Chapter 34: Thin Lenses
Now consider refraction through this piece of glass:
focal point
optic
axis
converging light
This is called a “Double Convex Lens”
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Chapter 34: Thin Lenses
Converging Lenses
(convex)
Diverging Lenses
(concave)
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Chapter 34: Thin Lenses
Diverging Lens
Where is the focal
point for these 4
incoming rays?
Don’t confuse these
reflections for something
meaningful.
Converging Lens
The focal point is
visible because real
rays go through it.
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Chapter 34: Thin Lenses
Optical Ray Diagram: a line drawing depicting a
small number of key light rays. For a lens, an
optical ray diagram should include:
1. Parallel Ray. A ray parallel to the optic axis which
passes through the object & the focal point.
2. Focal Ray. A ray that passes through both the
focal point and the object.
3. Chief Ray. A ray that passes through both the
center of the lens and the object.
These three rays intersect at the image.
Note: we don’t use reflected rays in lens analysis.
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Chapter 34: Thin Lenses
The Diverging Lens
parallel ray
f

f

Virtual part: where the
refracted ray appears
to come from.
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Chapter 34: Thin Lenses
The Diverging Lens
real part
virtual part


Virtual part: where the
refracted ray appears
to come from.
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Chapter 34: Thin Lenses
The Diverging Lens


The chief ray has
no virtual part.
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Chapter 34: Thin Lenses
Put all three rays together:


The three refracted rays have no intersection.
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Chapter 34: Thin Lenses
Put all three rays together:
object

focal
point

upright
image
There is an intersection of the virtual parts.
Need virtual parts to find the image?  Virtual image.
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Chapter 34: Thin Lenses
The Thin Lens Equation
Parallel ray
a converging lens


f
so
si
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Chapter 34: Thin Lenses
The Thin Lens Equation
Parallel ray
a converging lens


Positive side for
object distance
Positive side for
Negative side for
image distance
image distance
focal length
focal length (e.g. diverging lens)
Opposite for mirrors
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Chapter 34: Thin Lenses
The Thin Lens Equation
1 1
 P
so si
1 1 1
 
so si f
“Strength” or “Power” of lens
Note: our book
uses “P”. Other
books use “S”.
1
P
f
f, so and di all must have the same length units.
Units of P usually in [m-1] or rather [Diopters].
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Chapter 34: Thin Lenses
Why is 1/f called the “lens power”?
(or sometimes “strength”)
focal point
at 
1
if f   or ratherP   0
f
then thelens has NO EFFECT on thelight
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Chapter 34: Thin Lenses
Why is 1/f called the “lens power”?
(or sometimes “strength”)
focal point very
close to the lens
1
if f  0 or ratherP   
f
then thelens has A HUGE EFFECT on thelight
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Chapter 34: Thin Lenses
Example 1: A lens focuses light from an object 2.75m
away as an image 0.483m on the other side of the
lens. What are the focal length, lens type and image
type?
1 1 1
1
1
  

f so si 2.75m 0.483m
f  0.411meters
The lens is converging because:
 f>0
Converging lens: f>0
Diverging lens: f<0
What is the image type?
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Chapter 34: Thin Lenses
The image is real (si>0). Is it inverted or upright?
2.75 m
0.483m
6 cm = 1m
0.411m


Ray diagram shows the image is:
 Real
 Inverted
True whenever the object is outside the focal point
of a converging lens.
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Chapter 34: Thin Lenses
The ray diagram also shows the image is small.
positive side for
di and f
negative side for di and f
ho


hi
Magnification:
hi
di
m 
ho
do
Minus sign indicates that
real images are always
inverted.
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Chapter 34: Thin Lenses
How to do lens problems graphically
Use a full sheet – Landscape.
Sketch the lens on the optic axis.
Sketch the objects – correctly positioned.
Show a scale. You might wish to show a
different scale for vertical and horizontal
lengths
5. Sketch two principle rays per object and
find the image.
6. Refraction occurs on the vertical center-line.
1.
2.
3.
4.
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Chapter 34: Thin Lenses
Example 2: How far from a converging lens with a
focal length of 25 cm should an object be placed to
produce a real image which is the same size as the
object?
si >0
si
We want m    1
so
 si  so
(Minus because all
real images are
inverted.)
1 1 1
 
f so si
1
1 1
2
  
25 cm s o s o s o
s o  50 cm
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Chapter 34: Thin Lenses
How to make a magnifying glass
What kind of lens has an upright image with m>1?
si
m    1
so
si negative
|si| > |so|
image is farther from the
lens than the object
si <0

f

Place the object within the focal length of a converging lens.
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