Unit 3: Light

Electromagnetic Radiation (i.e., light)

--

--

E

B

waves of oscillating electric (E)& magnetic (B) fields

source is… vibrating electric charges

dir. ofwavetravel

E

Bv

E

vBE B

v

B

Ev

EB

v B

Ev

radio waves

IR

visible

UV

X-rays

gamm

a rays

cosmic rays

electromagnetic spectrum

ROYGBV

large l

low f

low energy

small l

high f

high energy

Most of the energy the Earthreceives from the Sun is

in the form of visible light.

microw

aves

Albert Michelson (1879)

-- first to get an accuratevalue for speed of light

speed of light invacuum (and air)

is constant

c = 3.00 x 108 m/s

c = f l

The Speed of Light

c = f l

Find the wavelength of a B-104 radiowave (FM 104.1, with f = 104.1 MHz).

fc

Hz 10 x 104.1m/s 10 x 3.00

6

8

= 2.88 m

c = f l

Find the wavelength of a WGN radiowave (AM 720, with f = 720 kHz).

fc

Hz 10 x 720m/s 10 x 3.00

3

8

= 420 m

light year:

MILKY WAY GALAXY

the distance light travels in one year

Earth

16,000 ly 3,000 ly

30,000 ly

100,000 ly

(~100 x 109 stars)

(T = 200 x 106 yrs.)

photos of variousspiral galaxies

Behavior of Light

For radiant objects, the brightness we sense dependson two factors: 1.

2.

r = 1 m r = 2 m r = 3 m

2r1

Brightness

the rate of energy emissionthe distance we are from the object

“bright” 1/4 as bright 1/9 as bright

Light-Material Interaction

transparent: most light rays travel through material and remain parallel

e.g., glass, water

-- objects on “other side”can be discerned clearly

light rays remainparallel

transparentmaterial

Light-Material Interaction (cont.)

e.g.,

translucent: many light rays travel through material, but the material scatters them

frosted glass

-- objects on “other side”CAN’T be discerned clearly

light rays DO NOTremain parallel

translucentmaterial

Light-Material Interaction (cont.)

e.g.,

opaque: essentially no light travels through material; all light is reflected and/or absorbed

SURFACE

normal:

Qr Qi

Qr: angle of reflectionQi: angle of incidence

Reflection

Qr and Qi are measured…

Law of Reflection: Qr = Qi

relative to normal

incident ray reflected ray

to surface imaginary line

Types of Reflection

specular diffuse Compared tolight l, surfaceirregularities are… …SMALL …LARGE

visible light +mirror

radio waves +like…everything.

visible light +clothing

An open-mesh radiotelescope acts like adiffuse reflector to visible light waves because those wave-lengths are smallcompared to the dimensions of the partsof the telescope. However, the telescopeacts as a specularreflector to radio waves,which have much largerwavelengths, on the order of tens orhundreds of meters.

toilet paper printer paper

human skincat hair

Spherical Mirrors convex mirror:

P.A. = principal axis C = center of curvature F = focal point f = focal length R = radius of curvature = 2f

P.A. (front of mirror) (behind mirror)

F C

f

R

reflectiveside ofmirror

concave mirror:

P.A. (front of mirror) (behind mirror)

F C

f

R

reflectiveside ofmirror

Mirror Ray Diagrams

Line up top of object…

Draw ray from top of object to mirror.

The light ray reflecting back to the left will be

along a line connecting pt. of intersection w/mirror…

// to P.A.w/F.

w/C.

…and F.

// to P.A.

…and C.

real image: rays actually intersect; can project iton a screen

virtual image: rays appear to intersect, but don’t; cannot project it on a screen

Only two rays are needed to locate the image.

F Cf

SMALLER;UPRIGHT;VIRTUAL

C F

f

INVERTED;REAL

C F

f

NO IMAGE

C F

f

LARGER;UPRIGHT;VIRTUAL

Mirror Variables

p = object dist. always + always on left

f = focal length

q = image dist. +, real, left –, virtual, right

h = object height always + always upright

h’ = image height +, upright –, inverted

R = radius of curvature

concave, +convex, –

measured L/R fromintersection ofP.A. and mirror

measured UP/DOWNfrom P.A.

