Transcript Chapter 26 - Purdue Physics

Optical Resolution
 For a circular opening of
diameter D, the angle
between the central
bright maximum and the
first minimum is
1.22
 
D
 The circular geometry
leads to the additional
numerical factor of 1.22
Section 25.8
Telescope Example
 Assume you are looking at a star through a telescope
 Diffraction at the opening produces a circular diffraction
spot
 Assume there are actually two stars
 The two waves are incoherent and do not interfere
 Each source produces its own different pattern
Section 25.8
Rayleigh Criterion
 If the two sources are sufficiently far apart, they can
be seen as two separate diffraction spots (A)
 If the sources are too close together, their diffraction
spots will overlap so much that they appear as a
single spot (C)
Section 25.8
Rayleigh Criterion, cont.
 Two sources will be resolved as two distinct sources of
light if their angular separation is greater than the angular
spread of a single diffraction spot
 This result is called the Rayleigh criterion
 For a circular opening, the Rayleigh criterion for the
angular resolution is
1.22
min 
D
 Two objects will be resolved when viewed through an
opening of diameter D if the light rays from the two
objects are separated by an angle at least as large as
θmin
Section 25.8
Scattering
 When the wavelength is
larger than the reflecting
object, the reflected waves
travel away in all direction
and are called scattered
waves
 The amplitude of the
scattered wave depends on
the size of the scattering
object compared to the
wavelength
 Blue light is scattered more
than red
 Called Rayleigh scattering
Section 25.9
Blue Sky
 The light we see from the
sky is sunlight scattered
by the molecules in the
atmosphere
 The molecules are much
smaller than the
wavelength of visible light
 They scatter blue light
more strongly than red
 This gives the
atmosphere its blue color
Section 25.9
Scattering, Sky, and Sun
 Blue sky
 Although violet scatters more than blue, the sky
appears blue
 The Sun emits more strongly in blue than violet
 Our eyes are more sensitive to blue
 The sky appears blue even though the violet light is
scattered more
 Sun near horizon
 There are more molecules to scatter the light
 Most of the blue is scattered away, leaving the red
Section 25.9
Nature of Light
 Interference and diffraction show convincingly that
light has wave properties
 Certain properties of light can only be explained with
a particle theory of light
 Color vision is one effect that can be correctly
explained by the particle theory
 Have strong evidence that light is both a particle and
a wave
 Called wave-particle duality
 Quantum theory tries to reconcile these ideas
Section 25.10
Quantum
Mechanics?!
 Single electrons fired
through double slit
 Interference? With…?
 Quantum Computing
Chapter 26
Applications of Optics
Applications of Optics
 Many devices are based on the principles of optics
 Eyeglasses around 1200s
 Perhaps the oldest optical instrument
 Microscopes and telescopes around 1600
 CDs and DVDs around 1980s
 Also improvements to devices have been made
Applications of a Single Lens
 The eye can be modeled as a single lens with a focal
length ƒeye
 Eyeglasses and contact lenses add a lens in front of
the eye
 A magnifying glass is also a single lens
Section 26.1
Normal Eye
 Light emanating from a
point on the object is
focused to a
corresponding point on
the retina
 The near-point distance,
sN, is the closest distance
an object can be that you
can focus (~25 cm)
 Objects nearer than the
near-point cannot be
focused on the retina
Section 26.1
Normal Eye, cont.
 The normal eye can also focus on objects that are
very far away
 s~∞
 The eye must adjust its focal length to values
between sN and ∞
 Does this by using muscles that deform and change
the shape of the eye’s lens
 Needs to change from about 2.3 cm to 2.5 cm
Section 26.1
Glasses and Contact Lenses
 Glasses or contact lenses are lenses placed in front
of the eye
 Along with the eye, these form a system of lenses
 One lens from the eye and one from the glasses or
contact
 Systems of lenses contain two or more lenses
 The same analysis idea will be applied to
telescopes, microscopes and other optical
instruments
Section 26.1
Analysis for a System with Two
or More Lenses
 Draw a picture showing the object of interest and the
lenses in the problem
 Use the rules for ray tracing along with the thin-lens
equations to find the location and magnification
produced by the first lens in the system
 The image produced by the first lens then acts as
the object of the second lens in the system
 Use the rules for ray tracing and the thin-lens
equations a second time to find the location and
magnification produced by the second lens in the
system
Section 26.1
Far-Sighted Vision
 The near-point distance
is greater than for a
normal eye
 Objects located closer
than the near-point
distance cannot be
focused
 To compensate, a lens
can be placed in front of
the eye
Section 26.1
Far-Sighted Correction
 The contact (or glasses)
lens is the first lens in the
system
 For example, if a person’s
near-point distance is 75
cm, the corrective lens
needs to be a converging
lens with ƒlens = 38 cm
 If the person’s near-point
distance is greater than
75 cm, the focal length of
the corrective lens needs
to be shorter
Section 26.1
Diopters
 The strength of a lens is sometimes measured in
terms of its refractive power
1
refractive power 
ƒlens
 Units are m-1 which is called a diopter
 For example, the lens with ƒ = 38 cm will have a
refractive power of 2.7 diopters
Section 26.1
Near-Sighted Vision
 A nearsighted person is
unable to focus light from
distant objects on the
retina
 The incoming rays from
an object very far away
are approximately parallel
to the axis (at infinity)
 A nearsighted eye
produces an image in
front of the retina
Near-Sighted Correction
 The object at ∞ needs
to focus on the retina
 For example, if the
person can focus
objects within 2.0 m, the
corrective lens needs to
be a diverging lens with
ƒlens = -2.0 m
Glasses
 The eyeglass lens is a
short distance in front of
the eye
 Instead of touching it as
with the contact lens
 The distance must be
taken into account
 This generally makes the
focal length of the
eyeglasses about 10%
shorter than a contact
lens
Section 26.1
Magnifying Glass
 The simplest magnifying glass is a single lens
 Again it can be considered a system of two lenses
 The magnifying lens and the eye
 The goal is to produce a greatly magnified image at
the retina
 Want the image on the retina to be as large as
possible
 Analysis is similar to that for contact lenses or
eyeglasses
Section 26.1
Magnifying Glass, cont.
 The largest clearly
focused image for the
unaided eye results
when the object is at the
near point
 The object’s apparent
size when it is located
at the near point can be
measured using the
angle θ
Section 26.1
Image Properties with a
Magnifying Glass
 The object is positioned inside the focal length of this
lens
 This position of the lens produces an upright virtual
image at a point farther from the eye
 The eye perceives the light as emanating from this
virtual image
 The image angle with the magnifying glass is greater
than the image angle for the eye alone
 The image on the retina is enlarged by the
magnifying glass
Section 26.1
Angular Magnification
 The enlargement of the image on the retina is given
by the angular magnification mθ
M
m 

