OpticsOptics

Mirrors, Lenses and StuffMirrors, Lenses and Stuff

The Electromagnetic The Electromagnetic SpectrumSpectrum

The Electromagnetic The Electromagnetic SpectrumSpectrum

What uses to we make for different What uses to we make for different types of EM radiation?types of EM radiation?

-radio-radio

-medical imaging-medical imaging

-seeing-seeing

-studying the universe-studying the universe

-cooking our delicious food(microwaves)-cooking our delicious food(microwaves)

The Electromagnetic The Electromagnetic SpectrumSpectrum• EM radiation is pretty crazy stuff—it EM radiation is pretty crazy stuff—it

exhibits wave-particle dualityexhibits wave-particle duality

• That means that you can think of light as That means that you can think of light as being both a wave(Maxwell and others) being both a wave(Maxwell and others) and a particle(photon)(Newton and others)and a particle(photon)(Newton and others)

• The way that you examine the light will The way that you examine the light will determine which of the properties it determine which of the properties it demonstratesdemonstrates

Wave-Particle DualityWave-Particle Duality

My Friend Roy G. BivMy Friend Roy G. Biv

Roy G. BivRoy G. Biv

• http://http://www.youtube.com/watch?vwww.youtube.com/watch?v=OQSNhk5ICTI=OQSNhk5ICTI

The EyeThe Eye

• Humans(among other Humans(among other animals) are trichromatsanimals) are trichromats

• We have three types of We have three types of cones; one optimised for cones; one optimised for blue, one for green and blue, one for green and one for redone for red

Colour AdditionColour Addition

http://http://phet.colorado.eduphet.colorado.edu/en/simulation/color-vision/en/simulation/color-vision

Colour AdditionColour Addition

Colour SubtractionColour Subtraction

Colour SubtractionColour Subtraction

• A—RedA—Red

• B—RedB—Red

• C--BlackC--Black

ColourColour

• Why does the Sun appear yellow?Why does the Sun appear yellow?

• What colour would it appear in What colour would it appear in space?space?

ReflectionReflection

• Light travels in straight linesLight travels in straight lines

• How do you know this is the case?How do you know this is the case?

Law of ReflectionLaw of Reflection

i R

Images in Plane MirrorsImages in Plane Mirrors

• Image seems to be the Image seems to be the same distance same distance “behind” the mirror as “behind” the mirror as the object is in frontthe object is in front

• Images are left-right Images are left-right invertedinverted

Describing ImagesDescribing Images

• SS—size, bigger or smaller than object—size, bigger or smaller than object

• AA—attitude, upright or inverted—attitude, upright or inverted

• LL—location—location

• TT—type, either real(can be projected on a —type, either real(can be projected on a screen) or virtualscreen) or virtual

Fancy MirrorsFancy Mirrors

Ooh la la

Concave MirrorsConcave Mirrors

C is the centre of curvature

F is the focal point

Describe the image

Convex MirrorsConvex Mirrors

Convex mirrors only produce virtual images.

RefractionRefraction

• Refraction is the bending of waves Refraction is the bending of waves when they travel from one substance when they travel from one substance into anotherinto another

• The bending is caused because the The bending is caused because the wave changes speed in the new wave changes speed in the new substancesubstance

• And now for the famous students And now for the famous students holding meter sticks demonstrating holding meter sticks demonstrating refraction demorefraction demo

• http://http://phet.colorado.eduphet.colorado.edu/en/simulation/bending-light/en/simulation/bending-light

Index of RefractionIndex of Refraction

• Materials in which lights Materials in which lights travels more slowly are travels more slowly are called optically densecalled optically dense

• To compare how To compare how optically dense a optically dense a medium is, we compare medium is, we compare the apparent speed of the apparent speed of light in the medium to light in the medium to the speed of light in the the speed of light in the vacuum of spacevacuum of space

• In space, c=3.0X10In space, c=3.0X1088 m/s m/s

• The ratio is called the The ratio is called the index of refractionindex of refraction

• n will always be n will always be greater than 1—why?greater than 1—why?

v

cn

Index of RefractionIndex of Refraction

Ex) Diamond has an Ex) Diamond has an index of refraction index of refraction of 2.42. What is of 2.42. What is the apparent speed the apparent speed of light in of light in diamond?diamond?

smXv

Xv

n

cv

v

cn

/102.1

42.2

103

8

8

Snell’s LawSnell’s Law

• n is the index of n is the index of refraction and is refraction and is physical property of physical property of the mediumthe medium

• A higher n, means A higher n, means that light travels that light travels more slowly through more slowly through that mediumthat medium

• sin is a trig sin is a trig ratio(from triangles)ratio(from triangles)

The vertical line is called the normal

Snell’s LawSnell’s Law

• Ex) Light travels Ex) Light travels from air into water from air into water at an angle of at an angle of incidence of 30incidence of 30oo. If . If the nthe nairair=1 and =1 and nnwaterwater=1.33, find the =1.33, find the angle of angle of refraction(the angle refraction(the angle the light travels in the light travels in the water)the water) r

r

r

r

ro

nn

2233.1

5.0sin

sin33.1

5.0

sin33.15.0

sin33.130sin1

sinsin

1

2211

Total Internal ReflectionTotal Internal Reflection

• What is going on in the What is going on in the diagram to the left?diagram to the left?

