Physics Holiday Homewory-suchith Prabhu (Optics)

7/30/2019 Physics Holiday Homewory-suchith Prabhu (Optics)

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Optics Reflection

Diffuse reflection Refraction

Index of refraction

Speed of light

Snells law

Geometry problems

Critical angle

Total internal reflectionMirages

Dispersion

Prisms

Rainbows Plane mirrors

Spherical aberration

Concave and convex mirrors

Focal length & radius of curvature

Mirror / lens equation

Convex and concave lenses

Human eyeTelescopes


3/75

Reflection

Most things we see are thanks to reflections, since most objects

dont produce their own visible light. Much of the light incidenton an object is absorbed but some is reflected. the wavelengths of

the reflected light determine the colors we see. When white light

hits an apple, for instance, primarily red wavelengths are

reflected, while much of the others are absorbed.A ray of light heading towards an object is called an incident ray.

If it reflects off the object, it is called a reflected ray. A

perpendicular line drawn at any point on a surface is called a

normal (just like with normal force). The angle between theincident ray and normal is called the angle of incidence, i, and

the angle between the reflected ray and the normal ray is called

the angle of reflection, r. The law of reflection states that the

angle of incidence is always equal to the angle of reflection.


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Law of Reflection

i r

i = r

Normal line (perpendicular to

surface)


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Diffuse ReflectionDiffuse reflection is when light bounces off a non-smooth surface.

Each ray of light still obeys the law of reflection, but because the

surface is not smooth, the normal can point in a different for

every ray. If many light rays strike a non-smooth surface, they

could be reflected in many different directions. This explains how

we can see objects even when it seems the light shining upon it

should not reflect in the direction of our eyes. It also helps toexplain glare on wet roads: Water fills in and smoothes out the

rough road surface so that the road becomes more like a mirror.


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Speed of Light & Refraction

As you have already learned, light is extremely fast, about

3108 m/s in a vacuum. Light, however, is slowed down by the

presence of matter. The extent to which this occurs depends on

what the light is traveling through. Light travels at about 3/4 of its

vacuum speed (0.75 c) in water and about 2/3 its vacuum speed(0.67 c) in glass. The reason for this slowing is because when

light strikes an atom it must interact with its electron cloud. If

light travels from one medium to another, and if the speeds in

these media differ, then light is subject to refraction (a changingof direction at the interface).

Refraction of

light waves

Refraction of

light rays
http://www.control.co.kr/java1/RefractionofLight/LightRefract.htmlhttp://www.control.co.kr/java1/RefractionofLight/LightRefract.htmlhttp://freespace.virgin.net/gareth.james/virtual/Optics/Refraction/refraction.htmlhttp://freespace.virgin.net/gareth.james/virtual/Optics/Refraction/refraction.htmlhttp://freespace.virgin.net/gareth.james/virtual/Optics/Refraction/refraction.htmlhttp://freespace.virgin.net/gareth.james/virtual/Optics/Refraction/refraction.htmlhttp://www.control.co.kr/java1/RefractionofLight/LightRefract.htmlhttp://www.control.co.kr/java1/RefractionofLight/LightRefract.html


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Reflection & Refraction

r

At an interface between two media, both reflection and refraction can

occur. The angles of incidence, reflection, and refraction are all measured

with respect to the normal. The angles of incidence and reflection arealways the same. If light speeds up upon entering a new medium, the angle

of refraction, r, will be greater than the angle of incidence, as depicted on

the left. If the light slows down in the new medium, r will be less than

the angle of incidence, as shown on the right.

normal

rnormal


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Axle Analogy

r

Imagine youre on a skateboard heading from the sidewalk toward some

grass at an angle. Your front axle is depicted before and after entering the

grass. Your right contacts the grass first and slows, but your left wheel isstill moving quickly on the sidewalk. This causes a turn toward the normal.

If you skated from grass to sidewalk, the same path would be followed. In

this case your right wheel would reach the sidewalk first and speed up, but

your left wheel would still be moving more slowly. The result this time

would be turning away from the normal. Skating from sidewalk to grass islike light traveling from air to a more

grasssidewalk

overhead viewoptically dense medium like glass

or water. The slower light travels in

the new medium, the more it bends

toward the normal. Light traveling

from water to air speeds up and

bends away from the normal. As

with a skateboard, light traveling

along the normal will change speedbut not direction.


