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Chapter 25
Optical Instruments2010-11-30
Optical Instrument It generally involves the laws of
reflection and refraction It uses the procedures of
geometric optics For 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
Sensor behind the lens receives the inverted image
Camera Operation Proper focusing leads to sharp images
The lens-to-sensor 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 sensor per unit area of the image The intensity of the light reaching the sensor
is proportional to the area of the lens The brightness of the image formed on
the sensor 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
f/4
f/3 f/16
Large f-number, or small lens dia.
f-number
The Eye – a biological camera
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 – 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 – muscle 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 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 Far-sighted
Light rays reach the retina before they converge to form an image
Near-sighted Person can focus on nearby objects but not those
far away
Far-sightedness
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
Near-sightedness
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
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
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
Diffraction Gratings
Diffraction Gratings 1
Diffraction Gratings 2
Diffraction Gratings 3
Diffraction Gratings 4
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
Michelson Interferometer
Fig 38-31, p.1227
Polarization
Polarization Application --Display