1

Optics•Electromagnetic spectrum•polarization•Laws of reflection and refraction•TIR

–Images–Mirrors and lenses–Real/virtual, inverted/straight, bigger/smaller

2

hitt

The Sun is about 1.5 X 1011 m away. The time for light to travel this distance is about:

A. 4.5 x 1018 s

B. 8 s

C. 8 min

D. 8 hr

E. 8 yr

3

The index of refraction n encountered by light in any medium except vacuum depends on the wavelength of the light. So if light consisting of different wavelengths enters a material, the different wavelengths will be refracted differently chromatic dispersion

Chromatic Dispersion

33-

Fig. 33-19Fig. 33-20

n2blue>n2red

Chromatic dispersion can be good (e.g., used to analyze wavelength composition of light) or bad (e.g., chromatic aberration in lenses)

4

Chromatic Dispersion

33-

Fig. 33-21

Chromatic dispersion can be good (e.g., used to analyze wavelength composition of light)

or bad (e.g., chromatic aberration in lenses)

prism

lens

5

Rainbows

33-

Fig. 33-22

Sunlight consists of all visible colors and water is dispersive, so when sunlight is refracted as it enters water droplets, is reflected off the back surface, and again is refracted as it exits the water drops, the range of angles for the exiting ray will depend on the color of the ray. Since blue is refracted more strongly than red, only droplets that are closer the the rainbow center (A) will refract/reflect blue light to the observer (O). Droplets at larger angles will still refract/reflect red light to the observer.

What happens for rays that reflect twice off the back surfaces of the droplets?

6

For light that travels from a medium with a larger index of refraction to a medium with a smaller medium of refraction n1>n1 2>1, as 1 increases, 2 will reach 90o (the largest possible angle for refraction) before 1 does.

Total Internal Reflection

33-

1 2 2sin sin 90cn n n

Fig. 33-24

n1

n2

Critical Angle:1 2

1

sinc

n

n

When 2> c no light is refracted (Snell’s Law does not have a solution!) so no light is transmitted Total Internal Reflection

Total internal reflection can be used, for example, to guide/contain light along an optical fiber

7

Polarization by Reflection

33-

Fig. 33-27

Brewster’s Law

Applications1. Perfect window: since parallel polarization

is not reflected, all of it is transmitted2. Polarizer: only the perpendicular

component is reflected, so one can select only this component of the incident polarization

1 2

1 2 2

90

sin sin

sin sin 90 cos

B r

B r

B B B

n n

n n n

Brewster Angle:1 2

1

tanB

n

n In which direction does light reflecting

off a lake tend to be polarized?

When the refracted ray is perpendicular to the reflected ray, the electric field parallel to the page (plane of incidence) in the medium does not produce a reflected ray since there is no component of that field perpendicular to the reflected ray (EM waves are transverse).

8

Chapter 34

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, security, and medicine

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

Images

34-

9

Image: a reproduction derived from light

Real Image: light rays actually pass through image, really exists 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

34-

object lensreal image

object mirror virtual image

10

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 sky.

A Common Mirage

34-

Fig. 34-1

11

Plane mirror is a flat reflecting surface.

Plane Mirrors, Point Object

34-

Fig. 34-2

Fig. 34-3

Ib Ob

Identical triangles

Plane Mirror: i p

Since I is a virtual image i < 0

12

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

Plane Mirrors, Extended Object

34-

Fig. 34-4 Fig. 34-5

13

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

Plane Mirrors, Mirror Maze

34-

Fig. 34-6

1

23

4

56

78

9

12

34

56

78

9

14

Plane mirror Concave Mirror

1. Center of Curvature C:

in front at infinity in front but closer

2. Field of view

wide smaller

3. Image

i=p |i|>p

4. Image height

image height = object height image height > object height

34-Fig. 34-7

Plane mirror Convex Mirror

1. Center of Curvature C:

in front at infinity behind mirror and closer

2. Field of view

wide larger

3. 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

15

Spherical Mirrors, Focal Points of Spherical Mirrors

34-

Fig. 34-8

concave convex

Spherical Mirror:1

2f r

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

16

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

34-

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 1

p i f Lateral Magnification:

'hm

h

Lateral Magnification:i

mp

17

Locating Images by Drawing Rays

34-

Fig. 34-10

1. A ray parallel to central axis reflects through F2. A ray that reflects from mirror after passing through F, emerges parallel to central axis3. A ray that reflects from mirror after passing through C, returns along itself4. A ray that reflects from mirror after passing through c is reflected symmetrically about the

central axis

18

Proof of the magnification equation

34-

Fig. 34-10

Similar triangles (are angles same)

, ,

(magnification)

de cd decd i ca p m

ab ca abi

mp

19

Spherical Refracting Surfaces

34-

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 n

p i r

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

2034-

Fig. 34-13

Converging lens

Diverging lens

Thin Lens:1 1 1

f p i Thin Lens in air:

1 2

1 1 11n

f r r

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

Thin Lenses

21

Images from Thin Lenses

34-

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.

22

Locating Images of Extended Objects by Drawing Rays

34-

Fig. 34-15

1. A ray initially parallel to central axis will pass through F22. A ray that initially passes through F1, will emerge parallel to central axis3. 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)

23

Two Lens System

34-

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 m

24

Optical Instruments, Simple Magnifying Lens

34-

Fig. 34-17

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 that 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 h

f

Simple Magnifier:

25 cmm

f

Object at F1

2534-

Fig. 34-18

Optical Instruments, Compound Microscope

obob

ob ey

since and

25 cm magnification compounded (microscope)

i sm i s p f

p f

sM mm

f f

I close to F1’O close to F1

Mag. Lens

26

Optical Instruments, Refracting Telescope

34-

Fig. 34-19

eyob ey

ob ob ey

ob

ey

' ' , ,

(telescope)

h hm

f f

fm

f

I close to F2 and F1’

Mag. Lens

27

Three Proofs, The Spherical Mirror Formula

34-

Fig. 34-20

and 2

1

2

,

12

2

1 1 1

2

22

ac ac ac ac

cO p cC r

ac ac

CI i

f r

ac ac ac

p i

r f

pf i f

28

Three Proofs, The Refracting Surface Formula

34-

Fig. 34-21

1 1 2 2

1 1 2 2 1 2

1 2

1 2

1 2 2 1

1 2 2

1 2 2 1

1

sin sin

if and are small

and

; ;

n n n n

ac ac acn n n

n n

n n

n

np

n

ac ac ac

p r i

n n n n

p i

i

r

r

2934-

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 1

1 1' '' ' '

-25' ' ''

n n n n

p i r

n n n

p i L

n nL

i L i r

n np i r r p

n n

p i r

n n

i r

i i

r

r

Three Proofs, The Thin Lens Formulas

30

hitt

A point source emits electromagnetic energy at a rate of 100W. The intensity 10 m from the

source is:

A. 10 W/m2

B. 1.6 W/m2

C. 1 W/m2

D. 0:024 W/m2

E. 0:080 W/m2