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Index of Refraction, n

The index of refraction of a substance is the ratio of the speed in light

in a vacuum to the speed of light in that substance:

n= Index of Refractionc= Speed of light in vacuum

v= Speed of light in medium

n =c

v

Note that a large index of refraction

corresponds to a relatively slow

light speed in that medium.

Medium

Vacuum

Air (STP)

Water (20 C)Ethanol

Glass

Diamond

n

1

1.00029

1.331.36

~1.5

2.42


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Snells Law

Snells law states that a ray of light bends in

such a way that the ratio of the sine of the

angle of incidence to the sine of the angle of

refraction is constant. Mathematically,

nisini = nrsinr

Here ni is the index of refraction in the original

medium and nris the index in the medium thelight enters. iandrare the angles of

incidence and refraction, respectively.

i

r

ni

nr

Willebrord

Snell


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Snells Law Derivation Two parallel rays are shown.Points A and B are directly

opposite one another. The top

pair is at one point in time, and

the bottom pair after time t.

The dashed lines connecting

the pairs are perpendicular to

the rays. In time t, point Atravels a distance x, while

point B travels a distance y.

sin1= x/d, so x = dsin1

sin2 = y/d, so y = dsin2

Speed of A: v1 = x/ t

Speed of B: v2 = y/ t

Continued

A

A B

B

1

2

x

y

d

n1

n2


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Snells Law Derivation(cont.)

v1/c sin1 1/n1 sin1 n2

v2/c sin2 1/n2 sin2 n1= = =

n1 sin1 = n2 sin2

v1 x/t x sin1=

v2 y/t y sin2= = So,

A

A B

B

1

2

x

y

d

n1

n2


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Refraction Problem #1

1. Find the first angle of refraction

using Snells law.

2. Find angle . (Hint: Use

Geometry skills.)

3. Find the second angle ofincidence.

4. Find the second angle of

refraction, , using Snells Law

19.4712

Glass, n2 = 1.5

Air, n1 = 1

30

79.4712

10.5288

Horiz. ray,

parallel tobase

15.9

Goal: Find the angular displacement of the ray after having passed

through the prism. Hints:


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120

d

glass

H20

H20

10m

20

20

0.504 m

5.2 10-8 s

26.4

n1 = 1.3

n2 = 1.5

Goal: Find the distance the light ray displaced due to the thick

window and how much time it spends in the glass. Some hints aregiven.

1. Find 1 (just for fun).

2. To show incoming & outgoing

rays are parallel, find .

3. Find d.

4. Find the time the light spends in

the glass.Extra practice: Find if bottom

medium is replaced with air.


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= ?

36

Goal: Find the exit angle relative to the horizontal.

19.8

glass

air

The triangle is isosceles.

Incident ray is horizontal,

parallel to the base.

=


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Reflection Problem

50

= 10

center of

semicircular mirror

with horizontal base

Goal: Find incident angle relative to horizontal so that reflected ray

will be vertical.


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Critical Angle Sample Problem

Calculate the critical angle for the diamond-air boundary.

c =sin-1

(nr/ni)= sin-1(1/2.42)

=24.4

Any light shone on this

boundary beyond this angle

will be reflected back into the

diamond.

c

air

diamond

Refer to the Index of Refraction chart for the information.


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Total Internal Reflection

Total internal reflection occurs when light attempts to pass

from a more optically dense medium to a less optically dense

medium at an angle greater than the critical angle. When this

occurs there is no refraction, only reflection.

n1

n2

Total internal reflection can be used for practical applications

like fiber optics.

>c

n1n2 >


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Mirage Pictures


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MiragesMirages are caused by the refracting properties of a

non-uniform atmosphere.

Several examples of mirages include seeing puddles

ahead on a hot highway or in a desert and the lingering

daylight after the sun is below the horizon.

