lecture25 lenses; optical instruments

8/3/2019 Lecture25 Lenses; Optical Instruments

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http://www.nearingzero.net(afterhrs016.jpg)


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Announcements

y Physics 24 spreadsheets with Exam 3 scores are nowavailable/not available (to be updated).

y Physics 24 Exam 3 will be returned in recitation tomorrow.Please check that points were added correctly. Review thecourse handbook and be sure to follow proper procedures

before requesting a regrade. Get your regrade requests inon time! (They are due by the following recitation.)

y Exam average 76.1% (11 sections out of 12). Good! Scores

ranged from a low of 41 to a high of 200 (15 students!).

y Caution: its the points in the spreadsheet that count, not the

percent. Your points can go down if you miss boardworks!


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Announcements

Physics 24 schedule for the rest of the semester:

November 16/17: LensesNovember 28/29 : Double Slit InterferenceNovember 30/December 1 : Thin Film InterferenceDecember 5/6 : DiffractionDecember 7/8 : Final Review

December 13, 1:30 pm:50 point all multiple choice End Material Test200 point all problem Final Exam

You may take one, or both, or neither

y Special Homework #9 is due tomorrow. Download and printit if you lost it.


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Announcements

y Critically important! Lab make-up schedule:Labs L02, L04, L06 will do their free Labor Daymakeup on Monday, November 28. Go to lab at yourregularly scheduled time and room. If you dont attend on

Nov. 28, you had better not miss any other labs.

Your lowest lab score is dropped. There are nomakeup labs (other than the Labor Day makeup describedabove).

The makeup lab is on the Monday after Thanksgiving break.You are going to forget about it!


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Todays agenda:

Death Rays.You must know when to run from Death Rays. Maybe skip for now.

Refraction at Spherical Surfaces.You must be able to calculate properties of images formed by refraction at spherical

surfaces.

Thin Lenses: Concave and Convex Lenses, Ray Diagrams,Solving the Lens Equation.You must understand the differences between these two kinds of lenses, be able to drawray diagrams for both kinds of lenses, and be able to solve the lens equation for both kindsof lenses.

If Time Allows: Lens Combinations, Optical Instruments.You should be aware of this useful information.


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News Flash!

Archimedes invents Death Ray that sets enemyships on fire!

Fishbane* and Mythbusters say its impossible!

*Author of text usedthrough spring 2006.


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News Flash!

MIT students set wooden ships on fire withdeath rays! Details here!


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Demo: the Missouri S&T death ray.


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Todays agenda:

Death Rays.You must know when to run from Death Rays.


surfaces.

Thin Lenses: Concave and Convex Lenses, Ray Diagrams,Solving the Lens Equation.You must understand the differences between these two kinds of lenses, be able to drawray diagrams for both kinds of lenses, and be able to solve the lens equation for both kinds

of lenses.



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Refraction at Spherical Surfaces

Convex surface:

C Faxis

R

f

1

U2

na nb>na

Geometry: a light ray parallel tothe axis passes through F.

b

b a

nf= R>R

n -n


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An extended object will form an image inside the nb medium.

C Faxis

R

f

U1

U2

na nb>na

This image is real and inverted.

s

s

Ray 1: parallel to the axis, through F.

Ray 3: through C.


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Concave surface:

CF

R

nb>na

Geometry: a light ray parallel tothe axis seems to have comefrom F.

b

b a

nf= R>R

n -n

axis

na

f


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CF

R

nb>na

The image is virtual and upright.

axis

na

f

An extended object will form an image inside the na medium.

Ray 1: parallel to the axis, through F.Ray 3: through C.

There are three different places to put the object. The different images

formed are always virtual and upright.


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We can use geometry to derive an equation relating the imageand source positions, and an equation for the magnification.

C Faxis R

f

na nb

s

s

a b b an n n -n

+ =

s s' R

a

b

n s'y'm= =-

y n s


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CF

R

nb

axis

na

f

The same equations work for concave surfaces.

s

s

a b b an n n -n

+ =

s s' R

a

b

n s'y'm= =-

y n s


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Approximations Were Used!

The equations in this section are excellent approximations ifboth the angles of incidence and refraction are small.


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Sign Conventions

y R is positive when it is in the medium into which the lightpropagates. R is negative when it is in the medium from whichthe light radiates.

y The image distance is positive when the image is in themedium into which the light propagates, and negative if it is inthe medium from which the light radiates (virtual image).

y The object distance is positive when the object is in the

medium from which the light radiates (the usual casea realobject), and negative if on the side opposite to the lightsource (a virtual object).