F C

R (–)

C F

p (+)

q (–)

h (+)h’ (+)

h’ (–)

h (+)

f (+)q (+)

p (+)

f (–)

Mirrors: Ray Diagrams and Mirror Calculations

Directions: For each problem, find the focal length; be sure to use (+) or (–), as appropriate. Then use a ruler and straight-edge to draw a ray diagram to find the location of each image. Use the ruler to measure the image distance qray and image height h’ray. Next, calculate the image distance qeq and image height heq using equations discussed in class. Also, calculate the magnification M using qeq. Finally, calculate the percent error of your ray diagram (rounded to the nearest 0.1%) using the equation:

% error = x 100qeq – qray

qeq

Value Prob. 7

R 12.60 cm

f

p 2.40 cm

h 1.50 cm

qray

h’ray

qeq

h’eq

M

% error

7.

+6.30 cm

F

h

p

Mirror Equation and Magnification

f1

q1

p1

pq-

hh'

M

p = object dist. always + always on left

f = focal length

q = image dist. +, real, left –, virtual, right

h = object height always + always upright

h’ = image height +, upright –, inverted

R = radius of curvature

concave, +convex, –

measured L/R fromintersection ofP.A. and mirror

measured UP/DOWNfrom P.A.

q = ?

Concave mirror has radius of mag. 55 cm. Object is

84 cm from mirror, is 24 cm tall. Find focal length,image distance, and magnification. Describe

image.R = +55 cmp = 84 cmh = 24 cm

f = +27.5 cm

M = ?

f1

q1

p1

p1

- f1

q1

p

1 f1

1 q

cm 841 cm 27.5

11

q

= 41 cm

cm 84cm 41 -

pq-

M = –0.49

SMALLER;REAL;INVERTED;on the left

C F

+27.5 cmSMALLER:INVERTED;

REAL

q = +41 cm

+55 cm

+84 cm

(h’ = –11.7 cm)

h = +24 cm

M = –0.49

Concave mirror has radius of mag. 55 cm. Object is

84 cm from mirror, is 24 cm tall. Find focal length,image distance, and magnification. Describe

image.

= –10.3 cm

Concave mirror has focal length of mag. 36.0 cm.Object has height 18.0 cm, is 8.00 cm from mirror.Describe image.

f = +36.0 cmh = 18.0 cmp = 8.00 cm

8.001 36.0

11

pq-

M 8.0010.3) (- -

= 1.29LARGER;UPRIGHT;VIRTUAL;on the right

Concave mirror with object in front of F? “LUV.”

p1 f

11

q

h = 18.0 cm

LARGER;UPRIGHT;VIRTUAL

F

+36.0 cm

+8.00 cm

q = –10.3 cm

M = 1.29

h’ = 23.2 cm

Concave mirror has focal length of mag. 36.0 cm.Object has height 18.0 cm, is 8.00 cm from mirror.Describe image.

Concave mirror has focal length of mag. 30 cm. Objectof height 10 cm is at mirror’s focal point. Describe image.

301 30

11

p

1 f1

1 q

f = +30 cm h = +10 cm p = +30 cm

No image.

C F

f

“I like your teddy.”

Convex mirror has radius of mag. 64.0 cm. Object hasheight 24.0 cm, is 30.0 cm from mirror. Describe image.

R = –64.0 cm h = +24.0 cm p = +30.0 cm

So… f = –32.0 cm

= –15.5 cm30

1 32-1

1

pq-

M 3015.5) (- -

= 0.517

h’ = 0.517 (24 cm) = 12.4 cm

SMALLER;UPRIGHT;VIRTUAL;on the right

p1 f

11

q

Convex mirror? “SUV.”

F Cf = –32 cm

q (–)

h = +24 cmh’ (+)

p = +30 cm

q = –15.5 cm

M = 0.517

h’ = 12.4 cm

SMALLER;UPRIGHT;VIRTUAL;on the right

Convex mirror has radius of mag. 64.0 cm. Object hasheight 24.0 cm, is 30.0 cm from mirror. Describe image.