More Mirages

Continued
http://www.polarimage.fi/http://www.polarimage.fi/


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Inferior Mirages

A person sees a puddle ahead on

the hot highway because the road

heats the air above it, while theair farther above the road stays

cool. Instead of just two layers,

hot and cool, there are really

many layers, each slightly hotter than the layer above it. The cooler air has aslightly higher index of refraction than the warm air beneath it. Rays of

light coming toward the road gradually refract further from the normal,

more parallel to the road. (Imagine the wheels and axle: on a light ray

coming from the sky, the left wheel is always in slightly warmer air than the

right wheel, so the left wheel continually moves faster, bending the axlemore and more toward the observer.) When a ray is bent enough, it

surpasses the critical angle and reflects. The ray continues to refract as it

heads toward the observer. The puddle is really just an inverted image of

the sky above. This is an example of an inferior mirage, since the cool are is

above the hot air.


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Superior Mirages

Superior mirages occur when a

layer of cool air is beneath a layer

of warm air. Light rays are bentdownward, which can make an

object seem to be higher in the air

and inverted. (Imagine the

wheels and axle on a ray coming

from the boat: the right wheel iscontinually in slightly warmer air

than the left wheel. Thus, the right

wheel moves slightly faster and

bends the axle toward the

observer.) When the critical angleis exceeded the ray reflects. These

mirages usually occur over ice, snow, or cold water. Sometimes superior image

are produced without reflection. Eric the Red, for example, was able to see

Greenland while it was below the horizon due to the light gradually refracting

and following the curvature of the Earth.


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Observer

Apparentposition

of sun

EarthActual

positionof sun

Atmosphere

Lingering daylight after the sun

is below the horizon is another

effect of refraction. Light travelsat a slightly slower speed in

Earths atmosphere than in

space. As a result, sunlight is

refracted by the atmosphere. In

the morning, this refractioncauses sunlight to reach us

before the sun is actually above

the horizon. In the evening, the

Sunlight after Sunset

Different shapes of Sun

sunlight is bent above the horizon after the sun has actually set. Sodaylight is extended in the morning and evening because of the

refraction of light. Note: the picture greatly exaggerates this effect as

well as the thickness of the atmosphere.
http://virtual.finland.fi/finfo/english/mirage2.htmlhttp://virtual.finland.fi/finfo/english/mirage2.html


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Dispersion of Light

Dispersion is the separation of light into a spectrum by refraction. The

index of refraction is actually a function of wavelength. For longerwavelengths the index is slightly small. Thus, red light refracts less than

violet. (The pic is exaggerated.) This effect causes white light to split

into it spectrum of colors. Red light travels the fastest in glass, has a

smaller index of refraction, and bends the least. Violet is slowed down

the most, has the largest index, and bends the most. In other words: the

higher the frequency, the greater the bending.Animation
http://www.physics.mun.ca/~jjerrett/dispersion/prism.htmlhttp://www.physics.mun.ca/~jjerrett/dispersion/prism.html


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There are many natural occurrences of light optics in our atmosphere.

Photo gallery of atmospheric optics.

One of the most common of these is

the rainbow, which is caused by

water droplets dispersing sunlight.

Others include arcs, halos, cloud

iridescence, and many more.

Atmospheric Optics

R i b
http://www.weather-photography.com/Atmospheric_Optics/index.htmlhttp://www.weather-photography.com/Atmospheric_Optics/index.htmlhttp://www.weather-photography.com/Atmospheric_Optics/index.htmlhttp://www.weather-photography.com/Atmospheric_Optics/index.html


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way out of the droplet, the light is once more refracted and dispersed.

Although each droplet produces a complete spectrum, an observer will

only see a certain wavelength of light from each droplet. (The wavelengthdepends on the relative positions of the sun, droplet, and observer.)

Because there are millions of droplets in the sky, a complete spectrum is

seen. The droplets reflecting red light make an angle of 42o with respect to

the direction of the suns rays; the droplets reflecting violet light make an

angle of 40o. Rainbow images

Rainbows A rainbow is a spectrumformed when sunlight is

dispersed by water droplets in

the atmosphere. Sunlight

incident on a water droplet is

refracted. Because of

dispersion, each color is

refracted at a slightly different

angle. At the back surface ofthe droplet, the light undergoes

total internal reflection. On the

i i b
http://www.sundog.clara.co.uk/rainbows/bowims.htmhttp://www.sundog.clara.co.uk/rainbows/bowims.htm


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Primary Rainbow


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Secondary RainbowThe secondary rainbow is a rainbow of radius

51, occasionally visible outside the primary

rainbow. It is produced when the lightentering a cloud droplet is reflected twice

internally and then exits the droplet. The color

spectrum is reversed in respect to the primary

rainbow, with red appearing on its inner edge.

