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Chapter 25
Optical Instruments
Optical Instruments
Analysis generally involves the laws of
reflection and refraction
 Analysis uses the procedures of
geometric optics
 To explain certain phenomena, the
wave nature of light must be used

The Camera
The single-lens
photographic
camera is an optical
instrument
 Components



Light-tight box
Converging lens


Produces a real image
Film behind the lens

Receives the image
Camera Operation

Proper focusing leads to sharp images

The lens-to-film distance will depend on the object
distance and on the focal length of the lens
The shutter is a mechanical device that is
opened for selected time intervals
 Most cameras have an aperture of adjustable
diameter to further control the intensity of
the light reaching the film


With a small-diameter aperture, only light from
the central portion reaches the film, and spherical
aberration is minimized
Camera Operation, Intensity

Light intensity is a measure of the rate
at which energy is received by the film
per unit area of the image


The intensity of the light reaching the film
is proportional to the area of the lens
The brightness of the image formed on
the film depends on the light intensity

Depends on both the focal length and the
diameter of the lens
Camera, f-numbers

The ƒ-number of a camera is the ratio
of the focal length of the lens to its
diameter
ƒ = f/D
 The ƒ-number is often given as a
description of the lens “speed”


A lens with a low f-number is a “fast” lens
Camera, f-numbers, cont
Increasing the setting from one ƒ-number to
the next higher value decreases the area of
the aperture by a factor of 2
 The lowest ƒ-number setting on a camera
corresponds to the aperture wide open and
the maximum possible lens area in use
 Simple cameras usually have a fixed focal
length and a fixed aperture size, with an ƒnumber of about 11


Most cameras with variable ƒ-numbers adjust
them automatically
The Eye


The normal eye focuses
light and produces a
sharp image
Essential parts of the
eye


Cornea – light passes
through this transparent
structure
Aqueous Humor – clear
liquid behind the cornea
The Eye – Parts, cont

The pupil
A variable aperture
 An opening in the iris

The crystalline lens
 Most of the refraction takes place at the
outer surface of the eye


Where the cornea is covered with a film of
tears
The Eyes – Parts, final

The iris is the colored portion of the eye
It is a muscular diaphragm that controls
pupil size
 The iris regulates the amount of light
entering the eye by dilating the pupil in low
light conditions and contracting the pupil in
high-light conditions
 The f-number of the eye is from about 2.8
to 16

The Eye – Operation

The cornea-lens system focuses light
onto the back surface of the eye
This back surface is called the retina
 The retina contains receptors called rods
and cones
 These structures send impulses via the
optic nerve to the brain


The brain converts these impulses into our
conscious view of the world
The Eye – Operation, cont

Rods and Cones

Chemically adjust their sensitivity according to the
prevailing light conditions



The adjustment takes about 15 minutes
This phenomena is “getting used to the dark”
Accommodation



The eye focuses on an object by varying the shape of
the crystalline lens through this process
An important component is the ciliary muscle which is
situated in a circle around the rim of the lens
Thin filaments, called zonules, run from this muscle to
the edge of the lens
The Eye – Focusing

The eye can focus on a distant object
The ciliary muscle is relaxed
 The zonules tighten
 This causes the lens to flatten, increasing
its focal length
 For an object at infinity, the focal length of
the eye is equal to the fixed distance
between lens and retina


This is about 1.7 cm
The Eye -- Focusing

The eye can focus on near objects
The ciliary muscles tenses
 This relaxes the zonules
 The lens bulges a bit and the focal length
decreases
 The image is focused on the retina

The Eye – Near and Far Points

The near point is the closest distance for
which the lens can accommodate to focus
light on the retina



Typically at age 10, this is about 18 cm
It increases with age
The far point of the eye represents the
largest distance for which the lens of the
relaxed eye can focus light on the retina

Normal vision has a far point of infinity
Conditions of the Eye
Eyes may suffer a mismatch between the
focusing power of the lens-cornea system and
the length of the eye
 Eyes may be


Farsighted


Light rays reach the retina before they converge to form
an image
Nearsighted

Person can focus on nearby objects but not those far
away
Farsightedness
Also called hyperopia
 The image focuses behind the retina
 Can usually see far away objects clearly, but
not nearby objects