Parabolic Mirrors

Drawback ofspherical mirrors:

-- resulting blurring =

-- remedied using parabolic mirrors

rays // to, and far from, P.A. areNOT reflected through F

C

spherical aberration

Examples of Parabolic Mirrors

flashlight

headlight

radiotelescope

satellitedish

Color

White light contains all visible ls.

Objects that “are”…

White

Colored

Black

reflect visible ls,and absorb

all

some

no

none

some

all

WHITE

R O Y G B V

Primary colors of light(NOT pigments):

Light is additive.

Two colors of light are complimentary if,when added, they produce white light.

red, green, blue

Cya

n

Magenta

Yellow

G

B

W

RR + G + B = W

W = B + Y

W = R + C

W = G + M

R+G

B+G

R+B

Pigments are subtractive.

blue pigment (incident W light)

yellow pigment

blue pigment + yellow pigment

R O Y G B V

R O Y G B V

R O Y G B V

G

Y

B

i.e., paints or dyes

Polarization

Normally, light is unpolarized;

i.e.,

polarized light: orderly vibrations

E and B fields areoriented randomly

(half as bright) unpolarized

lightpolarizing

filterpolarized light

(blocks )

glare: horizontally-polarized light reflected off horizontal surfaces

Sun

unpolarized

horizontally polarized (glare)

-- horiz. surface acts as a polarizer

JENNY

-- sunglasses are vertically polarized

“Polarized lenses are high-performance sunwear. Polarization blocks glare caused by light reflections and provides 100% UV protection. Polarized lenses allow you to see with greater clarity, improved color perception, and increased comfort for all your outdoor activities.” (from an advertisement for polarized sunglasses)

c = 3.00 x 108 m/s

c = f l

f1

q1

p1

pq-

hh'

M

R = 2 f

Refraction and Lenses

refraction: the bending of light as it travels at anangle from one transparent medium into another

When light goes from a… optically dense medium less

more

to a… optically dense medium, less

more

it bends… the normal. away fromtoward

It has been found that light obeysthe principle of least time.

AIR (less dense)

AIR (less dense)

GLASS (more dense)

angle of incidence, Qi

normal

angle of refraction, Qr

refracted ray Qi for 2nd boundary

Qr for 2nd boundary

incident ray

AIR (less dense)

AIR (less dense)

GLASS (more dense)

“ZAP!”

“LASER…”

“Costingone MILLION

dollars…”

Index of Refraction

n = index of refraction;c = 3.00 x 108 m/s;v = speed of light in mat’l (m/s)

In general...

vc

n

n > 1.000. airspace n1.000n

Snell’s Law

rrii sin n sin n

incidentmedium (ni)

refractingmedium (nr)

Qi

Qr

http://www.haverford.edu/physics/songs/resnell.mp3

Light in air is incident on diamond (n = 2.419)at 43.0o. Find the angle of refraction.

43.0o

Qr

n = 1.000

n = 2.419

rrii sin n sin n

i

r

i1-r sin

nn

sin

ir

ir sin

nn

sin

43 sin 2.4191.000

sin 1- = 16.4o

= 1.37 x 108 m/s

Light in water is incident on cubic zirconia at 31.5o. Angle of refraction is 18.5o. Water’s index of refractionis 1.333. Find speed of light in cubic zirconia.

31.5o

18.5o

n = 1.333

nr = nc.z. = ?

c.z.c.z. v

c n

rc.z.iOH sin n sin n2

2.195

m/s 10 x 3.00 v

8

c.z.

1.333 sin 31.5 = nc.z. sin 18.5

nc.z. = 2.195

Lenses

Types of Lenses

converging lenses diverging lenses

double convex double concave

plano-convex plano-concave

concavo-convex convexo-concave

Lens Ray Diagrams

First… 1. Draw a centerline vertically through lens. 2. Draw two F’s, measured from centerline.

F F F F

Line up top of object…

Draw ray from top of

object to lens’

centerline. Keeping in mind the type of lens…

…the light ray refracts and continues toward the right

along a line connecting pt. of intersection w/lens…

// to P.A.w/F.

w/center of lens

…and F.

