Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Chapter 24: Optical Instruments
•Combinations of Lenses
•The Camera
•The Eye
•The Magnifier
•The Compound Microscope
•The Telescope
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
§24.1 Combinations of Lenses
With lenses in combination, the image formed by one lens
is the object for the next lens.
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
The thin lens equation still applies.
1 1 1
 
p1 q1 f1
1
1
1
 
p2 q2 f 2
p2  s  q1
p is the object distance, q is the
image distance, f is the focal
length and s is the distance
between the lenses.
It is possible to have the object for the second lens be
virtual (p2<0); here the image formed by the first lens is
beyond the second lens.
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
The magnification of a combination of lenses is just the
product of the magnifications for the individual lenses.
mtotal  m1m2  mn
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Example (text problem 24.2): A converging and diverging
lens, separated by a distance of 30.0 cm, are used in
combination. The converging lens has f1 = 15.0 cm and the
diverging lens has an unknown focal length. An object is
placed at 20.0 cm in front of the converging lens; the final
image is virtual and is formed 12.0 cm before the diverging
lens. What is the focal length of the diverging lens?
1 1 1
 
p1 q1 f1
Given: p1 = 20 cm; f1 = 15 cm.
Find that q1 = 60 cm
p2  s  q1
Given: s = 30.0 cm. Find that
p2 = -30 cm.
1
1
1 Given: q2 = -12 cm and p2 = -30 cm.
 
p2 q2 f 2 Find that f2 = -8.6 cm.
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
§24.2 The Camera
A camera forms a real, inverted image. For far away
objects, the film must be placed one focal length from the
lens.
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Example (text problem 24.17): A person on safari wants to
take a photograph of a hippopotamus from a distance of
75.0 m. The animal is 4.00 m long and its image is to be
1.20 cm long on the film. (a) What focal length lens should
be used?
width on film h
q
m
 
object wid th
h
p
h
  1.2 cm 
q   p  
75.0 m   22.5 cm
h
 4.0 m 
1 1 1
 
Now use the thin lens equation
p q f
f  22.4 cm
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Example continued:
(b) What would be the size of the image if a lens of 50.0
mm focal length were used?
1 1 1
1 1 1
    
p q f
q f p
q  50.0 mm
width on film h
q
m
 
object wid th
h
p
q
50.0 mm 

h   h  
4.0 m   2.67 mm
p
 75.0 m 
The object is 2.67 mm long (inverted).
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
§24.3 The Eye
The lens is at a fixed distance from the retina (unlike in
some cameras where this is adjustable). The lens has a
variable focal length, which is adjusted to keep the image
distance (q) constant as the object distance (p) varies.
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
The near point is the closest distance from your eye that an
object can be seen clearly. For a normal eye this distance is
25 cm.
The far point is farthest distance from your eye that an
object can be seen clearly. For a normal eye this distance
is .
Refractive power of a lens is defined as:
1
P
f
where f is the focal length of
the lens; typical units of P are
diopters (1D = 1 m-1).
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
For a near sighted (myopic) person, light rays converge
before they strike the retina.
A diverging lens is placed in the light path. This creates a
virtual image closer to your eye than the actual object is.
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
For a far sighted (hyperopic) person, light rays converge after
they strike the retina.
A converging lens is placed in the light path. This creates a
virtual image farther from your eye than the actual object is.
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Example (text problem 24.63): If Harry has a near point of
1.5 m, what focal length contact lenses does he require?
The near point refers to the closest distance an object can be
to see it clearly, in this case 1.5 m. A normal eye has a near
point of 25 cm. These corrective lenses must take an object
at 25 cm and form a virtual image at a distance of 1.5 m.
1 1 1
 