Primary

Secondary

Alexandersdark region


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Supernumerary Arcs

Supernumerary arcs are faint arcs of color

just inside the primary rainbow. Theyoccur when the drops are of uniform size.

If two light rays in a raindrop are

scattered in the same direction but have

take different paths within the drop, then

they could interfere with each otherconstructively or destructively. The type

of interference that occurs depends on the

difference in distance traveled by the

rays. If that difference is nearly zero or amultiple of the wavelength, it is

constructive, and that color is reinforced.

If the difference is close to half a

wavelength, there is destructive

interference.


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Real vs. Virtual Images

Real images are formed by mirrors or lenses when light rays

actually converge and pass through the image. Real images will be

located in front of the mirror forming them. A real image can be

projected onto a piece of paper or a screen. If photographic film

were placed here, a photo could be created.

Virtual images occur where light rays only appear to have

originated. For example, sometimes rays appear to be coming from

a point behind the mirror. Virtual images cant be projected on

paper, screens, or film since the light rays do not really convergethere.

Examples are forthcoming.


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Pl Mi


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Object Image

P B

M

Pdo di

h h

Mirror

Two rays from object P strike the mirror at points B and M. Each ray is

reflected such that i = r.

Triangles BPM and BPM are

congruent by ASA (show this),

which implies that do= di and

h = h. Thus,the image is the

same distance behind the mirroras the object is in front of it, and

the image is the same size as the

object.

With plane mirrors, the image is reversed left to right (or the front and

back of an image ). When you raise your left hand in front of a mirror,

your image raises its right hand. Why arent top and bottom reversed?

object image

Plane Mirror (cont.)
http://images.google.com/imgres?imgurl=ebiomedia.com/gall/eyes/images/Jodi%27s-eye.jpg&imgrefurl=http://ebiomedia.com/gall/eyes/Images.html&h=181&w=240&prev=/images%3Fq%3Deye%26start%3D60%26svnum%3D10%26hl%3Den%26sa%3DN


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Concave and Convex Mirrors

Concave and convex mirrors are curved mirrors similar to portions

of a sphere.

light rays light rays

Concave mirrors reflect light

from their inner surface, like

the inside of a spoon.

Convex mirrors reflect light

from their outer surface, like

the outside of a spoon.


35/75

Concave Mirrors

Concave mirrors are approximately spherical and have a principal

axis that goes through the center, C, of the imagined sphere and ends

at the point at the center of the mirror, A. The principal axis is

perpendicular to the surface of the mirror at A.

CA is the radius of the sphere,or the radius

of curvature of the mirror, R.

Halfway between C and A is the focal

point of the mirror, F. This is the point

where rays parallel to the principal axis will

converge when reflected off the mirror.

The length of FA is the focal length, f.

The focal length is half of the radius of the

sphere (proven on next slide).

2f


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r= 2f

C F

r

f

s

To prove that the radius of curvature of a concave mirror is

twice its focal length, first construct a tangent line at the

point of incidence. The normal is perpendicular to thetangent and goes through the center, C. Here, i = r =. By

alt. int. angles the angle at C is also , and = 2. s is the

arc length from the principle axis to the pt. of incidence.

Now imagine a sphere centered

at F with radius f. If the incident

ray is close to the principle axis,

the arc length of the new sphereis about the same ass. From

s = r, we have s = r and

s f=2f.Thus,r2f,

and r =2f.


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Focusing Light with Concave Mirrors

Light rays parallel to the principal axis will be

reflected through the focus (disregarding spherical

aberration, explained on next slide.)

In reverse, light rays passing through the

focus will be reflected parallel to the

principal axis, as in a flood light.

Concave mirrors can form both real and virtual images, depending on

where the object is located, as will be shown in upcoming slides.

Spherical Aberration


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CF CF

Spherical Mirror Parabolic Mirror

Only parallel rays close to the principal axis of a spherical mirror will

converge at the focal point. Rays farther away will converge at a point

closer to the mirror. The image formed by a large spherical mirror will be

a disk, not a point. This is known as spherical aberration.

