Magnifiers, Projectors, CamerasPaul Avery (PHY 3400)1 Magnifiers, Projectors, Cameras Applied Optics...

Magnifiers, Projectors, Cameras

Paul Avery (PHY 3400) 1

Magnifiers, Projectors, CamerasApplied Optics

Paul AveryUniversity of Florida

http://www.phys.ufl.edu/~avery/avery@phys.ufl.edu

Phy 3400Light, Color and Holography

Magnifiers, Projectors, Cameras

Paul Avery (PHY 3400) 2

MagnifierConsider small object held in front of eye

Height yMakes an angle at given distance from the eye

Goal is to make object “appear bigger”: ' >

y

Magnifiers, Projectors, Cameras

Paul Avery (PHY 3400) 3

MagnifierSingle converging lens

Simple analysis: put eye right behind lensPut object at focal point and image at infinityAngular size of object is , bigger!

Outgoingrays Rays seen coming

from here

ff Image atInfinity

1 1 1

q f p

y

Magnifiers, Projectors, Cameras

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Angular Magnification (Standard)Without magnifier: 25 cm is closest distance to view

Defined by average near point. Younger people do better tan = y / 25

With magnifier: put object at distance p = f' tan ' = y / f

Define “angular magnification” m = ' /

Note that magnifiers work better for older people because near point is actually > 25 cm

/ 25

/

/ 25/

y

y f

m f

Magnifiers, Projectors, Cameras

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Angular Magnification (Maximum)Can do better by bringing object closer to lens

Put image at near point, q = -25 cm

Analysis tan = y / 25' tan ' = y / pm = ' / = 25 / p

Outgoingrays

Rays seen coming fromnear point. Can’t bringany closer!

ff

25 1 1 2525 1

25/ 1

p f q f

m f

y

Magnifiers, Projectors, Cameras

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ExampleFind angular magnification of lens with f = 5 cm

255 Standard

525

1 6 Maximum5

m

m

Magnifiers, Projectors, Cameras

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Size of Image from MagnifierHow big is projected image of sun?

Sun is 0.5 in diameter (0.0087 rad) Image located at focal point. Why?Size is f = 5 0.0087 = 0.0435 cm

Energy concentration of 10 cm lens?All solar rays focused on imageEnergy concentration is ratio of areasConcentration = (10 / 0.0435)2 = 53,000!Principle of solar furnace (mirrors)

f

Magnifiers, Projectors, Cameras

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Projectors Idea: project image of slide onto distant screenPut slide near focal point of lens

Upside down to make image upright

ScreenLens

pfq

p f

Magnifiers, Projectors, Cameras

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Projector ExampleProjector problem

5 cm focal length3 m from screenWhere and how should slide be placed?

Solution: real image required. Why?q = 3 m = +300 cm f = 5 cmFind p from lens equation

So 5.085 cm from lens, just past focal point

1 1 1

p f q

300 55.085 cm

300 5

qfp

q f

Magnifiers, Projectors, Cameras

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CameraLens projects image on filmDistance adjustment

Object at distance p Film at fixed position Fixed focal length f Solution: move lens

Light adjustment Shutter speed Aperture setting Film speed

1 1 1

q f p

Camera: Film replaces eyeImage projected on film

Magnifiers, Projectors, Cameras

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Other DetailsReal cameras have several lenses

6 lenses more commonCorrect for various defectsLens systems have equivalent focal length

“Standard” lens is 50 mm, i.e. f = 50 mmOther lenses possible, e.g. 28 – 210 mm28, 35 mm lens are “wide angle”> 50 mm are “telephoto” (100, 200, 300, 400, etc)

“Zoom” lenses allow variable f (using multiple lenses)35 – 105 mm28 – 80 mm70 – 210 mm

Film pressed flat against holderWant film to form perfect plane perpendicular to optic axis

Common varieties

Magnifiers, Projectors, Cameras

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Spherical Aberration in LensesThick lenses must be ground to accurate shapeSpherical is not the correct shape for best image

Magnifiers, Projectors, Cameras

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Chromatic Aberration in Lenses

Correction requiresmultiple lenses

n varies with

Magnifiers, Projectors, Cameras

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Multiple Lenses in CamerasMultiple lenses correct for various aberrations

Spherical aberration (poor focus at edge of lens)Chromatic aberration (index of refraction varies with )Gauss arrangement probably most common

Actual arrangements are compromises!No perfect corrections for all factorsBalance of many factors, including cost

Magnifiers, Projectors, Cameras

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Variation of Index of Refraction

Magnifiers, Projectors, Cameras

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Variation of Index of Refraction

blue red

aveDispersive Power

Magnifiers, Projectors, Cameras

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Single Lens Reflex (SLR) CamerasYou see exactly what film sees

Mirror, prism arrangement allows you to seeMirror flips out of the way when shutter is pressed

Magnifiers, Projectors, Cameras

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A Real SLR Camera!

Magnifiers, Projectors, Cameras

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FilmLens

p q

Image Size on FilmExample: 20 cm size object, 5 m distant

Use standard 50 mm lens (f = 50 mm)Size easily calculated from geometryLens equation: q = 5.05 cm f

20 0.0101 0.202 cmy

5.050.0101

500

y q

y p

Magnifiers, Projectors, Cameras

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Image Size (cont.) Image size proportional to focal lengthTelephoto lenses are magnifiers

100 mm lens makes 2 image200 mm lens makes 4 imageetc.

Telephotos and zoom lenses require stabilityShaking is also magnifiedRequire tripods, etc.

Magnifiers, Projectors, Cameras

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f-number and BrightnessDefine f-# = f / D

f = focal lengthD = lens diameter

f-number defines brightness of imageArea of image f 2

Amount of light D2

Brightness (D / f)2 = 1 / (f-#)2

Camera settings allow x2 brightness change per stepSetting is 1.4 = 2 per step1.4, 2.0. 2.84.0, 5.6, 811, 16, 22