These are really the same as for mirrors.


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Example: a Jurassic mosquito is discovered embedded in anamber sphere which has an index of refraction of 1.6. The

radius of curvature of the sphere is 3.0 mm. The mosquito islocated on the principal axis and appears to be imbedded 5.0mm into the amber. How deep is the mosquito really?

Rs

s

a b b an n n -n

+ =s s' R na=1.6nb=1

The object is in theamber, so na=1.6 andnb=1.

The image is in the mediumfrom which the light radiatesso s=-5.0 mm.


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Rs

s

na=1.6nb=1

R is negative because it is in the medium from which thelight radiates. R=-3.0 mm.

1.6 1 1-1.6+ =

s -5.0 -3

s = 4 mm


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Example: a Jurassic mosquito is discovered embedded in anamber sphere which has an index of refraction of 1.6. The

radius of curvature of the sphere is 3.0 mm. The mosquito islocated on the principal axis and appears to be imbedded 5.0mm into the amber. What is the magnification?

Rs

s

a

b

-n s'm=

n s na=1.6nb=1

na=1.6 and nb=1

s=4 mm and s=-5.0 mm.

- 1.6 -5 8m= = =2

1 4 4


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I need help!

I am coordinating one of Missouris eight Regional ScienceOlympiad competitions.

About 300 students from regionalmiddle school, junior high, and high

schools will be on campus Saturday,February 18, 2012 for thecompetition.

I depend on volunteers to supervisethe approximately 40 differentevents.


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I need many volunteers to assist;

could involve a few hours on the 18

th

(general-purpose help not requiringlots of preparation); or could involvetaking over an event.

Its a lot of fun. Generally not too much work. Your reward forvolunteer work at the Science Olympiad will be warm fuzzyfeelings and plenty of free food.

Please e-mail me if you might be interested. Also be patient if

I dont get back to you immediately.

Examples of events: Experimental Design, Mousetrap Vehicle,Optics, Storm the Castle, Fermi Questions, RobotArm,Thermodynamics, Water Quality.


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Todays agenda:



surfaces.

Thin Lenses: Concave and Convex Lenses, RayDiagrams, Solving the Lens Equation.You must understand the differences between these two kinds of lenses, be able to drawray diagrams for both kinds of lenses, and be able to solve the lens equation for both kinds

of lenses.



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Thin Lenses

A lens in this section is taken to be a single object made oftransparent material of refractive material n>1.

There are two surface boundaries.Light from an object incident on

the first surface forms an image,which becomes the object for thesecond surface.

A thin lens is one for which the

distance from the object to each ofthe two surfaces is the same(and the distance from the imageto each surface is the same).

This would NOTqualify as a thin lens.


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Due to Powerpoint issues, I will make mylenses look hollow, like this.Actually, Powerpoint 2007 shades in the lens fairly easily, but I prefer to save in Powerpoint 2003 format forcompatibility purposes.

There are several surface combinations fromwhich we can make lenses. Here are three(there are more).


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Thin lenses can be converging or diverging.

Converging and Diverging Lenses

The converging lens is thicker in the center. The diverginglens is thicker at the edges.

There are focal points on both sides of each lens. The focallength is the same whether light passes from left to right orright to left.


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There are two surfaces at which light

refracts. Our equations (provided later)automatically take care of this.

In your diagrams, simply draw the incidentray up to the center of the lens, then draw

the refracted ray in its final direction.


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Todays agenda:



surfaces.

Thin Lenses: Concave and Convex Lenses, RayDiagrams, Solving the Lens Equation.You must understand the differences between these two kinds of lenses, be able to drawray diagrams for both kinds of lenses, and be able to solve the lens equation for both kinds

of lenses.



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Ray Diagrams for Converging Lenses

Ray 1 is parallel to the axis and refracts through F.

Ray 2 passes through F before refracting parallel to the axis.

Ray 3 passes straight through the center of the lens.

The image is real and inverted. In this case, it is larger thanthe object.

O F FI


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Ray Diagrams for Diverging Lenses

Ray 1 is parallel to the axis and refracts as if through F.

Ray 2 heads towards F before refracting parallel to the axis.

Ray 3 passes straight through the center of the lens.

The image is virtual and upright. It is smaller than the object.

O F FI


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Converging and Diverging Lenses

The image formed by a diverging lens is always virtual,upright, and smaller than the object. See this web page.

The image formed by a converging lens may be real, inverted,and either smaller or larger than the object. It may also bevirtual, upright, and larger than the object. See this web page.

Do these lens properties remind you of anything youvestudied recently?


