Title: Optical Instruments
1Chapter 25
2Optical 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
3The 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
4Camera 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
5Camera 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
6Camera, 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
7Camera, 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
8The 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
9The 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
10The 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
11The 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
12The 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
13The 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
14The 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
15The 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
16Conditions 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
17Farsightedness
- Also called hyperopia
- The image focuses behind the retina
- Can usually see far away objects clearly, but not
nearby objects
18Correcting 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
19Nearsightedness
- 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
20Correcting 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
21Presbyopia 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
22Diopters
- 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 -
23Simple 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
24The 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
25Angular 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
26Magnification 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
27Compound Microscope
- A compound microscope consists of two lenses
- Gives greater magnification than a single lens
- The objective lens has a short focal length, ƒolt1
cm - The ocular lens (eyepiece) has a focal length,
ƒe, of a few cm
28Compound 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
29Magnifications 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
30Other 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 (?? 500 nm)
31Telescopes
- 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
32Refracting 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
33Angular 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
34Disadvantages 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
35Reflecting 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
36Reflecting 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
37Examples 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
38Resolution
- 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
39Rayleighs 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
Rayleighs 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 Rayleighs criterion
40Just Resolved
- If viewed through a slit of width a, and applying
Rayleighs 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 ?min
41Barely Resolved (Left) and Not Resolved (Right)
42Resolution 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
43Resolving Power of a Diffraction Grating
- If ?1 and ?2 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
44Resolving 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
45Michelson 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
46Michelson 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
47Measurements 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 ?/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