A
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W
S
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LENSES
Whereas mirrors produce images by reflection, lenses produce images by refraction. Depending upon their
“thickness”, lenses are classified as “thick” or “thin”. In this course, we will only consider “thin” lenses.
In effect, therefore, we disregard the thickness of the lens assuming it to be a line.
There are two main types of lenses called convex (also known as converging) and concave (also known as
diverging). Convex lenses are thicker in the middle than at the edges while concave lenses are thicker at
the edges than in the middle.
Both convex and concave lenses each have three variations as illustrated below.
CONVEX LENSES
CONCAVE LENSES
(CONVERGING)
(DIVERGING)
Double-convex
Concavo-convex
Plano-convex
Double-concave
Plano-concave
Concavo-concave
 REMEMBER: Convex lenses are thicker in the middle and thinner at the edges while concave lenses
are thinner in the middle and thicker at the edges.
When representing “thin” lenses in a diagram, it is sometimes more convenient to simply draw an arrow
rather than the actual lens. Using this method, an arrow is used to represent the lens as illustrated below.
or
or
Convex Lens
Concave Lens
 Sign convention:
 Object distance is always positive.
 Image distance is positive if the image is on the side of the lens where light emerges (from lens).
 Image distance is negative if the image is on the side of the lens where the light enters (the lens).
 The focal length of a convex or converging lens (or mirror) is positive.
 The focal length of a concave or diverging lens (or mirror) is negative.
PHYSICS 534  OPTICS  AnsPhysics Ex-52.DOC
© 1999 S. Lancione
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Just as with concave mirrors, the characteristics of the image formed by a converging lens depend upon the
location of the object. There are six "strategic" locations where an object may be placed. For each location,
the image will be formed at a different place and with different characteristics.
We will illustrate the six different locations and label them as CASE-1 to CASE-6.
CASE-1
CASE-2
Object
2F' F'
F
F
2F' F'
2F
Image
2F
Object at infinity
Object just beyond 2F'
No image
Image is real, inverted, reduced,
and located between F and 2F
CASE-3
CASE-4
Object
2F' F'
F
Object
2F' F'
2F
Image
F
2F
Image
Object at 2F'
Object between 2F' and F'
Image is real, inverted, same size
as object, and located at 2F
Image is real, inverted, enlarged,
and located beyond 2F
CASE-5
CASE-6
Object
2F' F'
Object at F'
No image
F
2F
Extended rays
Image
2F' F'
Object
F
2F
Parallel
Object within focal length
Image is virtual, upright, enlarged,
and located on same side as object
1. A lens that is thicker in the middle than at the ends is known as:
converging
convex
A _____________________
lens or a _____________________
lens.
2. A lens that is thicker at the ends than in the middle is known as:
diverging
concave
A _____________________
lens or a _____________________
lens.
PHYSICS 534  OPTICS  AnsPhysics Ex-52.DOC  Lenses Part-1 /2
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3. Trace the rays that emerge from the following glass mediums:
4.
For each case below, draw the appropriate lens that will produce the indicated rays.
(a)
5.
(b)
How is the image formed by a mirror different from the image formed by a lens?
A mirror forms an image by reflection (reflected rays) whereas a lens forms
________________________________________________________________________
an image by refraction (refracted rays).
________________________________________________________________________
________________________________________________________________________
PHYSICS 534  OPTICS  AnsPhysics Ex-52.DOC  Lenses Part-1 /2
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6.
For each convex lens illustrated below, draw the image.
a
Objet
2F
F
F
2F
b
Objet
2F
2F
F
F
F
F
c
Objet
2F
PHYSICS 534  OPTICS  AnsPhysics Ex-52.DOC  Lenses Part-1 /2
2F
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d
Objet
2F
F
F
2F
F
2F
e
Objet
2F
7.
F
For each concave lens illustrated below, draw the image.
a)
b)
F'
Virtual image
F
F'
F
Virtual image
PHYSICS 534  OPTICS  AnsPhysics Ex-52.DOC  Lenses Part-1 /2
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8.
An object that is 7 cm high is placed 20 cm in front of a convex (converging) lens whose
focal length is 15 cm. Determine the characteristics of the image:

h o  7 cm
hi  ?
d o  20 cm
di  ?
f  15 cm
Type:
(real or virtual)
1 1
1


f di do
60 cm
______________
-3
Magnification: ______________
21 cm
Height: ______________
Location:
or
1 1
1
1
1
 


d i f d o 15 cm 20 cm

hi
d
 i
ho
do
 M
R eal
______________
 hi  
 d i  60 cm
(60 cm )(7 cm )
  21 cm
20 cm
hi
 21 cm

 3
ho
7 cm
Attitude:
In v e r te d
______________
(upright or inverted)
Negative sign indicates inversion
9.
An object whose height is 4 cm is placed 50 cm from a concave (diverging) lens. If the
focal length of the lens is 30 cm, determine the characteristics of the image:
h o  4 cm
hi  ?
d o  50 cm
di  ?
f   30 cm
Type:
Virtual
______________
(real or virtual)
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. Location: ______________
18.75 cm
1 1 1
1
1
0.375
or
 


 d i   18.75 cm Magnification: ______________
d i f d o  30 cm 50 cm

1 1
1


f di do

hi
d
 i
ho
do
 M
 hi  
(18.75 cm )(4 cm )
 1.5 cm
50 cm
Height:
1.5 cm
______________
Attitude:
Upright
______________
(upright or inverted)
h i 1.5 cm

 0.375
ho
4 cm
10. An object that is 5 cm high is placed 70 cm in front of a convex (converging) lens whose
focal length is 20 cm. Determine the characteristics of the image:
h o  5 cm
hi  ?
f  20 cm
d o  70 cm d i  ?
1 1
1
 

f di do
1 1 1
1
1
or
 


 d i  28 cm
d i f d o 20 cm 70 cm
h
d
( 28 cm )(5 cm )
 i   i  hi  
  2 cm
ho
do
70 cm
h
 0.2 cm
 M i 
  0.04
ho
5 cm
Type:
Real
______________
(real or virtual)
28 cm
______________
-0.4
Magnification: ______________
2 cm
Height: ______________
Location:
Attitude:
Inverted
______________
(upright or inverted)
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