// to P.A.

NO; just keep going.

real image: rays actually intersect; can project iton a screen

virtual image: rays appear to intersect, but don’t; cannot project it on a screen

Only two rays are needed to locate the image.

A camera uses a lens to produce a real (upside-down) image on a pieceof film. The eye uses, in effect, two lenses – the cornea and “the lens” –to produce an upside-down, real image on the light-sensitive retina.

p = object dist. always + always on left

f = focal length

q = image dist. +, real, RIGHT –, virtual, LEFT

h = object height always + always upright

h’ = image height +, upright –, inverted

R = radius of curvature

converging, +diverging, –

measured L/R fromcenterline of lens

measured UP/DOWNfrom P.A.

Lens Variables

Thin Lens Equation and Magnification

f1

q1

p1

pq-

hh'

M

p = object dist. always + always on left

f = focal length

q = image dist. +, real, RIGHT –, virtual, LEFT

h = object height always + always upright

h’ = image height +, upright –, inverted

R = radius of curvature

converging, +diverging, –

measured L/R fromcenterline of lens

measured UP/DOWNfrom P.A.

Diverging lens has focal length ofmag. 10.0 cm. A wiener-dog puppy15.0 cm tall is 22.0 cm from lens.Describe image.

(f = –10.0 cm; h = +15.0 cm; p = +22.0 cm)

f1

q1

p1

p1

- f1

q1

p1 f

11

q

22

1 10-1

1

= – 6.88 cm

pq-

M 226.88 - -

= 0.313 image is uprightimage is smaller

SUV; on the left

image is virtual

Converging lens has focal length of mag. 7.7 cm. A 0.38 cm-tall real image of a thimbleis formed 9.1 cm from lens. How far fromlens is thimble? How tall is thimble?

f = +7.7 cm

q = +9.1 cm

h’ = –0.38 cm f1

q1

p1

q1

- f1

p1

q1 f

11

p

9.1

1 7.71

1

= 50. cm

h' -q

M h p

0.38 - 9.1

h 50 h = 2.1 cm

p

h

Correcting Vision with Lenses

farsighted nearsighted

What is in focus?

retina cornea

incomingrays fromfar-away objects

incomingrays fromnearby objects

What is blurred?

How do we correct the condition?

nearbyobjects

far-away objects

converging lens diverging lens

retina

cornea

incident light rays

“What happensin LASIK?”

Total Internal Reflection

Light traveling through water (n = 1.333) is incidenton the water/air boundary at 48.606626o. Find angleof refraction. sin n sin n rrii

Qr = 90.0o

1.333 sin 48.606626 = 1.000 sin Qr

At Qi < 48.6o, light in water ispartially reflected and partiallyrefracted. At Qi = 48.6o, the refracted beam has a Qr of 90o.At Qi > 48.6o, NO light isrefracted; ALL light is reflected,with the angle of incidence beingequal to the angle of reflection.

The Critical Angle, Qc the Qi for which Qr = 90o

refracted rays normal

reflected ray

boundary

(MORE opticallydense

medium)

(LESS opticallydense

medium)

Qc

= 53.23o

Equation for the Critical Angle:

Find critical angle for light traveling fromflint glass (n = 1.900) to crown glass (n = 1.522).

i

r1-c n

n sin

i

r1-c n

n sin

1.9001.522

sin 1-

crownglass

flintglass

total internal reflection

-- no light escapes from the MORE optically dense medium

-- light is incident from a MORE optically dense medium to a LESS optically dense medium at Qi > Qc

e.g., total internal reflection in fiber optic cables

light entering light exiting

demonstrations oftotal internal reflection

Examples of Refraction

atmospheric refraction

We continue to see the Sun after it has set.

