View
2
Download
0
Category
Preview:
Citation preview
Applied Optics
Professor 송 석호, Physics Department (Room #36-401)2290-0923, 019-539-0923, shsong@hanyang.ac.kr
Office Hours Mondays 15:00-16:30, Wednesdays 15:00-16:30
TA 김성필 (Ph.D. student, Room #36-415)2290-0921, digitist@ihanyang.ac.kr
Grades Midterm Exam 30%, Final Exam 30%, Homework 20%, Attend & Quiz 10%
Textbook Introduction to Optics (Wiley, New York, 1986)
Homepage http://optics.hanyang.ac.kr/~shsong
OpticsReference : www.optics.rochester.edu/classes/opt100/opt100page.html
Light is a Ray (Geometrical Optics)A. General Properties of Light RaysB. Reflection and RefractionC. Prisms and DispersionD. Images Formed by Light Rays Reflected and Refracted at Planar InterfacesE. Images Formed by Light Rays Reflected and Refracted at Curved InterfacesF. Thin LensesG. Ray Tracing Through More Complex Optical SystemsH. Ray AberrationsI. Optical Instruments Viewed by EyeJ . Ray Optics Description of a Waveguide — Trapping Light by TIR
Light is a Wave (Physical Optics)A. Wave BasicsB. Interference of Two WavesC. Interference in Thin Films
D. InterferometersE. HolographyF. Diffraction of LightG. Polarization of Light
Light is a Photon (Quantum Optics)A. Where Does Light Come From? — Sources of LightB. The LaserC. How Do You Know Light is There? — Detecting Light
Course outline
• Geometrical optics– Ignore wave nature of light.
• No diffraction.– Light travels in straight lines.
• ‘Rays.’– Rays subjected to reflection and refraction.
• Obey laws of reflection and refraction.
• Light Ray– Line in direction of flow of radiant energy
Geometrical Optics - light is a ray
Light Ray : the path along which light energy is transmitted from one point to another in an optical system.
Speed of Light : Speed of light (in vacuum): a fundamental (or a “defined”) constant of nature given byc = 299,792,458 meters / second = 186,300 miles / second.
Index of Refraction
Geometrical Optics - light is a ray
Reflection
Plane of incidence– Incident & reflected rays + normal in same plane
θi θrIncident ray
reflected ray
normal
Refraction
Refraction –Snell’s Law
Refraction –Snell’s Law
???? nn ti 0<×
ttii nn θθ sinsin =
Negative Refraction : n < 0
LHM
RHM N > 1
N = -1
Prism and Dispersion
Images Formed by Rays Reflected at Planar Interfaces
Images Formed by Rays Refracted at Planar Interfaces
Prisms to Alter the Orientation of Images
Images Formed by Rays Reflected at Curved Interfaces
Images Formed by Rays Refracted at Curved Interfaces
Image Formation by a Thin Lens
Spherical Lens
• Lens usually have both sides spherical– Or, one side flat and the other spherical.– Easier to make.
R2 R1
lens
Lensmaker’s Formula
( )1 2
1 1 1 11'
ns s R R
+ = − −
s S’
n
Sign Convention
• Rays travel from left to right.– Object distance, S
• positive if one left of lens• negative if on right of lens
– Image distance, S’• positive if one right of lens• negative if on left of lens
– R1 & R2• positive if centre on right of lens• negative if centre on left of lens
Lenses
R1> 0R2 < 0
R1= ∞R2 < 0
Plano-convexBi-convex Meniscus convex
R1> 0R2 > 0
Plano-concaveBi-concave Meniscus concave
R1< 0R2 > 0
R1 = ∞R2 > 0
R1> 0R2 > 0
Focal Points for Converging Lens
• Parallel rays made to cross at focal point by lens.
Focal point
f
Focal Length• Distance from lens to focal point.• Parallel rays means
– S = ∞, S’ = f
– so
– or
– Giving the thin lens equation
( )1 2
1 1 1 1 1 11'
ns s f R R
+ = + = − − ∞
( )1 2
1 1 11nf R R
= − −
1 1 1's s f
+ =
Focal point
f
Focal Points for Converging Lens
• Rays from focal point made parallel by lens.
Focal Points for Diverging Lens
• Point from which parallel rays appear to diverge after passing through the lens.
f
Focal point
Focal Points for Diverging Lens• Point to which converging rays are directed when
lens makes rays parallel.
Focal point
f
Positive and Negative Lenses
• For a converging lens
– So, f is positive.– Converging lenses called positive lens
• For a diverging lens
– So, f is negative.– Diverging lenses called negative lens
1 2
1 1 0R R − >
1 2
1 1 0R R − <
Real and Virtual Images
• Real image– One beyond lens (to right)– Rays converge onto it.
• Can be projected onto a screen– S’ positive
• Virtual image– One behind lens (to left)– Rays diverge from it.
• Cannot be projected onto a screen– S’ negative.
Real Image• Produced by convex (positive) lens
– Object beyond focus
Object
RealImage
Focus
Focus
u v
f f
Virtual Image• Can be by concave (negative) lens
– Object beyond focus• Image reduced
Object VirtualImage
Focus
Focus
u-v
f f
Real and Virtual Objects
• Real object– One in front of lens (to left)– Rays diverge from it.– S positive
• Virtual object– One beyond lens (to right)– Rays converge towards it.– S negative.
Numerical Aperture (N.A.)• Describes the quality of a lens.
– Depends on• size of the lens or aperture of lens• working distance• refractive index
– Given by equation
– n is refractive index between object and lens– α is the half acceptance angle of lens.
