chapter 25 optical instruments. analysis generally involves the laws of reflection and refraction...
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TRANSCRIPT
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
Opaque, light-tight box Converging lens
Produces a real image Film behind the lens
Receives the image
Digital Camera Image is formed on
an electric device CCD – Charge-coupled
device CMOS –
Complementary metal-oxide semiconductor
Both convert the image into digital form
The image can be stored in the camera’s memory
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-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 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 ƒ-number 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, cont The eye can focus on near objects
The ciliary muscles tense 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 Average is about 25 cm It increases with age, to 500 cm or more at age 60
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
1ƒ
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
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
o
angle with lensm
angle without lens
max
251
cmm
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 lenses, magnifications of up to about 20 can be achieved The multiple lenses 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 lenses are separated by a distance L L is much greater than either focal length
The approach to analysis is the same as for any two lenses in a row 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
The angular magnification of the eyepiece of the microscope is
The overall magnification of the microscope is the product of the individual magnifications
ƒl
ll o
q LM
p
25ƒe
e
cmm
25ƒ ƒl e
o e
L cmm M m
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 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 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 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
Angular magnification is particularly important for observing nearby objects Very distant objects still appear as a small
point of light
ƒƒ
o
o e
m
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
For the images to be resolved, the angle subtended by the two sources at the slit must be greater than θmin
min a
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 1.22D
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
All the wavelengths are nearly the same
2 1
R
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
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 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
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