lens 1lens 2

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

Optics

Reference : www.optics.rochester.edu/classes/opt100/opt100page.html

Light is a Ray (Geometrical Optics)

A. General Properties of Light Rays B. Reflection and Refraction

C. Prisms and Dispersion

D. Images Formed by Light Rays Reflected and Refracted at Planar Interfaces E. Images Formed by Light Rays Reflected and Refracted at Curved Interfaces F. Thin Lenses

G. Ray Tracing Through More Complex Optical Systems H. Ray Aberrations

I. Optical Instruments Viewed by Eye

J . Ray Optics Description of a Waveguide — Trapping Light by TIR Light is a Wave (Physical Optics)

A. Wave Basics

B. Interference of Two Waves C. Interference in Thin Films D. Interferometers

E. Holography

F. Diffraction of Light G. Polarization of Light Light is a Photon (Quantum Optics)

A. Where Does Light Come From? — Sources of Light B. The Laser

C. 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 by c = 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

θ

θ

Incident ray

reflected ray

normal

Refraction

Refraction –Snell’s Law

Refraction –Snell’s Law

????

n

n

×

< 0

t t

i

i

n

n sin θ = sin θ

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.

R

R

lens

Lensmaker’s Formula

( )

1 2

1 1 1 1

' n 1

s 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

– R

& R

• positive if centre on right of lens

• negative if centre on left of lens

Lenses

R₁> 0 R₂ < 0

R₁= ∞ R₂ < 0

Plano-convex

Bi-convex Meniscus convex

R₁> 0 R₂ > 0

Plano-concave

Bi-concave Meniscus concave

R₁< 0 R₂ > 0

R₁ = ∞ R₂ > 0

R₁> 0 R₂ > 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 1

' n 1

s s f R R

 

+ = + = ∞ −   −  

( )

1 2

1 1 1

n 1

f 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 0

R R

 −  >

 

 

1 2

1 1 0

R 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

Real Image Focus

Focus

u v

f f

Virtual Image

• Can be by concave (negative) lens

– Object beyond focus

• Image reduced

Object Virtual Image 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. = n sin α

Some examples of N.A

• In all cases, lens is in air (n = 1)

α α

5 mm

10mm

( )

(

)

tan 2.5 0.25 10

sin sin tan 0.25 sin 0.245 0.24 N.

3 A. 0.243

−

α = =

α

=

=

= =

α

5 mm

2.5 mm

(

)

tan 2.5 1 2.5

sin sin tan 1.0 sin 0.785 0.70 N.

7 A. 0.707

−

α = =

α

=

=

= =

20 mm

10mm

(

)

tan 10 1 10

sin sin tan 1.0 sin 0.785 0.707 N.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

P 1

= f

1 2 0

0 50 .

. = +

Magnification

• Magnification, M

– Ratio of image height to object height.

– So

• Positive when image erect

• Negative when image inverted

u

object v

image y

y

i o

M y

= y

Magnification

• Two similar triangles

– ABC and DEC – So

S

S’

object

image y

y

B

A

C D

E

'

i

o

y S

M = y = − S

Focal point Focal 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

Aberrations

Imperfections 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 Aberration

Different colours focused at different points.

– Combination of lenses decreases problem.

– Combination called an Achromat.

White White

source

source 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 of Focus of outer rays

outer rays Focus ofFocus of inner rays inner rays Circle of

Circle of

least confusion least 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 field Curved 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

Image f

f

Stop

f

f

Exit pupil Entrance pupil

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 sources Airy 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.

Resolving power 0.61

N.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 field Depth of field

In focus In focus

In focus In focus

Depth of Depth of field field

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 focus

depth of focus depth of focusdepth of focus

( _N.A. )

= λ

D

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.

2

R.P.

= N.A.

fo

D M

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 objective telescope

f

M = = f

α

α

Waveguides — Trapping Light by TIR