Chapter 36 Optical Instruments

1
Chapter 36 Optical Instruments
PHYS 2326-33
2
Concepts to Know

• f-number
• Fresnel Lens
• Eye
• Magnifier
• Microscope
• Telescope
• Aberrations

3
Combination of Thin Lenses

• Image formed by first lens must be located as if
  the second lens is not present
• A ray diagram is drawn for the second lens using
  the image of the first lens as the object of the
  second
• The second image is the image of the system
• If the first image is behind the second lens, it
  is virtual and has p2 for its location
• Magnification is a product of the individual
  magnifications M M1M2

4
Two Thin Lenses in Contact

• Given 2 thin lenses in contact with each other of
  focal lengths f1 and f2, this compound lens has a
  focal length
• 1/f 1/f1 1/f2 Eqn 36.19

5
Lens Aberrations

• Our equations make assumptions like small angles
  to the axis, that lenses are thin and even that
  the index of refraction is uniform at all
  wavelengths.
• Ray tracing permits precise analysis using
  Snells law.
• There are two common abberrations
• spherical aberration
• chromatic aberration

6
Spherical Aberration

• Caused by parallel rays coming in further away
  from the principal axis and intersect the
  principal axis after refraction at different
  points than rays closer in
• Parabolic mirrors and lenses are better but are
  much harder to make
• Parabolic mirrors are common in telescopes
• Cameras use adjustable apertures to control the
  amount of light and to reduce spherical aberration

7
Chromatic Aberration

• Chromatic aberration is related to dispersion and
  is caused by differences in the index of
  refraction for different wavelength. Shorter
  wavelengths like violet may refract more than
  red, changing the focal point inward
• Solutions to this are the use of more exotic
  lenses such as achromatic or apochromatic which
  are composed of two or even three different
  materials, some are more exotic than plain glass.

8
Cameras Eyes

• Cameras and eyes are quite similar
• Both have a lens and an aperture (usually
  adjustable to control incoming light)
• Both have a light sensitive medium at the back
  which captures the image
• Eyes tend to have a spherical sensing area which
  permits superior results with simpler optics
• Cameras tend to have a flat sensing area
• Both must create a real image on the sensor

9
Exposures

• The eye is logarithmic and can cover a tremendous
  dynamic range.
• It has an automatic iris control adjustable
  f-number
• Cameras are linear and can cover only a small
  part of their dynamic range
• To adjust, they offer shutter speed and aperture
  f/number which permit them to have the right
  exposure over a broad range of intensities
• More modern cameras also tend to offer electronic
  amplification which provides increased
  sensitivity at the expense of increased
  electronic noise in the image
• Some ccd cameras are so sensitive they can
  essentially count individual photons of light

10
Aperture

• Some optical systems, like most cameras have an
  adjustable aperture
• All optical systems have an aperture
• Aperture is f/D where f is the focal length and D
  is the diameter
• Apertures are called f-numbers
• Aperture is related to the amount of light that
  is permitted to enter which is proportional to D2

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• f-number is defined by f/D Eqn 36.20
• Intensity I is proportional to 1/f-number2
• A telescope usually doesnt have an adjustable
  aperture but rather D is the diameter of the main
  lens or the main mirror.
• The lower the f/number, the faster the lens and
  often the more expensive it is for a certain
  quality grade

12
f/numbers

• Nice cameras often run from f/1.2 or f/4 up to
  f/16 or f/22
• Astronomy telescopes usually run from f/4 up to
  f/15 with specialized imaging units running as
  low as f/2.2
• The 16 telescope upstairs is f/4.5
• f-number is also related to depth of field, the
  region where objects are in reasonably sharp
  focus. Larger f/numbers have larger depth of
  field regions

13
The Eye

• Eyes offer a marvelous tool
• Optical problems can included nearsightedness
  myopia, farsightedness hperopia, and
  astigmatism
• Optometrists use the unit diopters which is the
  inverse of focal length in meters P1/f.
• Astigmatism requires a lens with different focal
  lengths in each of two different planes
• Over ones lifetime one tends to become more
  farsighted as they lose the ability to focus over
  a broad area.

14
Simple Magnifier

• Even with a magnifying glass, the size of the
  object viewed by the eye depends upon the angle ?
  subtended by the object
• A converging lens (or magnifying glass) may be
  used to increase the apparent size of an object
  as seen by the eye.
• This is an angular magnification m ?/?o
• Assuming ones vision permits 25cm as the closest
  distance, eqn 36.24 mmax 1 25cm/f is the
  maximum magnification possible and mmin 25cm/f
  is the lowest for a magnifier

15
Compound Microscope

• A compound microscope consists of an objective
  lens near the sample being observed an an
  eyepiece
• The objective has a very short focal length lt 1cm
  and the eyepiece with f a few cm
• These lenses are placed at a distance L greater
  than the focal lengths of the lenses
• The object is placed just outside the focal point
  of the objective

16
Microscope Magnification

• Overall magnification is M Mome where Mo is the
  lateral magnification of the objective and me is
  the angular magnification of the eyepiece
• M -L/fo (25/fe) the sign indicates an
  inversion

17
Telescope

• Eqn 36.27 is shown in section 36.10 along with
  the approximations and derivation
• m ?/?o - fo/fe ratio of the focal length of
  the objective divided by that of the eyepeice
• The two common types are reflectors and
  refractors with mirrors or lenses for the
  objective
• The largest reflectors are 10 meters in diameter
  while the largest refractor is about 1meter.

18

• Most objects of interest in the sky are dim and
  not necessarily small in apparent size
• The moon and sun are both about ½ degree across
• There are a number of dim objects youve probably
  never seen that are several degrees across
• As such its not the power of the telescope but
  its aperture which is actually important to the
  amateur and professional astronomer
• Aperture fever anxious physiological condition
  which occurs when one realizes that a 4 or 8 inch
  telescope is not enough and that 24 inch diameter
  might suffice. It is highly infectious and
  affects primarily visual observers rather than
  those involved in imaging. There is no know cure
  although larger telescopes mask symptoms