# Magnification ```Magnification
Image Size
 The image produced by a
lens is typically a different
size than the object.
 An object and image are
image
measured by relative
distance.
• Distance from the lens s
• Distance in plane y
yo
so
object
si
yi
Inverted Image
 Images in a single convex lens
are inverted.
• Negative planar distance
• yi &lt; 0
image
 Images can have negative
distance from the lens.
• Virtual image
yo
so
object
si
yi
Magnification Ratio
 The ratio of the image size to
image
yo
so
si
yi
the object size is the
magnification M.
• Negative for inverted images
 From geometry this equivalent
to the ratio of the image
distance to the object distance.
object
yi
si
M

yo
so
Single Lens
 A single converging lens will
image
magnify objects.
• Always inverts
yo
si
so
yi
 A real image requires a
positive object distance.
• so &gt; f
object
 A real image requires a
1 1 1
 
s o si
f
M
yi
s
 i
yo
so
positive image distance.
• si &gt; f
Photocopier
 A photocopier needs to create
an image exactly the same
size as the object.
• Object at twice focal length
yi  Myo   1yo
M  1  
si
so
1 1
2 1
  
so so so f
si  so  2 f
si  so
Projector
si  M so
1
1
M 1 1



so Mso
Mso
f
so 
M 1
f
M
 A projector needs a larger
image at a distant screen.
• Real image
• Inverted object
• Object between f and 2f
Magnifying Glass
 A magnifying glass works on
objects within the focal length.
• Upright virtual image
• Eye needed to focus
si
M 3
so
1
1
2
1



s o 3 s o 3s o f
2
so  f
3
si  3so  2 f
next
```