Parabolic mirrors dont have spherical aberration. They are used to focus

rays from stars in a telescope. They can also be used in flashlights and

headlights since a light source placed at their focal point will reflect light

in parallel beams. However, perfectly parabolic mirrors are hard to make

and slight errors could lead to spherical aberration. Continued

Spherical Aberration


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Spherical vs. Parabolic MirrorsParallel rays converge at the

focal point of a sphericalmirror only if they are close to

the principal axis. The image

formed in a large spherical

mirror is a disk, not a point

(spherical aberration).

Parabolic mirrors have no

spherical aberration. Themirror focuses all parallel rays

at the focal point. That is why

they are used in telescopes and

light beams like flashlights and

car headlights.


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Concave Mirrors: Object beyond C

C F

object

image

The image formed

when an object is

placed beyond C islocated between C and

F. It is a real, inverted

image that is smaller insize than the object.

Animation 1

Animation 2
http://www.physicsclassroom.com/mmedia/optics/rdcma.htmlhttp://www.physicsclassroom.com/mmedia/optics/ifcma.htmlhttp://www.physicsclassroom.com/mmedia/optics/ifcma.htmlhttp://www.physicsclassroom.com/mmedia/optics/rdcma.html


41/75

Concave Mirrors: Object between C and F

C F

object

image

The image formed

when an object is

placed between C and F

is located beyond C. It

is a real, inverted image

that is larger in sizethan the object.

Animation 1

Animation 2
http://www.physicsclassroom.com/mmedia/optics/rdcmc.htmlhttp://www.physicsclassroom.com/mmedia/optics/ifcmb.htmlhttp://www.physicsclassroom.com/mmedia/optics/ifcmb.htmlhttp://www.physicsclassroom.com/mmedia/optics/rdcmc.html


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Concave Mirrors: Object in front of F

C F

object

image

The image formedwhen an object is

placed in front of F is

located behind the

mirror. It is a virtual,

upright image that is

larger in size than the

object. It is virtualsince it is formed only

where light rays seem

to be diverging from.

Animation
http://www.physicsclassroom.com/mmedia/optics/rdcmd.htmlhttp://www.physicsclassroom.com/mmedia/optics/rdcmd.html


43/75

Concave Mirrors: Object at C or F

What happens when an object is placed at C?

What happens when an object is placed at F?

The image will be formed at C also, but it

will be inverted. It will be real and the

same size as the object.

No image will be formed. All rays willreflect parallel to the principal axis and will

never converge. The image is at infinity.

Animation

C Mi
http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/optics/rdcmb.htmlhttp://www.glenbrook.k12.il.us/gbssci/phys/mmedia/optics/rdcmb.html


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Convex Mirrors

A convex mirror has the

same basic properties as aconcave mirror but its focus

and center are located behind

the mirror.

This means a convex mirrorhas a negative focal length

(used later in the mirror

equation).

Light rays reflected fromconvex mirrors always

diverge, so only virtual

images will be formed.

light rays

Rays parallel to the principal

axis will reflect as if coming

from the focus behind the

mirror. Rays approaching the mirror

on a path toward F will reflect

parallel to the principal axis.


45/75

Convex Mirror Diagram

CF

object

image

The image formed by

a convex mirror no

matter where the

object is placed will

be virtual, upright,and smaller than the

object. As the object

is moved closer to themirror, the image will

approach the size of

the object.

Mirror/Lens Equation Derivation


46/75

Mirror/Lens Equation Derivation

FromPCO, =+, so 2=2+2.

From PCO, =2+, so -= -2-.

Adding equations yields 2-=.

= sr

s

di

sdo

(cont.)

C

sobject

image

di

O

P

T

From s = r, we have

s = r, sdi

,and

sdi (for rays

close to the principle

axis). Thus:

do

Mirror/Lens Eq ation Deri ation ( )


47/75

Mirror/Lens Equation Derivation (cont.)

2sr

- sdi

=sdo

1

do

2

r =1

di +

2

2f=

1do

1di

+

1

f=

1

do

1

di+

From the last slide,= s/r, s/d0, s/di, and2- = .

Substituting into the last equation yields:

C

sobject

image

di

do

O

P

T

The last equation applies to convex and concave mirrors, as well as to

lenses, provided a sign convention is adhered to.

