Chapter 25
LECTURE NOTES
OPTICAL INSTRUMENTS
Camera
The camera consists of a converging lens one focal length away from film that records an image
of a very distant object. The lens can be moved away from the film to image closer objects (with
di > f).
The shutter speed can be set for a variety of exposure times usually differing by a factor of two.
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Exposures less than
s can stop the blurring caused by shaking hands holding the camera.
100
f-stop is defined as lens focal length divided by lens diameter (or clear aperture if part of the lens
is covered): f-stop = f/D. This dimensionless number also comes in a variety of settings
differing by 2 . The camera adjusts to a setting by covering part of the lens using an iris
diaphragm thus changing D by 2 . Since the area of the lens opening determines the amount of
light reaching the film, and area  D2 changing the f-stop from f/2.8 to f/4.0 means half as much
light reaches the film and we should double the exposure time (one step change of shutter speed,
1
1
s to
s . Note an f/4.0 setting would imply a 50mm focal length lens has a
perhaps from
60
30
clear diameter opening of 12.5mm.
 di
and di  f. Note the image formed
do
on the film is inverted, real and reduced. To increase depth of field (the range of distances where
objects do not become a blur on film), we want a small diameter lens opening. Different films
are made to work faster or slower, in dimmer or brighter light with more or less grain. The
choice of settings takes fine judgment about the desired image.
A longer focal length lens produces a larger image: m =
The Human Eye
Much like a camera, the eye has a lens of adjustable focal length, an iris to decrease the effective
diameter of the lens, and a retina about one focal length from the lens where a real, inverted,
reduced image is formed.
Most of the refraction occurs in the cornea, not the lens. The lens, by changing shapes under
stress from the ciliary muscles, makes fine focus adjustment. When the muscles are relaxed, the
lens should focus at  . When they contract, the center of the lens thickens, shortening the focal
length so near by objects focus on the retina. This is called accommodation. Your eyes can hurt
or you can get a headache from focusing on close objects for long times.
We define the near point as the closest distance at which an object is in clear focus. This
increases as we age due, in part, to degenerative changes in the lens material and ciliary muscles.
We define the far point as the farthest distance at which an object is clearly focused. For a
normal eye, the near point is 25cm (closer for young people) and the far point  .
If a person is nearsighted (perhaps the eyeball is too long or the cornea too curved), the far point
is <  . Diverging lenses correct this condition.
If a person is farsighted (perhaps the eyeball is too short or the cornea too flat), the near point is
>25cm. Converging lenses correct this.
Presbyopia also moves the near point farther than 25cm. This form of farsightedness occurs in
older people. It is a loss of accommodation as discussed above and is corrected by converging
lenses.
Astigmatism, caused by an out-of-round cornea or lens, results in points being imaged as lines.
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Corrective lenses are prescribed by power. Recall P (in diopters) = where f is the focal length
f
of the lens in meters.
Example:
An aging teacher finds he cannot read papers closer than 1 meter from his eye. What lens would
correct this? We want the near point at 25cm, and the eye can bring things to focus if they are
100 cm away. The lens should take an object at 25cm and produce its image at 100cm on the
same side of the lens as the object. Thus do = 25cm, di = –100cm, and f = 33cm = +3D, where
1
1 1

 . This supposes the lens-eye distance can be ignored (contacts).
we used
di do f
Example:
A nearsighted person has a far point of 22cm. If glasses are worn 2cm from the eye, what
prescription will correct this?
The far point should be  (do =  ) and produce an image 22cm from the eye (20cm from the
lens) on the same side of the line as the object (di = –20cm. Thus f = -20cm = -5D corrects the
problem. Note these glasses will change the near point also. For nearsighted people this is often
much less than 25cm. If the person in the example had a near point of 12cm (from eye or 10cm
from glasses) we find now that with di = -10cm and f = -20cm that do = 20cm and this is the
nearest point for clear vision while wearing glasses.
Do you require vision correction? What is your prescription? What do the numbers mean?
Simple Magnifiers
A magnifying glass is a converging lens held less than one focal length from an object. The
image we see is thus virtual, erect, and enlarged. This lets us place an object closer to the eye
than its near point to achieve greater magnification.
For a relaxed eye focused at  , angular magnification M = 25cm/f where f is the focal length
(in cm) of the magnifying lens.
2
If the eye focuses at the near point M =
25cm
+ 1.
f
Telescope
The simple refractor consists of a pair of lenses. The objective lens (closest to the object) has a
large focal length fo while the eyepiece lens focal length fe is small. The objective produces a
real, inverted, reduced image slightly less than one focal length fe from the eyepiece lens. The
latter acts as a simple magnifier and we view an inverted, enlarged, virtual image. The lenses are
about fo + fe apart. We will make a simple telescope in labs.
Modern telescopes use mirrors of great size to gather light from very dim objects.
Aberrations
Lenses and mirrors suffer from defects that limit the quality of the image. Spherical aberration,
for lenses or mirrors that are parts of spheres, make rays farther from the center focus at a
different distance than central rays. Parabolic mirrors do not suffer from this defect.
Off-axis images can suffer from coma (points look like commas), astigmatism, curvature of field,
and distortion. Play with computer monitor controls to see some of these distortions.
Chromatic aberration is a failure of lenses only, and is caused by dispersion. Red light focuses at
a different distance from a lens than blue light. This can be overcome by making doublet or
triplet lenses from different types of glasses.
Resolution
This is the ability to produce distinct images of two objects (points) that are close together.
1.22
is the smallest angle  (in
D
radians) the objects can be separated by and still be distinguished as discrete objects. D is the
lens or mirror diameter and  the observing wavelength. The atmosphere of the earth severely
degrades image quality and a large D without adaptive optics rarely can distinguish objects as
close as Rayleigh would predict.
For a telescope, the Rayleigh criterion is often quoted:  
Note: It is generally not possible to resolve details of objects smaller than the observing
wavelength.
Note: The resolution of the human eye is 5 x 10-4 radians. At the 25cm near point, we can
separate objects 0.1mm apart.
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