 From geometry and the small angle approximations,
m 
hi
s
s
s
 N  N 1  N
ho
so
ƒ
ƒ
 The angular magnification of a typical magnifying
glass is usually 10 or 20
Section 26.1
Microscopes
 Lenses with focal lengths less than a few mm are difficult





to make
There is a practical limit to the magnification of a single
lens
A more useful way to achieve higher magnification is
using two lenses arranged as a compound microscope
The image produced by one lens is used as the object of
the second lens
The image produced by the second lens is then viewed
by the eye
The total magnification is the product of the
magnifications of the two lenses
Section 26.2
Compound Microscope
 The two lenses are called the objective and the eyepiece
 To analyze the image produced first apply ray tracing and the
thin-lens equation to find the image produced by the objective
lens
 This image acts as the object for the eyepiece
 The image produced by the eyepiece is viewed by the eye
Section 26.2
Compound Microscope, cont.
 The distance between the objective lens and the
original object is adjusted so that the image
produced by the objective falls at the focal point of
the eyepiece
 This gives a final virtual image for the observer
 The linear magnification of the objective lens is
mobj
hi
si


ho
ƒ obj
Section 26.2
Compound Microscope,
Magnification
 The total magnification of the microscope is the
product of the linear magnification of the objective
and the angular magnification of the eyepiece
mtotal  mobj m , eyepiece
si
sN