Mirror Sign Convention


48/75

Mirror Sign Convention

+ for real image

- for virtual image

+ for concave mirrors

- for convex mirrors

1f = 1do1di

+

f= focal length

di= image distance

do = object distance

di

f

M ifi ti


49/75

Magnification

m= magnification

hi = image height (negative means inverted)

ho = object height

m=

hi

hoBy definition,

Magnification is simply the ratio of image height

to object height. A positive magnification means

an upright image.

-dihi


50/75

Magnification Identity: m=di

do

hi

ho=

C

object

image,

height = hi

dido

To derive this lets look at two rays. One hits the mirror on the axis.

The incident and reflected rays each make angle relative to the axis.A second ray is drawn through the center and is reflected back on top

of itself (since a radius is always perpendicular to an tangent line of a

ho

circle). The intersection of

the reflected raysdetermines thelocation ofthe tip of the image. Our

result follows

from similar triangles, withthe negative sign a

consequence of our sign

convention. (In this picture

hi is negative and di is

positive.)


51/75

Mirror Equation Sample Problem

Suppose AllStar, who is 3 and

a half feet tall, stands 27 feet

in front of a concave mirror

with a radius of curvature of20 feet. Where will his image

be reflected and what will its

size be?

di =

hi =

C F

15.88 feet

-2.06 feet


52/75

Mirror Equation Sample Problem 2

CF

Casey decides to join in

the fun and she finds a

convex mirror to stand

in front of. She sees her

image reflected 7 feetbehind the mirror which

has a focal length of 11

feet. Her image is 1

foot tall. Where is shestanding and how tall is

she? do =

ho =

19.25 feet

2.75 feet

Lenses


53/75

Lenses

Lenses are made of transparent

materials, like glass or plastic, that

typically have an index of refractiongreater than that of air. Each of a lens

two faces is part of a sphere and can be

convex or concave (or one face may be

flat). If a lens is thicker at the centerthan the edges, it is a convex, or

converging, lens since parallel rays will

be converged to meet at the focus. A

lens which is thinner in the center thanthe edges is a concave, or diverging,

lens since rays going through it will be

spread out.

Convex (Converging)

Lens

Concave (Diverging)

Lens

Lenses: Focal Length


54/75

Lenses: Focal Length

Like mirrors, lenses have a principal axis perpendicular to their

surface and passing through their midpoint.

Lenses also have a vertical axis, or principal plane, through their

middle.

They have a focal point, F, and the focal length is the distance from

the vertical axis to F.

There is no real center of curvature, so 2F is used to denote twice

the focal length.

Ray Diagrams For Lenses


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Ray Diagrams For Lenses

When light rays travel through a lens, they refract at both surfaces of

the lens, upon entering and upon leaving the lens. At each interface the

bends toward the normal. (Imagine the wheels and axle.) To simplifyray diagrams, we often pretend that all refraction occurs at the vertical

axis. This simplification works well for thin lenses and provides the

same results as refracting the light rays twice.

F F 2F2F F F 2F2F

Reality Approximation

Convex Lenses


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Convex Lenses

Rays traveling parallel to the principal

axis of a convex lens will refract towardthe focus.

Rays traveling directly through the center

of a convex lens will leave the lens

traveling in the exact same direction.

F F 2F2F

F F 2F2F

Rays traveling from the focus will

refract parallel to the principal axis.

F F 2F2F


57/75

Convex Lens: Object Beyond 2F

F F 2F2F

object

image


placed beyond 2F

is located behindthe lens between F

and 2F. It is a real,

inverted image

which is smaller

than the object

itself.Experiment with

this diagram
http://www.geocities.com/CapeCanaveral/Hall/6645/lens_e/lens_eg.htmhttp://www.geocities.com/CapeCanaveral/Hall/6645/lens_e/lens_eg.htmhttp://www.geocities.com/CapeCanaveral/Hall/6645/lens_e/lens_eg.htmhttp://www.geocities.com/CapeCanaveral/Hall/6645/lens_e/lens_eg.htm


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Convex Lens: Object Between 2F and F

F F 2F2F

object

image


placed between

2F and F islocated beyond 2F

behind the lens. It

is a real, invertedimage, larger than

the object.

