Transcript Near Point - Department of Physics and Astronomy

Chapter 25
Optical Instruments
© 2006, B.J. Lieb
Some figures electronically reproduced by permission of
Pearson Education, Inc., Upper Saddle River, New Jersey
Giancoli, PHYSICS,6/E © 2004.
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1
Camera
•A camera lens must produce a real image on the film. This may
require adjusting the lens position (di) to focus it.
•The iris diaphragm controls the area of the lens through which light
can pass.
•The shutter opens briefly to expose the film.
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2
Digital Cameras
•Charge Coupled Devices (CCD) are rapidly replacing film in
cameras.
•Light that passes through a color filter can produce an electron by
the photoelectric effect (Chapter 27)
•Total charge stored is read out.
•A color pixel is two greens and a red and a blue.
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3
Camera Lens
•Shutter speed: How long the shutter is open
•Focusing: Moves the lens to produce the sharpest image on
the film or CCD.
•Diameter of lens = D
•Focal length of lens = f
•The f-stop of a lens is defined as
f  stop 
f
D
•The smallest f-stop is referred to as the speed of the lens.
(Smaller is better since a large D means more light is
admitted.)
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4
Camera Lens
Lens moves to
focus image on
CCD or film. So
image distance is
adjusted.
•Normal lens – gives picture with field of view similar to human
eye. f = 50 mm.
•Telephoto lens – magnifies image. Typical telephoto has f = 200
mm which magnifies image by factor of ~ 4.
•Wide Angle – field of view larger than human eye. f = 30 mm.
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•Zoom lens – focal length is variable. Combines a converging lens
with a diverging lens that moves to adjust the focal length of the
combination.
5
Human Eye
Optics is similar to a camera:
•Iris (colored part of eye) controls light input
•Pupil is the hole in the iris
•Retina takes place of film- has rods and cones which are sensitive to
light
•Cones give fine detail and color
•Rods provide a gray image in low light situations
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6
Human Eye
•No shutter but nervous system “sees” about 30 images per second,
similar to a video camera
•Cornea does most of the bending of the light rays
•Lens does fine adjustment to focal length to focus image. Unlike the
camera, the image distance is fixed.
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Accommodation
•Accommodation is the adjustment of lens shape to focus the image onto
the retina. Muscles pull on lens and change its shape.
•Near Point ( N ) closest distance that the eye can focus clearly. For
“normal” eye, near point  25 cm.
•Far Point: farthest point that eye can focus. For “normal” eye, far point
is infinity (i.e. parallel rays).
•Nearsightedness: eye that can focus only on nearby objects.
•Farsightedness: eye that cannot focus on nearby objects
•Relaxed Eye: focused on infinity
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Correcting Eye Defects with Lenses
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Example 25-1: A person is to be fitted with bifocals. She can see an object
clearly when it is between 50 cm and 1.5 m from the eye.
A. The upper portion of the bifocals should enable her to see distant
objects clearly. What power should they have?
do  
di   1.5 m
negative because not on side of lens to which light is going.
1 1 1
 
do di
f
1
1
1


  1.5 m
f
f   1.5 m
power 
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1
 0.67 D ( diopters )
f
10
Example 25-1
B. The lower portion of the bifocals should enable her to see objects at a distance of
25 cm from the lens. What power should they have?
An object held at the near point, 25 cm, should have an image at 50 cm from the
eye so she can focus on it.
d o  25 cm
di   50 cm
negative because not on side of lens to
which light is going.
1
1
1


do di
f
1
1
1


25 cm  50 cm f
f   50 cm
power 
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1
1

  2.0 D
f 0.50 m
11
Magnifying Glass
•As an object is moved closer, the image of the object on the retina is
larger, so it appears larger to us
•If object is brought closer than the near point, we can not focus it
•A magnifying glass allows us to bring the object closer, while still
having the image at the near point.
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Magnifying glass with eye focused at near point.
•The greatest magnification results if the eye is focused on the near point
N (Note di = -N)
1
1
1
1
1




do
f
di
f
N
M
1 1
' h / d o N


 N   
 h / N do
 f N
M 
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N
1
f
Eye focused on near point.
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Astronomical Refracting Telescope
•The telescope shown above produces an inverted image
•Objective lens forms real image at its focal point (fo)
•Eyepiece ( fe ) acts as a magnifying glass on this image
•Θ  h / fo where h is image from objective and tanθ  θ
•θ’  h / fe (look at thick ray which is parallel to axis)
•The magnification is: M = θ’ / θ and thus:
• Negative M indicates an inverted image.
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M 
fo
fe
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Astronomical Reflecting Telescope
•Mirror takes place of objective lens in previous telescope but optics is the same
•Drawing shows two ways of getting light “out”
•Mirrors can be made much larger because they can be supported from below.
•Diameter of mirror determines light-gathering ability which is most important
in astronomy
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Example 25-2: (72) An astronomical telescope has a magnification of 8.0. If the two
lenses are 28 cm apart, determine the focal length of each lens.
fo
 8.0
fe
M 
f  8.0 f
o
e
f  f  28 cm
o
e
8.0 f e  f e  28 cm
9.0 f  28 cm
e
f  3.1cm
e
f o  8.0 f e  25 cm
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Compound Microscope
•Unlike telescope, object is very close
•Objective (fo ) and eyepiece (fe) play similar role as with telescope.
•If l is distance between lenses and N is near point:
M
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Nl
fe fo
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Example 25-3: A microscope uses an eyepiece with a focal length of 1.5
cm. Using a normal eye with a final image at infinity, the tube length is
17.5 cm and the focal length of the objective lens is 0.65 cm. What is the
magnification of the microscope?
N  25cm
( near point )
f  1.5 cm
f  0.65 cm
e
o
l  17.5 cm
Nl
M 
fe fo
M 
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(25 cm)(17.5 cm)
(1.5 cm)(0.65 cm)
 450 X
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Lens Aberrations
Spherical aberration: rays that pass through the outer regions of the lens
are brought to a different focal point then those that pass through the
center.
Chromatic aberration: different colors are focused at different
points. Can be reduced with compound lens. Some camera lenses
have 6 to 8 elements.
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Rayleigh Criterion
•Resolution: ability of a lens to produce distinct images of two point objects
•Resolution is limited by
•Various aberrations
•Diffraction
•Rayleigh Criterion: angular limit of resolution of light of wavelength 
passing through a lens of diameter D. The factor of 1.22 results from
treating a circular hole as the average of a slit.

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1.22 
D
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Example 25-4: A spy satellite carries out surveillance with a special highresolution camera with a lens diameter of 40.0 cm that is limited only by
diffraction. Estimate the separation of two small objects on the surface of
the earth that can be resolved in the light of 500 nm if the satellite is 250
km above the surface of the earth.
1.22 (1.22)(500  109 m)


D
(0.40 cm)
  1.53  10 rad
6
r
s
θ
s  r
s  (250 103 m)(1.53 106 rad )
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s  0.38 m
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X-Ray Diffraction
•Useful technique for studying crystals, molecules such as DNA etc.
•X-rays are produced when accelerated electrons strike a glass or metal
surface.
•X-rays have  smaller than atomic spacing
Conditions for constructive interference
between subsequent layers of the crystal
separated by distance d.
i   r
m  2 d sin 
m  1, 2, 3....
Note that angle definition is not the same as in optics chapter.
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