ƒ obj ƒ eyepiece
 The negative sign indicates that the image is
inverted
Section 26.2
Advances in Microscope Design
 The index of refraction of the glass used to make the
lenses is slightly different for light of different colors
 This makes the focal length slightly different for
different colors
 This affects the focusing properties of a microscope
 Called chromatic aberration
 Chromatic aberration can be corrected by using an
achromatic lens
 This is a lens composed of different types of glass with
different indices of refraction which approximately
cancels the aberrations
Section 26.2
Resolution of a Microscope
 There is a fundamental limit to the resolution that
can be achieved with any microscope that relies on
focusing
 This limit is due to the diffraction of light passing
through the aperture of the microscope
 Diffraction prevents the size of the focused spot from
being less than a value approximately equal to the
wavelength of the light
Section 26.2
Resolution, cont.
 It is possible to resolve
the outgoing light from
two features only if they
are separated by a
distance approximately
equal to the wavelength
of the light that is used
 If they are closer, it is
not possible to tell that
there are two separate
features
Section 26.2
Resolution, final
 Optical resolution is set by diffraction
 It is approximately equal to the wavelength of the light
used
 Applications requiring the best possible resolution
use blue or ultraviolet light
 These color have the shortest wavelength compared
with other colors of visible light
Section 26.2
Confocal Microscope
 A confocal microscope
is designed so that
features at only one
particular depth form the
final image
 This is done by placing a
pinhole in front of the
observer
 The depth of resolution is
again limited by diffraction
effects
 Depths must be greater
than λ to be separated
Section 26.2
Telescopes
 When using a telescope, the light rays from the
object are nearly parallel
 The object is approximately at infinity
 One purpose of a telescope is to increase the
angular separation between two stars
 This allows your eye to distinguish one star from the
other
Section 26.3
Refracting Telescope
 A refracting telescope use lenses
 Objective lens and eyepiece
 Was invented around 1600 and was the type used by
Galileo
 The objective lens forms an image of the object
 This image then acts as the object for the second lens
Section 26.3
Refracting Telescope – Image
 For the objective lens
 The object is at infinity (approximately)
 The image forms at the focal point of the lens
 Eyepiece
 The eyepiece is located such that the image formed by
the objective is very close to the focal point of the
eyepiece
 The rays from the first image form a bundle of nearly
parallel rays that are perceived by the observer
Section 26.3
Refracting Telescope –
Magnification
 The magnification is determined by the angles the
incident ray (θ) and ray refracted by the eyepiece
(θT) make with the axis
T
m 

 Actually, this is the angular magnification
 From geometry and the small angle approximation
m 
ƒobj
ƒeyepiece
Section 26.3
Reflecting Telescope – Newtonian
Design
 Newton designed a
reflecting telescope
 Uses mirrors
 Advantages
 The mirrors will not have
any chromatic aberration
 Easier to make a highquality mirror than a lens
 For a given diameter, a
mirror is lighter and
easier to support
Section 26.3
Reflecting Telescope – Cassegrain
Design
 In the Cassegrain design,
light reflects from the
primary mirror, then from
a secondary mirror and
travels through a small
hole in the primary mirror
 The light then travels
through an eyepiece to
the observer
 The Hubble Space
Telescope is an example
of a Cassegrain design
Section 26.3
Magnification – Reflecting
Telescope
 The concave mirror forms a real image of a distant
object very close to the focal point of the mirror
 A second mirror is positioned in front of the focal
point and reflects the light to an eyepiece
 The magnification is similar to that for the refracting
telescope, with ƒM being the focal length of the
primary mirror
m 
ƒM
ƒ eyepiece
Section 26.3
Resolution of a Telescope
 Resolution determines how close together in angle
two stars can be and yet still be seen as two
separate stars
 The resolution is limited by two factors
 Diffraction at the telescope’s aperture
 Atmospheric turbulence
 The aperture is generally the same diameter as the
primary mirror
 From the Rayleigh criterion, the limiting angular