C Obj i hi


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Convex Lens: Object within F

F F 2F2F

object

image

The image formed when an

object is placed in front ofF is located somewhere

beyond F on the same side

of the lens as the object. It

is a virtual, upright imagewhich is larger than the

object. This is how a

magnifying glass works.

When the object is broughtclose to the lens, it will be

magnified greatly.convex lens used

as a magnifier

Concave Lenses


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Rays traveling parallel to the

principal axis of a concave lens will

refract as if coming from the focus.

Rays traveling directly through the

center of a concave lens will leave

the lens traveling in the exact same

direction, just as with a convex lens.

Concave Lenses

F F 2F

2

F

F F 2F

2F

F F 2

F

2F

Rays traveling toward thefocus will refract parallel to

the principal axis.


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Concave Lens Diagram

F F 2F2F

object

image

No matter where the

object is placed, the

image will be on thesame side as the

object. The image is

virtual, upright, and

smaller than the object

with a concave lens.

Experiment with

this diagram

Lens Sign Convention
http://www.geocities.com/CapeCanaveral/Hall/6645/concav_e/cavele_z.htmhttp://www.geocities.com/CapeCanaveral/Hall/6645/concav_e/cavele_z.htmhttp://www.geocities.com/CapeCanaveral/Hall/6645/concav_e/cavele_z.htmhttp://www.geocities.com/CapeCanaveral/Hall/6645/concav_e/cavele_z.htm


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Lens Sign Convention

di+ for real image

- for virtual image

f+ for convex lenses

- for concave lenses

1f =

1do

1di +

f= focal length

di = image distance

do = object distance


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Lens/Mirror Sign Convention

The general rule for lenses and mirrors is this:

di+ for real image

- for virtual image

and if the lens or mirror has the ability to converge light,

f is positive. Otherwise, fmust be treated as negative for

the mirror/lens equation to work correctly.

L S l P bl


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Lens Sample Problem

F F 2F2F

Tooter, who stands 4 feet

tall (counting his

snorkel), finds himself 24

feet in front of a convex

lens and he sees his

image reflected 35 feetbehind the lens. What is

the focal length of the

lens and how tall is his

image?

f =

hi =

14.24 feet

-5.83 feet


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This application shows where images will be formed

with concave and convex mirrors and lenses. You can

change between lenses and mirrors at the top. Changing

the focal length to negative will change between concave

and convex lenses and mirrors. You can also move the

object or the lens/mirror by clicking and dragging onthem. If you click with the right mouse button, the object

will move with the mirror/lens. The focal length can be

changed by clicking and dragging at the top or bottom of

the lens/mirror. Object distance, image distance, focal

length, and magnification can also be changed by typing

in values at the top.

Lens and Mirror Applet

Lens and Mirror Diagrams

Convex Lens in Water
http://www.control.co.kr/java1/ThinLens/lens%26mirror/lensDemo.htmlhttp://www.control.co.kr/java1/ThinLens/lens%26mirror/lensDemo.html


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H2O

Glass Glass

Air

Because glass has a higher index of refraction that water the convex

lens at the left will still converge light, but it will converge at a

greater distance from the lens that it normally would in air. This is

due to the fact that the difference in index of refraction between

water and glass is small compared to that of air and glass. A largedifference in index of refraction means a greater change in speed of

light at the interface and, hence, a more dramatic change of

direction.

Convex Lens Made of Water


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Air

Glass

n= 1.5

Air

H2O

n= 1.33

Since water has a higher index of

refraction than air, a convex lens made ofwater will converge light just as a glass

lens of the same shape. However, the

glass lens will have a smaller focal length

than the water lens (provided the lensesare of same shape) because glass has an

index of refraction greater than that of

water. Since there is a bigger difference in

refractive index at the air-glass interface

than at the air-water interface, the glass

lens will bend light more than the water

lens.

Convex Lens Made of Water

Air & Water Lenses


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H2O

Convex lens made of Air

Concave lens made of H2O

Air

On the left is depicted a concave lens filled

with water, and light rays entering it from an

air-filled environment. Water has a higherindex than air, so the rays diverge just like

they do with a glass lens.

To the right is an air-filled convex lens

submerged in water. Instead of

converging the light, the rays diverge

because air has a lower index than water.