p q f
The refractive power
of these lenses is
Given p = 25 cm; q = -1.5m.
Here f = +30.0 cm
1
1
P 
 3.3 D
f 0.30 m
(Diopter)
Harry is farsighted.
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
§24.4 The Magnifier
The farther an object is from your eye, the smaller it will
look.
For an object to look bigger the image of it formed on the
retina must be made bigger.
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Using the triangles in the figure, the angular size  of an
object is:
size of object
tan    
object distance
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
The angular magnification is
 aided
M
.
 unaided
The largest angular size an object can have and still be
seen clearly is when it is placed at your near point.
size of object
h
 unaided 

object distance N
Now the object is placed at the focal point of a converging
lens
 aided
size of object
h


object distance
f
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
h
 aided
f N
M


 unaided h
f
N
N is the near point for a person (typically 25 cm) and f is the
focal length of the lens used in the magnifier.
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Example (text problem 24.34): An insect that is 5.00 mm
long is placed 10.0 cm from a converging lens with a focal
length of 12.0 cm.
(a) What is the position of the image?
1 1 1
 
p q f
Given: p = 10.0 cm and f = 12.0 cm.
Find that q = -60.0 cm; on the same
side of the lens as the insect.
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Example continued:
(b) What is the size of the image?
h
q
m 
h
p
h  
q
  60 cm 
h  
5.00 mm   30.0 mm
p
 10 cm 
(c) Is the image upright or inverted?
Since h’>0, the image is upright.
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Example continued:
(d) Is the image real or virtual?
Since q<0 (the image forms on the same side of the
lens as the object), the image is virtual.
(e) What is the angular magnification if the lens is close to
the eye?
 aided
N 25 cm
M
 
 2.5
 unaided p 10 cm
Object is at a
distance of p, not
f from the lens.
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
§24.5 The Compound Microscope
Two converging lenses
are used to produce a
highly magnified image.
The objective lens forms an
enlarged real image here.
The eyepiece is used
to view this image.
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
The eyepiece is used as a magnifier; the image formed by
the objective is placed at the focal point of the eyepiece.
The total magnification is the product of the individual
magnifications:
M total  mobjmeye
 L  N 


 
 f  f 
 obj  eye 
where L = “tube length” = q0 - f0; N = near point distance;
and fobj & feye are focal lengths of the objective and eyepiece
respectively.
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Example (text problem 24.42): A microscope has an objective
lens of focal length 5.00 mm. The objective forms an image
16.5 cm from the lens. The focal length of the eyepiece is
2.80 cm.
(a) What is the distance between the lenses?
Using figure 24.16, the distance between the lenses
is d = feye + qo = 2.80 cm + 16.5 cm = 19.3 cm.
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Example continued:
(b) What is the angular magnification? The near point is
25.0 cm.
M total  mobjmeye
 L  N 


 
 f  f 
 obj  eye 
 qo  f obj  N 

  286
 
 f
 f 
obj

 eye 
(c) How far from the objective should the object be placed?
1 1 1
 
p q f
Given: q = 16.5 cm and f = 0.5 cm.
Find that p = 0.52 cm.
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
§24.6 The Telescope
A telescope is a combination of lenses and/or mirrors used
to collect a large amount of light and bring it to a focus.
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
A refracting telescope (or refractor) uses lens.
The barrel (or
tube) length is
The angular
magnification is
L  f obj  f eye .
 eye
f obj
M

.
 obj
f eye
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
A reflecting telescope uses mirrors (and lenses).
Light path of a Cassegrain telescope:
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Example (text problem 24.49): A refracting telescope is used
to view the moon (diameter of 3474 km & distance from Earth
384,500 km). The focal lengths of the objective and eyepiece
are +2.40 m and +16.0 cm, respectively.
(a) What should be the distance between the lenses?
L  f obj  f eye  2.56 m
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Example continued:
(b) What is the diameter of the image produced by the
objective?
image size h
q
m
 
object size h
p
h  
q
 2.40 m 
h  
3474 m   2.17 cm
p
 384,500 km 
(c) What is the angular magnification?
M 
f obj
f eye
2.40 m

 15
0.16 m
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Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Summary
•Combinations of Lens
•The Camera
•The Eye
•The Magnifier
•The Compound Microscope
•The Telescope
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