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Handy quick reference card from Dr. Hale:

http://web.mst.edu/~hale/courses/Physics24/Quick.Reference.Cards/mirror.lens.table.pdf


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Todays agenda:



surfaces.

Thin Lenses: Concave and Convex Lenses, Ray Diagrams,Solving the Lens Equation.You must understand the differences between these two kinds of lenses, be able to drawray diagrams for both kinds of lenses, and be able to solve the lens equation for both kinds

of lenses.



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The Lensmakers Equation

a b

1 1 1= n-1f R R

1 1 1+ =

s s' f

a b

1 1 1 1+ = n-1

s s' R R

The Lensmakers Equation

s s

s

s

y' s'M= = -

y s


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Sign Conventions for The Lens Equation

1 1 1+ =s s' f

y' s'M= = -y s

The object distance s is positive if the object is on the side ofthe lens from which the light is coming; otherwise s isnegative.

The image distance s is positive if the image is on theopposite side of the lens from where the light is coming;otherwise s is negative. (If s is negative, is the image real?)

The focal length f is positive for converging lenses andnegative for diverging lenses.

The image height y is positive if the image is upright and

negative if the image is inverted relative to the object.


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Example: an object is located 5 cm in front of a converginglens of 10 cm focal length. Find the image distance andmagnification. Is the image real or virtual?

O FF

1 1 1 1 1 1= - = - = -

s' f s +10 +5 10

Image distance is 10 cm, image is on side of lens light is

coming from, so image is virtual. M=2 so image is upright.

s' -10M= - = - = 2

s 5

Its just a coincidence thatthe image is located at F.


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Todays agenda:


Refraction at Spherical Surfaces.You must be able to calculate properties of images formed by refraction at sphericalsurfaces.

Thin Lenses: Concave and Convex Lenses, Ray Diagrams,Solving the Lens Equation.You must understand the differences between these two kinds of lenses, be able to drawray diagrams for both kinds of lenses, and be able to solve the lens equation for both kindsof lenses.

If Time Allows: Lens Combinations, OpticalInstruments.You should be aware of this useful information.


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Lens Combinations

To determine the image formed by a combination of twolenses, simply...

calculate the image formed by the first lens

then use the first lens image as the source (object) forthe second lens.

There is no homework on lens combinations.

Skip to sign conventions.


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Optical Instruments

ASimple Magnifier

h UO

hU

Magnifier

FI

q

p

} 25 cm (near point)

O


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Refracting Telescope

tan

e

h

fU U

d} }tan

o o

o

h

fU U

d} }

e o

o eo

hf f

Mh f

f

UU

d

! ! ! d

For viewing very far objects. Object distance taken as infinity.


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Terrestrial Telescopes

For producing upright images:

Galilean telescope Field-lens telescope


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Reflecting Telescope

Newtonian-focus reflecting telescope


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Compound Microscope

Again has objective and eyepiece, but because it is for viewing very

near objects it is very different from the telescope.

.25

e

e

Mf

!

Eyepiece magnification:

i eo

o

h l fqm

h p p

! ! !

Objective magnification:

Overall magnification:

.25 .25ee o

e e o

l f l M M m

f p f f

! ! }


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Summary of Sign Conventions

When the object, image, or focal

point is on the reflecting side of themirror, the distance is positive.

When the object, image, or focalpoint is behind the mirror, the

distance is negative.

The image height is positive if theimage is upright, and negative if theimage is inverted relative to the object.

Mirrors

The object distance s is positive if the

object is on the side of the lens fromwhich the light is coming; otherwise s isnegative (and the object is virtual).

The image distance s and radius ofcurvature R are positive if the image is

on the side of the lens into which thelight is going; otherwise negative.

The focal length f is positive forconverging lenses and negative fordiverging lenses.

The image height is positive if theimage is upright, and negative if theimage is inverted relative to the object.

Lenses


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Summary of Sign Conventions

Object Distance. When the object is on the same side asthe incoming light, the object distance is positive (otherwise

is negative).

Heres a more compact way of expressing the signconventions all at once.

Image Distance. When the image is on the same side asthe outgoing light, the image distance is positive (otherwiseis negative).

Radius of Curvature. When the center of curvature C is onthe same side as the outgoing light, R is positive (otherwiseis negative).


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Image Distance. When the image is on the same side asthe outgoing light, the image distance is positive (otherwiseis negative).

If the image distance is negative, can the image be real?


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One more thing: have a safe Thanksgiving, and remember, say noto

carrots,

cabbages,and

cauliflower

lecture25 lenses; optical instruments

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