N.A. sin= αn
Some examples of N.A• In all cases, lens is in air (n = 1)
αα
5 mm
10mm
( )( )1
2.5tan 0.2510
sin sin tan 0.25
sin0.245 0.24N.
3A. 0.243
−
α = =
α
=
=
= =
α
5 mm
2.5mm
( )( )1
2.5tan 1 2.5
sin sin tan 1.0
sin0.785 0.70N.
7A. 0.707
−
α = =
α
=
=
= =
20 mm
10mm
( )( )1
10tan 1 10
sin sin tan 1.0
sin0.785 0.707N.A. 0.707
−
α = =
α =
= ==
Power of Lens
• Power of lens– Inverse of the focal length in meters– Measured in dioptres, D.
– I.e. lens focal length 50 cm has power of
1Pf
=
1 2 00 50 .. = +
Magnification
• Magnification, M– Ratio of image height to object height.
– So• Positive when image erect • Negative when image inverted
u
vobject
image
yo
yi
i
o
yM y=
Magnification
• Two similar triangles– ABC and DEC– So
S
S’object
image
yo
yi
B
AC D
E
'i
o
y SM y S= = −
Focal pointFocal point
Single Lens
Combining Lenses• More than one lens
– Thin lens equation applied in turn.• Image of one lens is object of next.
object Final image
intermediate image
Ray Tracing Through Complex Optical Systems
Losses and Aberrations of Rays
AberrationsImperfections reduce theoretical resolution of lens.
– As N.A. increases, aberrations get worse.• Increases with increasing lens power
– Many different types of aberrations.• Chromatic• Spherical• Coma• Curvature of field• etc.
Chromatic AberrationDifferent colours focused at different points.
– Combination of lenses decreases problem.– Combination called an Achromat.
WhiteWhitesourcesource BlueBlue GreenGreen RedRed
Achromatic Doublet• Positive lens from crown glass
– Low dispersion• Negative lens form flint glass
– High dispersion
Achromatic Doublet
• First lens stronger than second– Pair are positive
• First lens focuses blue more strongly• Second lens corrects for this
– Greater dispersion• Only correct for two colours
– Usually red and blue• If two close surfaces made same curvature
– Lenses can be cemented together.
Spherical aberration
• Edges of a lens refract light more then the centre. – Most of the rays focus together to form a disc– Called the circle of least confusion.
Focus ofFocus ofouter raysouter rays Focus ofFocus of
inner raysinner rays
Circle ofCircle ofleast confusionleast confusion
Coma• Edge of lens different focal length to centre
– Rays at angle focused at different points– Produces comet like image
Curvature of field• Lens focuses on surface of a sphere.
– As object moves off the optical axis focal distance to the lens is farther.
– Gives either pin cushion or barrel distortion.– minimised by the use of compensating lenses.
Curved focal fieldCurved focal field
Distortion• Off-axis magnification different from central magnification
– Pincushion or barrel distortion
Object Barrel Distortion
Pin cushion Distortion
Astigmatism
Stops• A stop is an aperture in a system
– Often to reduce aberrations• Aberrations greater at edge of lens
Object
Imagef1f2
Stop
f2
f1
Exitpupil
Entrancepupil
lens
1
lens
2
Entrance and Exit Pupil
• Entrance pupil– Virtual image of stop by lens 1
• Exit pupil– Virtual image of stop by lens 2
• Size of pupil depends on viewing direction– Gives diameter of aperture of light for system
Resolution• Ability to discern fine details.
– Expressed as a linear dimension. – For typical electron microscope is ~ 0.2nm.
• Objects separated by >0.2nm will be resolved as being separate.
• Lord Rayleigh in 1896 first described resolution as a function of the Airy disc.
Airy discs of two point light sourcesAiry discs of two point light sources
Rayleigh Criterion• Rayleigh: Limit of resolution
– Two light sources must be separated by at least the diameter of first dark band.
Light distribution of a cross section of respective airy disc.
Resolution• Abbé derived an expression for resolution
– Comes from size of the lens that captures light.
• The resolution will be expressed in the same units as the wavelength of the light.
0.61Resolving powerN.A.×λ
=
Depth of Field• Area in front of and behind the specimen that will be
in acceptable focus.
• Determined by numerical aperture.
Depth of fieldDepth of field
In focusIn focusIn focusIn focusDepth ofDepth offieldfield
Depth of Field & Focus• Depth of field concerns focus plane of
specimen.
• Range of acceptable focus for the image is called depth of focus.
depth of focusdepth of focus depth of focusdepth of focus
( )2N.A.λ
=fiD
Depth of Focus
• Nearly same as depth of field – Determined by magnification as well. – Higher magnification depth of field
becomes shorter, higher magnification increase depth of focus for image.
– Depth of focus given by
• R.P. is the resolving power.
2R.P.N.A.
=foMD
Near Point
• Size of image on retina depends on distance from eye• Closest distance called near point.
– Varies with age and eye defects.• Varies with age as lens becomes less flexible.
– 10 years old ~ 7cm– 25 years old ~ 12 cm– 45 years old ~ 28 cm– 50 years old ~ 40 cm– 60 years old ~ 100 cm– 70 years old ~ 400 cm
– Normally given as 25 cm
Optical Instruments Viewed by Eye : Microscope
L=16cm in general, 20X means that f = 16cm/20 = 8 mm
Optical Instruments : Telescope
eyepiece
objectivetelescope f
fM ==
αα '
Waveguides — Trapping Light by TIR
Recommended