What would be the situation with a concave lens made of air

submerged in water?

Refracting Telescopes


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Refracting telescopes are comprised of two convex lenses. The objective

lens collects light from a distant source, converging it to a focus and

forming a real, inverted image inside the telescope. The objective lens

needs to be fairly large in order to have enough light-gathering power sothat the final image is bright enough to see. An eyepiece lens is situated

beyond this focal point by a distance equal to its own focal length. Thus,

each lens has a focal point at F. The rays exiting the eyepiece are nearly

parallel, resulting in a magnified, inverted, virtual image. Besidesmagnification, a good telescope also needs resolving power, which is its

ability to distinguish objects with very small angular separations.

g p

F

Reflecting Telescopes


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g pGalileo was the first to use a refracting telescope for astronomy. It is

difficult to make large refracting telescopes, though, because the

objective lens becomes so heavy that it is distorted by its own weight. In

1668 Newton invented a reflecting telescope. Instead of an objective

lens, it uses a concave objective mirror, which focuses incoming parallel

rays. A small plane mirror is placed at this focal point to shoot the light

up to an eyepiece lens (perpendicular to incoming rays) on the side of

the telescope. The mirror serves to gather as much light as possible,while the eyepiece lens, as in the refracting scope, is responsible for the

magnification.

Diffraction: Single Slit Pscreen


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a

Diffraction: Single Slit

Continued

Light enters an opening of width a and isdiffracted onto a distant screen. All points at the

opening act as individual point sources of light.These point sources interfere with each other, both

constructively and destructively, at different points

on the screen, producing alternating bands of

light and dark. To find the first dark spot, lets

consider two point sources: one at the left edge,and one in the middle of the slit. Light from the

left point source must travel a greater distance to

point P on the screen than light from the middle

point source. If this extra distance

is a half a wavelength, /2,

destructive interference will

occur at P and there will

be a dark spot there.

Extradistance

a/2

applet

Single Slit (cont.)
http://www.phys.hawaii.edu/~teb/optics/java/slitdiffr/http://www.phys.hawaii.edu/~teb/optics/java/slitdiffr/


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g

Lets zoom in on the small triangle in the last slide. Since a/2 isextremely small compared to the distanced to the screen, the two

arrows pointing to P are essentially parallel. The extra distance isfound by drawing segment AC perpendicular to BC. This means that

angle A in the triangle is also . Since AB is the hypotenuse of a

right triangle, the extra distance is given by (a/2)sin.Thus, using

a/2

A

C

B

(a/2)sin=/2, or equivalently,

a sin=, we can locate the first darkspot on the screen. Other dark spots can

be located by dividing the slit further.

PscreenDiffraction: Double Slit


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a

Light passes through two openings, each

of which acts as a point source. Here a isthe distance between the openings rather

than the width of a particular opening. As

before, if d1 - d2 = n (a multiple of thewavelength), light from the two sources

will be in phase and there will a bright

spot at P for that wavelength. By thePythagorean theorem, the exact difference

in distance is

d1 d2 L

x

d1 - d2 = [L2

+ (x+ a/

2)2

]

- [L2 + (x- a/2)2]

Approximation on next slide.

Link 1 Link 2

Double Slit (cont.) Pscreen
http://vsg.quasihome.com/interfer.htmhttp://www.colorado.edu/physics/2000/schroedinger/two-slit2.htmlhttp://www.colorado.edu/physics/2000/schroedinger/two-slit2.htmlhttp://vsg.quasihome.com/interfer.htm


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Double Slit (cont.)

a

d1 d2 L

In practice, L is far greater than a, meaningthat segments measuring d1 and d2 are

virtually parallel. Thus, both rays make anangle relative to the vertical, and the

bottom right angle of the triangle is also

(just like in the single slit case). This means

the extra distance traveled is given by asin.Therefore, the required condition for a brightspot at P is that there exists a natural number,

n, such that:

asin = nIf white light is shone at the

slits, different colors will be

in phase at different angles.

Electron diffraction
http://phys.educ.ksu.edu/vqm/html/doubleslit/http://phys.educ.ksu.edu/vqm/html/doubleslit/


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Physics Holiday Homewory-suchith Prabhu (Optics)

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