-- n increases in lower atmosphere,

so light bends continually until it

reaches the observer

Earth

image

object

actual pathof light

o , o , NORMAL, ILLINOIS Applications Dept.Location: W088 59, N40 31 Rise and Set for the Sun for 2011 20392-5420 Central Standard Time Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. Day Rise Set Rise Set Rise Set Rise Set Rise Set Rise Set Rise Set Rise Set Rise Set Rise Set Rise Set Rise Set h m h m h m h m h m h m h m h m h m h m h m h m h m h m h m h m h m h m h m h m h m h m h m h m01 0719 1640 0706 1714 0630 1747 0540 1820 0455 1851 0428 1920 0429 1930 0453 1911 0523 1828 0552 1739 0626 1653 0700 163002 0719 1641 0705 1715 0629 1748 0538 1821 0454 1853 0427 1921 0430 1930 0454 1910 0524 1827 0553 1737 0627 1652 0701 163003 0720 1642 0704 1716 0627 1749 0537 1822 0453 1854 0427 1922 0430 1930 0455 1909 0525 1825 0554 1735 0628 1651 0702 162904 0720 1642 0703 1717 0626 1751 0535 1823 0452 1855 0427 1922 0431 1930 0456 1908 0526 1823 0555 1734 0629 1649 0703 162905 0720 1643 0702 1719 0624 1752 0534 1824 0450 1856 0426 1923 0431 1930 0457 1907 0527 1822 0556 1732 0630 1648 0704 162906 0720 1644 0701 1720 0622 1753 0532 1826 0449 1857 0426 1924 0432 1929 0458 1905 0528 1820 0557 1730 0631 1647 0705 162907 0719 1645 0700 1721 0621 1754 0530 1827 0448 1858 0426 1924 0432 1929 0459 1904 0529 1819 0558 1729 0633 1646 0706 162908 0719 1646 0658 1722 0619 1755 0529 1828 0447 1859 0426 1925 0433 1929 0500 1903 0530 1817 0559 1727 0634 1645 0706 162909 0719 1647 0657 1724 0618 1756 0527 1829 0446 1900 0425 1925 0434 1928 0501 1902 0531 1815 0600 1726 0635 1644 0707 162910 0719 1648 0656 1725 0616 1757 0526 1830 0445 1901 0425 1926 0434 1928 0502 1900 0532 1814 0601 1724 0636 1643 0708 162911 0719 1649 0655 1726 0614 1758 0524 1831 0444 1902 0425 1926 0435 1927 0503 1859 0533 1812 0602 1722 0637 1642 0709 162912 0718 1650 0654 1727 0613 1759 0523 1832 0443 1903 0425 1927 0436 1927 0503 1858 0534 1810 0603 1721 0639 1641 0710 162913 0718 1651 0652 1728 0611 1800 0521 1833 0442 1904 0425 1927 0437 1926 0504 1857 0535 1809 0605 1719 0640 1640 0711 163014 0718 1653 0651 1730 0610 1801 0519 1834 0441 1905 0425 1928 0437 1926 0505 1855 0535 1807 0606 1718 0641 1639 0711 163015 0717 1654 0650 1731 0608 1803 0518 1835 0440 1906 0425 1928 0438 1925 0506 1854 0536 1805 0607 1716 0642 1639 0712 163016 0717 1655 0649 1732 0606 1804 0516 1836 0439 1906 0425 1928 0439 1925 0507 1852 0537 1804 0608 1715 0643 1638 0713 163017 0717 1656 0647 1733 0605 1805 0515 1837 0438 1907 0425 1929 0440 1924 0508 1851 0538 1802 0609 1713 0644 1637 0713 163118 0716 1657 0646 1734 0603 1806 0513 1838 0437 1908 0425 1929 0440 1923 0509 1850 0539 1800 0610 1712 0646 1636 0714 163119 0716 1658 0645 1736 0601 1807 0512 1839 0436 1909 0425 1929 0441 1923 0510 1848 0540 1759 0611 1710 0647 1636 0715 163120 0715 1659 0643 1737 0600 1808 0510 1840 0435 1910 0425 1930 0442 1922 0511 1847 0541 1757 0612 1709 0648 1635 0715 163221 0714 1700 0642 1738 0558 1809 0509 1841 0435 1911 0426 1930 0443 1921 0512 1845 0542 1755 0613 1707 0649 1634 0716 163222 0714 1702 0640 1739 0557 1810 0508 1842 0434 1912 0426 1930 0444 1920 0513 1844 0543 1753 0614 1706 0650 1634 0716 163323 0713 1703 0639 1740 0555 1811 0506 1843 0433 1913 0426 1930 0445 1920 0514 1842 0544 1752 0615 1705 0651 1633 0717 163324 0712 1704 0638 1741 0553 1812 0505 1844 0432 1914 0426 1930 0446 1919 0515 1841 0545 1750 0617 1703 0652 1633 0717 163425 0712 1705 0636 1743 0552 1813 0503 1845 0432 1915 0427 1930 0446 1918 0516 1839 0546 1748 0618 1702 0653 1632 0718 163526 0711 1706 0635 1744 0550 1814 0502 1846 0431 1915 0427 1931 0447 1917 0517 1838 0547 1747 0619 1701 0655 1632 0718 163527 0710 1708 0633 1745 0548 1815 0501 1847 0430 1916 0427 1931 0448 1916 0518 1836 0548 1745 0620 1659 0656 1631 0718 163628 0709 1709 0632 1746 0547 1816 0459 1848 0430 1917 0428 1931 0449 1915 0519 1835 0549 1743 0621 1658 0657 1631 0719 163729 0708 1710 0545 1817 0458 1849 0429 1918 0428 1931 0450 1914 0520 1833 0550 1742 0622 1657 0658 1630 0719 163730 0708 1711 0543 1818 0457 1850 0429 1919 0429 1930 0451 1913 0521 1832 0551 1740 0623 1655 0659 1630 0719 163831 0707 1713 0542 1819 0428 1919 0452 1912 0522 1830 0625 1654 0719 1639 Add one hour for daylight time, if and when in use.

