Magnifiers, Projectors, Cameras
Paul Avery (PHY 3400) 1
Magnifiers, Projectors, CamerasApplied Optics
Paul AveryUniversity of Florida
http://www.phys.ufl.edu/~avery/[email protected]
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
Paul Avery (PHY 3400) 4
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
Paul Avery (PHY 3400) 5
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
Paul Avery (PHY 3400) 6
ExampleFind angular magnification of lens with f = 5 cm
255 Standard
525
1 6 Maximum5
m
m
Magnifiers, Projectors, Cameras
Paul Avery (PHY 3400) 7
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
Paul Avery (PHY 3400) 8
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
Paul Avery (PHY 3400) 9
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
Paul Avery (PHY 3400) 10
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
Paul Avery (PHY 3400) 11
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
Paul Avery (PHY 3400) 12
Spherical Aberration in LensesThick lenses must be ground to accurate shapeSpherical is not the correct shape for best image
Magnifiers, Projectors, Cameras
Paul Avery (PHY 3400) 13
Chromatic Aberration in Lenses
Correction requiresmultiple lenses
n varies with
Magnifiers, Projectors, Cameras
Paul Avery (PHY 3400) 14
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
Paul Avery (PHY 3400) 15
Variation of Index of Refraction
Magnifiers, Projectors, Cameras
Paul Avery (PHY 3400) 16
Variation of Index of Refraction
blue red
aveDispersive Power
Magnifiers, Projectors, Cameras
Paul Avery (PHY 3400) 17
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
Paul Avery (PHY 3400) 18
A Real SLR Camera!
Magnifiers, Projectors, Cameras
Paul Avery (PHY 3400) 19
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
Paul Avery (PHY 3400) 20
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
Paul Avery (PHY 3400) 21
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