• When light travels into When light travels into faster media, their faster media, their rays refract AWAY rays refract AWAY from the normalfrom the normal

• At a special At a special angle(special to the angle(special to the two media), called the two media), called the critical angle, the ray critical angle, the ray will not be refracted will not be refracted but all its energy will but all its energy will be reflected internallybe reflected internally

Total Internal ReflectionTotal Internal Reflection

What is the critical What is the critical angle for light angle for light travelling from travelling from water, n=1.33, into water, n=1.33, into air, n=1.00?air, n=1.00?

oc

c

c

49

33.1

1sin

90sinsin33.1

1

LensesLenses

LensesLenses

• A device that refracts lightA device that refracts light

• What do we use them for?What do we use them for?

LensesLenses

Convex Lenses(Converging)Convex Lenses(Converging)

Convex LensesConvex Lenses

Convex LensesConvex Lenses

• Rays through the optical centre do Rays through the optical centre do not refractnot refract

• Rays parallel to the principal axis Rays parallel to the principal axis refract through the focal pointrefract through the focal point

• Rays through the secondary focus Rays through the secondary focus refract parallel to the principal axisrefract parallel to the principal axis

• How many rays are needed to find How many rays are needed to find the image?the image?

Convex LensesConvex Lenses

Concave LensesConcave LensesNotice that the focus is on the same side as the object. How is that different from convex lenses? Why?

Concave Lenses(Diverging)Concave Lenses(Diverging)

Concave LensesConcave Lenses

• The ray rules for concave lenses are The ray rules for concave lenses are the same as for convex lenses but the same as for convex lenses but the rays diverge on the other side of the rays diverge on the other side of the lensthe lens

• Your eye plays a trick on you and Your eye plays a trick on you and converges the rays on the same side converges the rays on the same side of the lens as the object, creating a of the lens as the object, creating a virtual imagevirtual image

http://http://phet.colorado.eduphet.colorado.edu/en/simulation/geometric-optics/en/simulation/geometric-optics

The Thin Lens EquationThe Thin Lens Equation

• Relationship Relationship between the focal between the focal length of a lens and length of a lens and the distances from the distances from the lens to the the lens to the object and to its object and to its imageimage

• Does it remind you Does it remind you of another formula?of another formula?

Sign Conventions Sign Conventions

• heights above the axis are heights above the axis are considered “+”; those below, “-”considered “+”; those below, “-”

• object distances on the same side as object distances on the same side as the light source are considered “+”; the light source are considered “+”; those on the opposite side “-”those on the opposite side “-”

• image distances on the opposite side image distances on the opposite side to the object are considered “+”; to the object are considered “+”; those on the same side as the object those on the same side as the object “-”“-”

Sign ConventionSign Convention

• Which values in the diagram are Which values in the diagram are positive?positive?

hhoo, h, hii, d, doo

• Which negative?Which negative?

ddii

The Magnification EquationThe Magnification Equation

• Another(and I promise the last) Another(and I promise the last) relationship that exists for lenses is relationship that exists for lenses is the magnification equation—it is a the magnification equation—it is a ratio of the hratio of the hoo to h to hii

o

ii

d

d

h

hM

0

QuestionsQuestions

1)1) A diverging lens has an f of 29 cm. A virtual A diverging lens has an f of 29 cm. A virtual image of a unicorn is located 13 cm in front of image of a unicorn is located 13 cm in front of the lens. Where is the unicorn located?the lens. Where is the unicorn located?

2)2) A tiny unicorn of height 8.4 cm is balanced in A tiny unicorn of height 8.4 cm is balanced in front of a converging lens. An inverted, real front of a converging lens. An inverted, real image of height 23 cm is noticed on the other image of height 23 cm is noticed on the other side of the lens. What is the magnification of side of the lens. What is the magnification of the lens?the lens?

3)3) A unicorn statue of height 53 cm produces a A unicorn statue of height 53 cm produces a virtual image of 78 cm. The statue is located virtual image of 78 cm. The statue is located 1.3 m in front of the lens. What is the image 1.3 m in front of the lens. What is the image distance?distance?