Lecture 26
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Optical Instruments
Optical Instruments
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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
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The single-lens
photographic camera
is an optical
instrument
Components
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Light-tight box
Converging lens
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Produces a real
image
Film behind the lens
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Receives the image
Camera Operation
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Proper focusing leads to sharp images
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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-number = 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
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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
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The normal eye
focuses light and
produces a sharp
image
Essential parts of the
eye

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Cornea – light passes
through this
transparent structure
Aqueous Humor –
clear liquid behind the
cornea
The Eye – Parts, cont
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The pupil
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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
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The iris is the colored portion of the eye
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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
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The cornea-lens system focuses light
onto the back surface of the eye
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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
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Rods and Cones
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Chemically adjust their sensitivity according to the
prevailing light conditions
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The adjustment takes about 15 minutes
This phenomena is “getting used to the dark”
Accommodation
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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
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The eye can focus on a distant object
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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, cont
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The eye can focus on near objects
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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
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The near point is the closest distance
for which the lens can accommodate to
focus light on the retina
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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
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Normal vision has a far point of infinity
Conditions of the Eye
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Eyes may suffer a mismatch between
the focusing power of the lens-cornea
system and the length of the eye
Eyes may be
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Farsighted
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Light rays reach the retina before they converge
to form an image
Nearsighted
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Person can focus on nearby objects but not those
far away
Farsightedness
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Also called hyperopia
The image focuses behind the retina
Can usually see far away objects
clearly, but not nearby objects
Correcting Farsightedness
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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
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This allows the rays to converge and focus on the
retina
Nearsightedness
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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
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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
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Presbyopia is due to a reduction in
accommodation ability
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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
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The power of a lens in diopters equals
the inverse of the focal length in
meters
1

ƒ
Simple Magnifier
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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
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When an object is
placed at the near
point, the angle
subtended is a
maximum
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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
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Angular magnification is defined as

angle with lens
m

 o angle without lens
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The angular magnification is at a
maximum when the image formed by
the lens is at the near point of the eye
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q = - 25 cm
25 cm
Calculated by mmax  1 
q
Magnification by a Lens
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With a single lens, it is possible to
achieve angular magnification up
to about 4 without serious
aberrations
With multiple lenses,
magnifications of up to about 20
can be achieved
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The multiple lenses can correct for
aberrations
Compound Microscope
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A compound
microscope consists
of two lenses
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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
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The lenses are separated by a distance L
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The approach to analysis is the same as
for any two lenses in a row
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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
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The lateral magnification of the microscope is
Ml  
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ql
L

pl
ƒo
The angular magnification of the eyepiece of
the microscope is
25 cm
m 
e
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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
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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
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Two fundamental types of telescopes
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Refracting telescope uses a combination of
lenses 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
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The image of the first element becomes the
object of the second element
Refracting Telescope
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The two lenses are arranged
so that the objective forms a
real, inverted image of a
distant 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 ƒe
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Angular magnification is particularly
important for observing nearby objects
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Very distant objects still appear as a small
point of light
Disadvantages of
Refracting Telescopes
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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
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Helps overcome some of the
disadvantages of refracting telescopes
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Replaces the objective lens with a mirror
The mirror is often parabolic to overcome
spherical aberrations
In addition, the light never passes
through glass
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Except the eyepiece
Reduced chromatic aberrations
Reflecting Telescope,
Newtonian Focus
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The incoming rays
are reflected from
the mirror and
converge toward
point A
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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
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Reflecting Telescopes
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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
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Largest in the world is Yerkes Observatory
in Wisconsin
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Has a 1 m diameter
Resolution
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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 noncoherent sources
Because of diffraction, the images
consist of bright central regions flanked
by weaker bright and dark rings
Rayleigh’s Criterion
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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
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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
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If viewed through a slit
of width a, and applying
Rayleigh’s criterion, the
limiting angle of
resolution is
min 
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
a
For the images to be
resolved, the angle
subtended by the two
sources at the slit must
be greater than θmin
Barely Resolved (Left) and
Not Resolved (Right)
Resolution with Circular
Apertures
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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
Resolving Power of a
Diffraction Grating
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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 
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All the wavelengths are nearly the same
Resolving Power of a
Diffraction Grating, cont
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A grating with a high resolving power
can distinguish small differences in
wavelength
The resolving power increases with
order number
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R = Nm
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N is the number of lines illuminated
m is the order number
All wavelengths are indistinguishable for the
zeroth-order maximum
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m = 0 so R = 0
Michelson Interferometer
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The Michelson Interferometer is an
optical instrument that has great
scientific importance
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
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A beam of light provided
by a monochromatic
source is split into two
rays by a partially
silvered 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
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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