Examples of Refraction (cont.)

mirages

actual path of light

object

image

-- NOT an optical illusion; can be photographed

-- “water” on road is an image of the sky

Inferior mirages are formed when the air below the line of sight is warmerthan the air above. Inferior mirages are NOT stable (i.e., they shimmer)because of the constant mixingbetween the warm air below(which tends to rise) and thecooler air above (which tends tosink). Light reflecting off the object going toward the groundlevels off and then bendsback up to the eye-level of theobserver.

Superior mirages are formed when the air below the line of sight is colderthan the air above. This is called a temperature inversion, and is a fairlyrare occurrence. When superior mirages DO form, however, they tend tobe stable because the more-dense, cold air stays below the less-dense,warmer air. Depending on the observer’s distance from the object,superior mirages may be either upright (if the observer is farther away) or inverted (if the observer is closer).

Dispersion when polychromatic light is separated into its component ls

--

--

-- By convention, the accepted index of refraction for a material is for l = 589 nm.

occurs because different ls interactdifferently w/matter

n differs for different ls

Because n differs for different ls of light, the variousls traveling through a lens focus at slightly differentpoints.

resulting blurring =

-- reduced by...

chromatic aberration

F F

WHITE

R

V 589 nm

combining converging and

diverging lenses made from

different materials

Refraction, Dispersion, Reflection, and Rainbows

sunlight

raindrop

Sun

Various photos of rainbows

Sun

atmospheresliver of sunlight

at horizonLooking to the west at

a not-at-all-dusty horizon…

The Green Flash

(i.e., a horizon over an ocean)

The green flash is caused by the atmospheric dispersion of sunlight.Only a sliver of the Sun is still visible. The blue/violet rays are refracted“too much” and hit the ground before reaching the observer. The red/orange/yellow rays aren’t refracted enough and pass over the observer’sline of sight. The green wavelengths are refracted “just right,” resulting in the ephemeral green flash. Because the many dust particlesthat are kicked up over land areas during the day block all wavelengthsexcept oranges/reds, green flashes are most often seen over VERY wideexpanses of water (i.e., oceans). Therefore, your chances of seeing agreen flash in Illinois are slim-to-none.

a green flash from the Moon (!!!)

vc

n

rrii sin n sin n

f1

q1

p1

pq-

hh'

M

i

r1-c n

n sin