Chapter 5

Geometrical OpticsOptical systems

Phys 322Lecture 16

Magnifying glassPurpose: enlarge a nearby object by increasing its image size on retina

Requirements:• Image should not be inverted• Image should be magnified• Rays entering eye should not be converging

Use positive lensand so < f

Largest image without aid:

Magnifying glassMagnifying power MP, or angular magnification - the ratio of the size of the retinal image as seen through the instrument to that as seen by bare eye at a normal viewing distance:

u

aMP

a - aided, u - unaided

Near point, do :closest point at which image can be brought into focusStandard observer: do=0.25 m

Magnifying glass

u

aMP

Lyia /

oou dy /

Using paraxial approximation and lens equation (page 211):

lLLdMP o D1

f1

D

DoL dMP

unaided viewaided view

Standard observer: do=0.25 m

If D=10, MP=2.5, notation 2.5XTypically limited to 2.5X - 3X

Most common case: so=f, L=

Eyepiece (ocular)Eyepiece is essentially a magnifying glass that is designed to magnify image created by the previous optical system.

The Huygens eyepiece

Virtual object!Virtual image at Center of exit pupil -

at eye plane

More complex:

M1 M2

Image plane #1

Eye-piece

Objective Image plane #2

Microscopes goal: to magnify objects that are really close.

When two lenses are used, it’s called a compound microscope.

Microscopes

Compound microscope

~1595, Zacharias Janssen: compound microscope

~1660, Robert Hooke’smicroscope,

~30X magnification

~1700, Anton Van Leeuwenhoek microscope (single lens)270X magnification

“Father of microscope”

Compound microscope

Total magnification:MP = MTo MAe

angular magnification of eyepiece

Transverse magnification of objective

Standard design: L = 160 mm

Tube lengthAssuming standard tube length and standard viewing distance 25 cm:

eo fmm

fmmMP 250160

Respective powers are marked as 10X, 20X etc.

Compound microscope

Amount of light (brightness of image) depends on numerical aperture of the objective:NA = nisinmax

Power = 40X

NA=0.65

Maximum NA in air is 1Can be as large as 1.4 - in oil

Microscope summary

The pinhole camera

Object

Image

Pinhole

If all light rays are directed through a pinhole, it forms an image with an infinite depth of field.

The first person to mention this idea was Aristotle.

The concept of the focal length is inappropriate for a pinhole lens. The magnification is still –di/do.

With their low cost, small size and huge depth of field, they’re useful in security applications.

1769

Camera obscuraLatin: dark room

pinhole cameraPortable tent version

1620

Inside camera obscura Central Park, 1877

1665:VermeerThe Girl with the Red HatProbably used camera obscura

http://www.acmi.net.au/AIC/CAMERA_OBSCURA.html

Camera

1826: First photograph by Joseph Nicephore Niepce

Exposure time: 8 hours!

Photography lenses

Double Gauss Petzval

Photography lenses are complex! Especially zoom lenses.

These are older designs.

Photography lenses

Modern lenses can have up to 20 elements!

Canon EF 600mm f/4L IS USM Super Telephoto Lens17 elements in 13 groups$12,000

Canon 17-85mm f/3.5-4.5 zoom

Modern SLR Camerasingle lens reflex

Diaphragm=variable aperture stopcontrols f-number, or amount of light

For sharp image lens is moved back and forth - changing sichanges so

Film size is fixed (field stop) -changing f can change angular field of view.f=6-40 mm - wide-anglef~50 mm - normal anglef=80-1000 - telephoto lens

Telescopes

A telescope should image an object, but, because the object will have a very small solid angle, it should also increase its solid angle significantly, so it looks bigger.

M1 M2

Image plane #1

Image plane #2

Keplerian telescope

The telescopetele-skopos (Greek) - seeing at a distance

1608, Hans Lippershey tried to patent “kijker”

1609: Galileo, two lenses and an organ pipe

“looker” (Dutch)

Telescope Terminology

Refracting telescope

Notes:image is invertedobject is typically at infinity

Angular magnification:e

o

u

a

ffMP

Terrestrial (non-inverting) telescope

Binoculars

Telescope aperture

Telescope aperture: * determines amount of light collected

more light - more low-brightness distant stars could be seen

* determines the angular resolution diffraction limited angle is 1.22/D radians (chapter 10)

- wavelength of lightD - diameter of lens (or mirror)

ExerciseA friend tells you that the government is using Hubble telescope to read car license plates. Is it possible?

Assume best case scenario: the car’s license plate faces up

Solution: To resolve license plate number need ~2 cm resolution

Dnm 50022.1

m 000,600cm 2

must have D 20 m

Orbit height 600 km, aperture 2.4 m

Hubble

2.4 m telescope could resolve ~15 cmNote: atmospheric turbulence will most probably lower the resolving power below theoretical limit

Refracting telescope aperture

Lens versus mirror:- harder to make (need large diameter to collect more light)- focal length depends on wavelength: n=n()

Largest refracting telescope (~1900): 40” doublet, 500 pounds. Net weight: 20 tonsYerkes, Williams Bay, WI

http://www.wavian.com/aip/cosmology/tools/tools-refractors.htm

Reflecting telescopes

Keck 10 m telescopeHawaii, 1993

Arecibo Observatory305 m radio telescope

Reflecting telescope

prime focus

1661: Invented by Scottsman James Gregory

1668: Constructed successfully by Newton

Newtonian telescope

The Cassegrain TelescopeTelescopes must collect as much light as possible from the generally very dim objects many light-years away.

It’s easier to create large mirrors than large lenses (only the surface needs to be very precise).

Object

It may seem like the image will have a hole in it, but only if it’s out of focus.

Liquid mercury telescope

Liquid mercury mirror3m NASA’s Debris Observatory

Spinning liquid in equilibrium: parabolic surface

grz

2

22

• One turn in ~10 seconds• must be maintained at 10-6 level• ~30 L of Hg for 6 m mirror• Surface smoothness ~10-7 (.3mm bump on Earth)• Points only up• Costs $1M instead of $100M

r

z

6 m liquid mercury telescope f/1.5

http://www.astro.ubc.ca/LMT/lzt/gallery.html

mirror support

Zenith telescope70 km East of Vancouver

f/1.5, f=10 m

Correcting aberrationsSpherical mirrors do not work:spherical aberrations and coma

Aplanatic reflectors:Both primary and secondary mirrors are hyperbolic

Example: Hubble telescope

Catadioptric systems:Correct spherical aberrations using specially profiled lens

Wavefront shapingLenses, mirrors - reshape wavefronts, designed to work with spherical or plane wavesMore complex elements - more complex wavefronts

Light from star passes turbulent air -wavefront is not plane anymore, it has few m distortions (> ~0.5 m)

In a good night, the planar area of the wave from distant star is ~20 cm - no matter how large the telescope is resolution is the same as that of 20 cm telescope!

Need techniques that could constantly adapt optical elements to restore plane wave: Adaptive optics

Wavefront distortions

Phys 322Lecture 16

Adaptive optics

Phase conjugation

If we could at the same instant turn the wave direction backwards we can restore the initial (plane) wave shapeThe light propagation is reversible.

1972: Zeldovich et al.Use Stimulated Brillouin Scattering

/2

Intense electric field increases n at minima and maxima (sound wave) - constructive backward scattering (simplified view)