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Human Eye • Human eye is a simple single lens system • Crystalline lens provide focus • Cornea: outer surface protection • Iris: control light • Retina: where image is focused • Note images are inverted
Human Eye Distance • Crystalline lens to retina distance 24.4 mm • Eye focuses object up to 25 cm from it • Called the near point or Dv = 25 cm • Eye muscles to change focal length of lens over 2.22<f<2.44 cm • Near sighted: retina to lens distance too long, focused in front • Infinity object focused in front of retina: out of focus at it • When bring objects closer focus moves to retina • Near sighted people can see objects with Dv < 25 cm • Far sighted: eye is too short, focuses behind retina, Dv > 25 cm
Magnification of Lens • Lateral change in distance equals change in image size • Measures change in apparent image size
ss
yyMm
′−=
′==
Magnification with Index Change • Many different ways of measuring magnification • With curved index of refraction surface measure apparent change in distance to image • Called Lateral Magnification
rsrsm
+−′
−=
• m is + if image virtual, - if real
Angular Magnification • For the eye look at angular magnification
θθ ′
== Mm
• Represents the change in apparent angular size
Simple Magnifying Glass • Human eye focuses near point or Dv = 25 cm • Magnification of object: ratio of angles at eye between unaided and lens • Angle of Object with lens
θθ ≈==25y
Dy)tan(
v
• For maximum magnification place object at lens f (in cm)
fy
=′θ
• Thus magnification is (where f in cm)
fm 25
=′
=θθ
• e.g. What is the magnification of a lens f = 1 inch = 2.5 cm
1052
2525===
′=
.fm
θθ
Power of a Lens or Surface • Power: measures the ability to create converging/diverging light by a lens • Measured in Diopters (D) or 1/m • For a simple curved surface
rnnP −′
=
• For a thin lens
fP 1=
• Converging lens have + D, diverging - D • eg f = 50 cm, D = +2 D f = -20 cm, D = -5 D • Recall that for multiple lens touching
L321
1111ffffe
++=
• Hence power in Diopters is additive
L21 DDD +=
Eyeglasses • Use Diopters in glasses • Farsighted, Hypermetopia: focus light behind retina Use convex lens, +D to correct • Nearsighted, Myopia: focus in front of retina use concave lens, -D to correct • Normal human eye power is ~58.6 D • Nearsighted glasses create a reverse Galilean telescope • Makes objects look smaller.
Classical Compound Microscope • Classical system has short fo objective lens object is near focal length when focused • Objective creates image at distance g from focal point • Objective working distance typically small (20-1 mm) • Eyepiece is simple magnifier of that image at g • Magnification of Objective
oo f
gm =
• where g = Optical tube length • Eyepiece magnification is
ee f
m 25=
• Net Microscope Magnification
eoeo ff
gmmM 25==
Infinite Corrected Microscopes • Classical Compound Microscope has limited tube length • New microscope "Infinite Corrected" • Objective lens creates parallel image • Tube lens creates converging image • Magnification now not dependent on distance to tube lens: thus can make any distance • Good for putting optics in microscope • Laser beam focused at microscope focus
Telescope • Increases magnification by increasing angular size • Again eyepiece magnifies angle from objective lens • Simplest "Astronomical Telescope" or Kepler Telescope two convex lenses focused at the same point • Distance between lenses:
eo ffd +=
• Magnification is again
e
o
o
e
ffm ==
θθ
Different Types of Telescopes • Galilean: concave lens at focus of convex
eo ffd +=
• Eyepiece now negative fe • Most others mirror types
Telescopes as Beam Expanders • With lasers telescopes used as beam expanders qc� Parallel light in, parallel light out • Ratio of incoming beam width W1 to output beam W2
11
22 W
ffW =
Telescopes as Beam Expanders • Can be used either to expand or shrink beam • Kepler type focuses beam within telescope: • Advantages: can filter beam • Disadvantages: high power point in system • Galilean: no focus of beam in lens • Advantages: no high power focused beam more compact less corrections in lenses • Disadvantages: Diverging lens setup harder to arrange
Lens Aberrations: Spherical • Aberrations are failures to focus to a "point" • Some are failures of paraxial assumption
L!!
)sin(53
53 θθθθ +−=
• Formalism developed by Seidel • Light through edge of lens at different focus • Longitudinal Spherical Aberration along axis • Transverse Spherical Aberration across axis • Make Aspheric surfaces to compensate • Or can use combine two or more spherical surfaces
Astigmatism Aberration • Off axis rays are not focused at the same plane as the on axis rays • Called "skew rays" • Principal ray, from object through optical axis to focused object • Tangental rays (horizontal) focused closer • Sagittal rays (vertical) further away • Corrected using multiple surfaces
Coma Aberration • Comes from third order sin correction • Off axis distortion • Results in different magnifications at different points • Single point becomes a comet like flare • Coma increase with NA • Corrected with multiple surfaces
Field Curvature Aberration • All lenses focus better on curved surfaces • Called Field Curvature • positive lens, inward curves • negative lens, outward (convex) curves • Reduced by combining positive & neg lenses
Distortion Aberration • Distortion means image not at paraaxial points • Grid used as common means of projected image • Pincushion: pulled to corners • Barrel: Pulled to sides
Index of Refraction & Wavelength: Chromatic Aberration • Different wavelengths have different index of refraction • Often list wavelength by spectral colour lines (letters) • Index change is what makes prism colour spread • Typical changes 1-2% over visible range • Generally higher index at shorter wavelengths
Chromatic Aberration • Chromatic Aberrations different wavelength focus to different points • Due to index of refraction change with wavelength • Hence focuses rays at different points • Generally blue closer (higher n) Red further away (lower index) • Important for multiline lasers • Achromatic lenses: combine different n materials whose index changes at different rates • Compensate each other
Lateral Colour Aberration • Blue rays refracted more typically than red • Blue image focused at different height than red image
Singlet vs Achromat Lens • Combining two lens significantly reduces distortion • Each lens has different glass index • positive crown glass • negative meniscus flint • Give chromatic correction as well
Combined lens: Unit Conjugation • Biconvex most distortion • Two planocovex significant improvement • Two Achromats, best