and/or principle rays to locate the final image I2.

Lens 1 Lens 2

p1

OI1

i1

O2

p2

I2

i2

1 2The net magnification is: M m m21

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The human eye

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24

25

The refractive power of a lens. The diopter.

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Contact lens should bring the image of the object positioned at the near point of normal eye (0.25m) to the near point of farsighted eye (0.80m).

=+0.36 m; refractive power = 1/0.36 m = 2.75 Diopters

Focal point of contact lens

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Optical Instruments, Simple Magnifying Lens

Fig. 34-17

You can make an object appear larger (greater angular magnification) by simply bringing it closer to your eye. However, the eye cannot focus on objects closer than the near point: pn~25 cmBIG & BLURRY IMAGE

A simple magnifying lens allows the object to be placed close by making a large virtual image that is far away.

'

and '25 cm

m

h hf

Simple Magnifier:

25 cmmf

Object at F1

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Fig. 34-18

Optical Instruments, Compound Microscope

obob

ob ey

since and

25 cm magnification compounded (microscope)

i sm i s p fp f

sM mmf f

I close to F1’O close to F1

Mag. Lens

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Optical Instruments, Refracting Telescope

Fig. 34-19

eyob ey

ob ob ey

ob

ey

' ', ,

(telescope)

h hmf f

fmf

I close to F2and F1’

Mag. Lens

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Three Proofs, The Spherical Mirror Formula

Fig. 34-20

and 212

,

1 22

122

1

2

1ac ac acp

ac ac ac accO p cC r

ac acCI

i f

i

f r r f

p i f

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Three Proofs, The Refracting Surface Formula

Fig. 34-21

1 1 2 2

1 1 2 2 1 2

1 2

1 2

1

1 2

2 2 1

1 2 2 1

2 1

sin sin if and are small

and

; ;

n n n n

a

n nn n

n n

ac ac acp r i

n n n np i r

c ac acn n n np i r

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Fig. 34-22

1 2 2 1

1 2

where 1 and

'' '1 1 ; if small

1 1 Eq. 34-22' ' '

1 1 Eq. 34-25' '' ''

Eq. 34-22 Eq. 34

' '' ''1 1 1 1 1 1 1 11 1

' '' ' '-25

' ' ''

n n n np i r

n n n

p i Ln n L

i L i r

n np i r r p

n np i r

n n

i r

i i

r

r

Three Proofs, The Thin Lens Formulas

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