Correcting Farsightedness
A converging lens placed in front of the eye can
correct the condition
 The lens refracts the incoming rays more toward the
principle axis before entering the eye


This allows the rays to converge and focus on the retina
Nearsightedness



Also called myopia
In axial myopia the nearsightedness is caused by the
lens being too far from the retina
In refractive myopia, the lens-cornea system is too
powerful for the normal length of the eye
Correcting Nearsightedness
A diverging lens can be used to correct the
condition
 The lens refracts the rays away from the
principle axis before they enter the eye


This allows the rays to focus on the retina
Presbyopia and Astigmatism

Presbyopia is due to a reduction in
accommodation ability



The cornea and lens do not have sufficient
focusing power to bring nearby objects into focus
on the retina
Condition can be corrected with converging lenses
In astigmatism, the light from a point source
produces a line image on the retina

Produced when either the cornea or the lens or
both are not perfectly symmetric
Diopters

Optometrists and ophthalmologists
usually prescribe lenses measured in
diopters

The power of a lens in diopters equals the
inverse of the focal length in meters

P = 1/ƒ
Simple Magnifier
A simple magnifier consists of a single
converging lens
 This device is used to increase the
apparent size of an object
 The size of an image formed on the
retina depends on the angle subtended
by the eye

The Size of a Magnified Image

When an object is
placed at the near
point, the angle
subtended is a
maximum


The near point is about
25 cm
When the object is
placed near the focal
point of a converging
lens, the lens forms a
virtual, upright, and
enlarged image
Angular Magnification

Angular magnification is defined as

angle with lens
m

o angle without lens

The angular magnification is at a
maximum when the image formed by
the lens is at the near point of the eye
q = - 25 cm
 Calculated by

mmax
25cm
 1
q
Magnification by a Lens
With a single lens, it is possible to
achieve angular magnification up to
about 4 without serious aberrations
 With multiple lens, magnifications of up
to about 20 can be achieved


The multiple lens can correct for
aberrations
Compound Microscope

A compound
microscope consists of
two lenses



Gives greater
magnification than a
single lens
The objective lens has a
short focal length, ƒo<1
cm
The ocular lens
(eyepiece) has a focal
length, ƒe of a few cm
Compound Microscope, cont

The lens are separated by a distance L


The approach to analysis is the same as for
any two lenses in a row


L is much greater than either focal length
The image formed by the first lens becomes the
object for the second lens
The image seen by the eye, I2, is virtual,
inverted and very much enlarged
Magnifications of the
Compound Microscope

The lateral magnification of the microscope is
Ml  

ql
L

pl
ƒo
The angular magnification of the eyepiece of
the microscope is
me 

25 cm
ƒe
The overall magnification of the microscope is
the product of the individual magnifications
m  Ml me  
L  25 cm 


ƒo  ƒe 
Other Considerations with a
Microscope

The ability of an optical microscope to
view an object depends on the size of
the object relative to the wavelength of
the light used to observe it

For example, you could not observe an
atom (d  0.1 nm) with visible light (λ
500 nm)
Telescopes

Two fundamental types of telescopes



Refracting telescope uses a combination of lens to
form an image
Reflecting telescope uses a curved mirror and a
lens to form an image
Telescopes can be analyzed by considering
them to be two optical elements in a row

The image of the first element becomes the object
of the second element
Refracting Telescope




The two lenses are arranged
so that the objective forms a
real, inverted image of a
distance object
The image is near the focal
point of the eyepiece
The two lenses are
separated by the distance ƒo
+ ƒe which corresponds to
the length of the tube
The eyepiece forms an
enlarged, inverted image of
the first image
Angular Magnification of a
Telescope

The angular magnification depends on the
focal lengths of the objective and eyepiece
 ƒo
m

o ƒ e

Angular magnification is particularly important
for observing nearby objects

Very distance objects still appear as a small point
of light
Disadvantages of Refracting
Telescopes
Large diameters are needed to study
distant objects
 Large lenses are difficult and expensive
to manufacture
 The weight of large lenses leads to
sagging which produces aberrations