resolution set by diffraction is min  1.22
D
Section 26.3
Resolution, cont.
 Most telescopes do not attain the resolution limit
 Starlight must pass through many kilometers of air
before reaching an observer on Earth
 The turbulent motion of the air causes fluctuations in
the refractive index from place to place
 The fluctuations act like lenses and refract the
incoming light from the star
 The “lenses” are constantly changing, so the direction
of the starlight changes as well

This makes the star “twinkle”
Section 26.3
Atmospheric Effects
 For a location on the Earth’s surface, the angular
spread caused by atmospheric turbulence is typically
1" (one arc second)
 1° = 60 arc minutes
 1 arc minute (1') = 60 arc seconds
 The value for this angular spread is smaller at higher
altitudes
 Telescopes in space eliminate atmospheric effects
and the resolution is determined by the diffraction
limit of the primary mirror
Section 26.3
Adaptive Optics
 The technology of building telescopes with adjustable mirrors to
compensate for atmospheric distortion is called adaptive optics
 A reference star is an object known to appear as a point source
 As the atmosphere causes the image of the reference star to be
smeared out, the telescope’s mirror is adjusted to make the image as
perfect as possible
 Computers allow for rapid and accurate control of the mirror shape
Section 26.3
Cameras
 Cameras are common
optical devices
 A simple camera consists
of a single lens positioned
in front of a light-sensitive
material
 The lens forms an image
on the detector
 An aperture is opened for
a short time to allow
sufficient light energy to
enter
Section 26.4
Film Camera
 The distance between
the camera’s lens and
the film determines
which objects are in
focus
 The standard lens for a
35 mm camera is 40
mm
 The “35 mm” is from
the size of the film
 24 mm x 35 mm
Section 26.4
Film Camera, cont.
 Other lenses can be purchased with different focal
lengths
 Since the object is far away from the camera, a good
approximation is that the image forms at the focal
point
 The linear magnification of the image is
hi
ƒ
m

ho
so
 The image is real and inverted
Section 26.4
Digital Camera
 A digital camera replaces film with a CCD
 A CCD is a charge-coupled device
 A CCD uses a type of capacitor to detect light and
record its intensity
 The optical system of a digital camera is basically
the same as that of a film camera
 There are important differences
Section 26.4
CCD
 A CCD is fabricated in an integrated circuit chip
 The chip contains many capacitors arranged in a
grid
 When light strikes the chip, it is absorbed in the
dielectric layer and ejects some electrons from their
normal chemical bonds
Section 26.4
CCD, cont.
 The ejected electrons move to the capacitor plate
 This leads to a voltage across the capacitor that is
closest to where the light was absorbed
 This voltage is detected by additional circuitry and its
value is stored in a computer memory in the camera
 The magnitude of the voltage depends on the light
intensity
 The greater the intensity, the higher the voltage
 The pattern of voltages on the capacitors gives the
light intensity as a function of position
Section 26.4
CCD, final
 One way to measure
the color is to combine
the information from
four adjacent capacitors
 Filters allow different
colors to pass through
to the capacitor
 The camera’s computer
can estimate the
average color over the
region
Section 26.4
Pixels
 Each region forms a pixel
 From picture element
 The image produced by the CCD is stored by the
camera as a set of intensity and color values for
each pixel
 An important specification is the number of pixels in
each photograph
 A larger number of pixels indicates a finer level of
detail in the photograph
Section 26.4
Optics of a Digital Camera
 The size of the CCD is much smaller than the area
of the film
 Typically about 6 mm x 8 mm
 The magnification is still
hi
ƒ
m

