Converging lens and its focal length, f

1
Converging lens and its focal length, f
Light collection
The parallel rays pass through the lens and
converge at the focal point. The parallel rays
can come from the left or right of the lens.
A thin lens has two focal points, corresponding
to parallel rays from the left and from the
right. A thin lens is one in which the distance
between the surface of the lens and the center of
the lens is negligible compared with the focal
length, f.
2
Diverging lens and its focal length, f
The parallel rays diverge after passing through
the diverging lens. The focal point is the point
where the rays appear to have originated.
Light collection?
3
Imaging
Every point of the object is a point source of
light with the rays going in all possible
directions. All the rays originating from a
point P of the object that go through the lens
are also going through another point P behind
the lens. This is the essence of imaging by the
lens. For every point of an object there are
three principal rays emanating from it, which are
especially convenient to trace.
4
f
l

• Three principal rays emanating from every point
  of the object
• Goes parallel to the axis of the lens on the
  front side and through the focal point on the
  back side.
• Goes through the center of the lens and does not
  get refracted.
• Goes through the focal point on the front side
  and parallel to the axis of the lens on the back
  side.

5
Ray Diagram for Converging Lens. The object is
further away from the lens than the front focal
point, l gt f
f
l

• The image is real the light actually goes
  through the image location.
• The image is inverted.

Where do you find this type of image formation?
6
Ray Diagram for Converging Lens. The object is
closer to the lens than the front focal point, l
lt f
l
f

• The image is virtual the light only appear to
  come from the image location. The image can only
  be seen through the lens, not on a screen.
• The image is upright and is always magnified.

Where do you find this type of image formation?
7
Ray Diagram for Converging Lens. The situation
is pretty much the same no matter where the
object is located.
f
l

• The image is virtual, and can only be seen
  through the lens.
• The image is upright and is always reduced in
  size compared with the object.

Where do you find this type of image formation?
8
Lens Equation
The equation connecting the distances from the
object to the lens, l, and from the lens to the
image, l.l and l are both considered
positive for the case shown. They become equal,
when l l 2f
9
Lens magnification
The two shaded triangles, blue and gold, are
right-angled and similar. Therefore, for the lens
magnification, M, we haveThe - sign is taken
to signify the fact that the image is inverted.
http//www.mtholyoke.edu/mpeterso/classes/phys301
/geomopti/lenses.html
10
Real, inverted reduced (magnified for l lt 2f )
Virtual, upright, magnified
11
Virtual, upright, reduced
12
What happens to the image if we put an
aperture?If we remove the lens?
13
Who has seen the lens?!
I
O
14
Who has seen the lens?!
I
O
I
O
15
Who has seen the lens?!
O
I
I
O
16
Lens aberrations, spherical
Ideally, the surface of a lens should be
parabolicThose are very difficult to make,
though! Spherical shape is rather close to a
parabola for paraxial rays, which are close to
the axis of the lens.The rays, which come at
greater angles (further away from the axis)
converge in a different, closer point.The image
of the point O gets blurry
17
Lens aberrations, chromatic
Regular glass materials are dispersive indices
of refraction are different for different
colors.Rays of different colors are refracted
through different angles and converge in
different points the image gets
blurry!Remedies try to use a single color
illumination or a composite lens compensating for
the dispersion.
18
High end microscope objective collect light from
wide angles and compensate for all possible
aberrations