Reflecting Telescope

Helps overcome some of the disadvantages of
refracting telescopes



Replaces the objective lens with a mirror
The mirror is often parabolic to overcome
spherical aberrations
In addition, the light never passes through
glass


Except the eyepiece
Reduced chromatic aberrations
Reflecting Telescope,
Newtonian Focus

The incoming rays are
reflected from the
mirror and converge
toward point A


At A, a photographic
plate or other detector
could be placed
A small flat mirror, M,
reflects the light toward
an opening in the side
and passes into an
eyepiece
Examples of Telescopes

Reflecting Telescopes
Largest in the world are 10 m diameter
Keck telescopes on Mauna Kea in Hawaii
 Largest single mirror in US is 5 m diameter
on Mount Palomar in California


Refracting Telescopes

Largest in the world is Yerkes Observatory
in Wisconsin

Has a 1 m diameter
Resolution
The ability of an optical system to distinguish
between closely spaced objects is limited due
to the wave nature of light
 If two sources of light are close together, they
can be treated as non-coherent sources
 Because of diffraction, the images consist of
bright central regions flanked by weaker
bright and dark rings

Rayleigh’s Criterion
If the two sources are separated so that their
central maxima do not overlap, their images
are said to be resolved
 The limiting condition for resolution is

Rayleigh’s Criterion


When the central maximum of one image falls on
the first minimum of another image, they images
are said to be just resolved
The images are just resolved when their angular
separation satisfies Rayleigh’s criterion
Just Resolved

If viewed through a slit of
width a, and applying
Rayleigh’s criterion, the
limiting angle of resolution
is
min



a
For the images to be
resolved, the angle
subtended by the two
sources at the slit must
greater than θmin
Barely Resolved (Left) and Not
Resolved (Right)
Resolution with Circular
Apertures
The diffraction pattern of a circular
aperture consists of a central, circular
bright region surrounded by
progressively fainter rings
 The limiting angle of resolution depends
on the diameter, D, of the aperture

min

 1.22
D
QUICK QUIZ 25.1
Suppose you are observing a binary star
with a telescope and are having difficulty
resolving the two stars. You decide to use a
colored filter to help you. Should you
choose a blue filter or a red filter?
QUICK QUIZ 25.1 ANSWER
We would like to reduce the minimum angular
separation for two objects below the angle
subtended by the two stars in the binary
system. We can do that by reducing the
wavelength of the light—this in essence makes
the aperture larger, relative to the light
wavelength, increasing the resolving power.
Thus, we would choose a blue filter.
Resolving Power of a
Diffraction Grating

If λ1 and λ2 are nearly equal
wavelengths between which the grating
spectrometer can just barely
distinguish, the resolving power, R, of
the grating is


R

 2  1 

All the wavelengths are nearly the same
Resolving Power of a
Diffraction Grating, cont
A grating with a high resolving power can
distinguish small differences in wavelength
 The resolving power increases with order
number


R = Nm



N is the number of lines illuminated
m is the order number
All wavelengths are indistinguishable for the
zeroth-order maximum

m = 0 so R = 0
Michelson Interferometer
The Michelson Interferometer is an
optical instrument that has great
scientific importance, but is unfamiliar
to most people
 It splits a beam of light into two parts
and then recombines them to form an
interference pattern


It is used to make accurate length
measurements
Michelson Interferometer,
schematic
A beam of light provided
by a monochromatic
source is split into two
rays by mirror M
 One ray is reflected to M1
and the other transmitted
to M2
 After reflecting, the rays
combine to form an
interference pattern
 The glass plate ensures
both rays travel the same
distance through glass

Measurements with a
Michelson Interferometer


The interference pattern for the two rays is
determined by the difference in their path lengths
When M1 is moved a distance of λ/4, successive light
and dark fringes are formed
 This change in a fringe from light to dark is called
fringe shift


The wavelength can be measured by counting the
number of fringe shifts for a measured displacement
of M
If the wavelength is accurately known, the mirror
displacement can be determined to within a fraction
of the wavelength