ho
so
 Since the detector is smaller, the image height must
be smaller
 The focal length must be smaller for a digital camera
 About 4 times smaller
Section 26.4
Optics, cont.
 The lens in the digital camera must be closer to the
detector
 The distance between the lens and the CCD is
approximately the focal length of the lens
 This allows the digital camera to be much thinner than a
film camera
 The optical zoom function changes the magnification of a
digital camera by moving the lens relative to the CCD
detector
 A digital zoom process constructs the entire photo using
just the image data from near the center of the CCD grid
 This uses fewer pixels and has poorer resolution than
without the digital zoom
Section 26.4
ƒ-Number
 Settings for both film and digital cameras include
shutter speed and the ƒ-number
 Shutter speed is the amount of time the film or CCD
is exposed to light from the object
 The ƒ-number is associated with the camera’s
aperture
 The aperture is an opening that controls the open area
of the lens
Section 26.4
ƒ-Number, cont.
 The ƒ-number is the
ratio of the focal length
to the aperture diameter
ƒ
ƒ  number 
D
 A large aperture gives a
small ƒ-number
 This allows more light
to reach the film or the
CCD
Shutter Speed and ƒ-Number
 There is a trade-off between
shutter speed and ƒ-number
 If you reduce shutter speed,
you need to compensate by
increasing the ƒ-number
 Same Exposure Value
(Camera settings) can have
different f-number and time
 Halving f-number reduces EV
by sqrt(2)
2
fn
EV 
time
Section 26.4
Depth of Focus and ƒ-Number
 With a small aperture (large ƒ-number) the blurring of images away
from the best focus is small
 With a large aperture (small ƒ-number) some rays make a large
angle with the central ray
 They diverge more quickly as one moves away from the image point
 The ƒ-number is also related to the depth of focus
 Having a large depth of focus means that objects that are not at the
best focusing point will produce images that are still close to ideal
Section 26.4
Pinhole Camera
 The pinhole camera
makes the aperture very
tiny
 No lens is needed
 A sharp image can result
 The intensity is very low
and so you need long
exposure times
 Allows safe viewing of
intense light sources such
as the Sun
Section 26.4
CD
 CDs and DVDs are
applications of optics that
can only be understood in
terms of the ideas of wave
optics
 CDs and DVDs operate
through similar principles
 Structure is a plastic layer
that is smooth on the
bottom and contains a
pattern of pits on the top
Section 26.5
CD Structure
 The pattern of pits on the top surface is used to encode






information on the CD
The top surface is coated with a thin layer of aluminum to
make it reflecting
It is then covered with a protective layer of lacquer
The label is placed over the lacquer
The pits are arranged in a long spiral track
Information encoded in the pits is read by reflecting a
laser beam from the aluminum surface
Laser light passes in and out through the bottom surface
of the plastic, so the surface must be kept clean
Section 26.5
Reading a CD
 The layer of aluminum
acts as a mirror
 It reflects the laser light
 The pits influence this
reflection through thinfilm interference effects
 The pit depth is
designed to produce
destructive interference
Reading a CD, cont.
 There is no reflected light when the laser beam is
over a pit edge
 The intensity is large when the laser beam is over
the center of a pit or is outside a pit
 As the laser beam travels along a track, the reflected
light intensity varies between zero and a large value
 These high and low values of the intensity
correspond to ones and zeros in a binary encoding
of information on the CD
Section 26.5
Reading a CD, final
 To store as much information as possible on the CD,
the pits must be as small as possible
 The minimum size is approximately equal to the
wavelength
 The limit is set by wave optics
 Differences in DVDs
 Shorter wavelength lasers allow pits to be closer
together
 Multiple layers of aluminum
 Pits probed on both sides
Section 26.5