Transcript 11a - Convex and Concave Lenses

Convex and Concave Lenses
Refracting Light Through Transparent
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Types of Lenses
• Lenses are used in our everyday lives
• They are in microscopes, telescopes,
binolculars, cameras (even the ones in
cell phones)
• A lens is a curved transparent material
that is smooth and regularly shaped so
that when light strikes it, the light
refracts in a predictable and useful way
Types of Lenses (cont’d)
• There are two types of lenses you will
examine in this lesson
– Convex or Converging Lenses: light rays are
focussed through a focal point
– Concave or Diverging Lenses: light rays are
spread out from a focal point
• The following diagrams will demonstrate
these properties
Types of Lenses (cont’d)
focal point,
F
focal point,
F'
convex lens
(side profile)
focal point,
F’
focal point,
F
concave lens
(side profile)
Lens Terminology
• Similar to mirrors, there is a principal
axis that is an imaginary horizontal line
drawn through the optical centre of the
lens
• The axis of symmetry is an imaginary
vertical line drawn through the optical
centre of the lens
• The exact centre of the lens is called the
optical centre
Lens Terminology (cont’d)
axis
of symmetry
principal
axis
optical
centre
convex lens
(side profile)
axis
of symmetry
principal
axis
optical
centre
concave lens
(side profile)
Lens Terminology (cont’d)
There are two principal focuses
– The focal point where the light either comes
to a focus or appears to diverge from a focus
is given the symbol F
– On the opposite side is the focal point on the
other side of the lens is given the symbol F′
• The following slide illustrates this more clearly
Lens Terminology (cont’d)
focal point,
F
Focal points on the
opposite side are
called, F’
focal point,
F'
Rays go through
focal point, F.
convex lens
(side profile)
Rays
Focalappear
points to
on be
the
coming
from
focal
opposite
side
are
point,
called,F.F’
focal point,
F’
focal point,
F
concave lens
(side profile)
Lens Terminology (cont’d)
• The focal length, f, is the distance from
the axis of symmetry to the principal
focus
– Since the light behaves the same way
travelling in either direction through the
lens, both types of thin lenses have two
equal focal lengths.
Lens Terminology (cont’d)
f
f
principal
axis
focal point,
F
focal point,
F'
convex lens
(side profile)
f
principal
axis
focal point,
F
f
focal point,
F’
concave lens
(side profile)
Concave or Diverging Lenses
• A diverging or concave lens refracts light away
from the principal axis of the lens.
• This means that light rays will never cross once
they have passed through the lens.
• The image formed is always upright and smaller
than the object.
– The reasons for this will be illustrated in the next
few slides that describe how to draw ray diagrams
for concave lenses.
• The image formed is a virtual image.
Ray Diagrams for Concave or
Diverging Lenses
Notice how the image
that is formed is smaller
and a virtual image
1. The first ray is drawn
from the object to the
axis of symmetry
principal
axis
object
4. A second ray is drawn
from the object through
the optical centre of the
lens.
F
virtual
image
2. The first ray continues
on an angle that is in line
with the focal point, F.
3. A dotted line is used to
show the continuation of
the refracted ray back to
the focal point.
F’
If someone looked
through the lens
they would see the
arrow on the other
5. Where the dotted line and the
side, right side up
second ray intersect is the position
of
and smaller.
concave lens
the virtual image.
(side profile)
Ray Diagrams for Concave or
Diverging Lenses (cont’d)
• Go to www.explorelearning.com and login
• Go to the “Ray Tracing (Lenses)” Gizmo to see
how moving the object closer to the focal point
makes it bigger.
– Choose concave lens in the lens options
– Move around the focal point to observe what
happens to the lens and the image that is formed.
– Notice how they use three rays instead of two
Convex or Converging Lenses
• A convex or converging lens refracts light
towards the principal axis.
• This means that all light rays focus though a
single focal point.
• Images formed by a convex lens depend on
where the object sits relative to the focal
point, F’.
– Convex lenses can form both real and virtual images
• The following slides will illustrate how to draw
ray diagrams for convex lenses.
Ray Diagrams for Concave or
Converging Lenses
Notice how the image
that is inverted and a real
image
1. The first ray is drawn
from the object to the
axis of symmetry.
principal
axis
object
3. A second ray is drawn
from the object through
the focal point, F’ to the
axis of symmetry.
2. The first ray continues
on an angle that runs
through the focal point, F.
5. Where the two rays
cross is the location of the
image.
real
image
F’
F
4. The second ray continues on,
parallel to the principal axis
concave lens
(side profile)
Ray Diagrams for Concave or
Converging Lenses (cont’d)
Let’s look at what
happens if the object is
closer to the focal point,
F’
1. The first ray is drawn
from the object to the
axis of symmetry.
principal
axis
object
3. A second ray is drawn
from the object through
the focal point, F’ to the
axis of symmetry.
F’
2. The first ray continues
on an angle that runs
through the focal point, F.
Compared with the previous
5. Where
the image
two rays
example,
the real
cross
is thelarger.
location of the
formed
is much
image.
real
image
F
4. The second ray continues on,
parallel to the principal axis
concave lens
(side profile)
Ray Diagrams for Concave or
Converging Lenses (cont’d)
5. A dotted line is drawn
Let’s look at what
back from the intersection
happens if the object is
between the second ray the
closer to the lens than
axis of symmetry
focal point, F’.
1. The first ray is drawn
from the object to the
axis of symmetry.
virtual
image
principal
axis
object
F’
6. Where the two dotted
line cross, is where the
virtual image is formed.
Notice that the image
formed is upright and a
virtual image.
4. A second ray is drawn from
the object to the axis of
symmetry in line with the
focal point, F’. The line is
refracted parallel to the
principal axis
3. A dotted line is drawn
back from the first ray.
F
If someone looked
through
the lens
2. The first
ray continues
they
the
on anwould
anglesee
that
runs
arrow
on the
the focal
otherpoint, F.
through
side, right side up
and larger.
concave lens
(side profile)
Ray Diagrams for Concave or
Diverging Lenses (cont’d)
• Go to www.explorelearning.com and login
• Go to the “Ray Tracing (Lenses)” Gizmo to see
how moving the object closer to the focal point
makes it bigger.
– Choose convex lens in the lens options
– Move around the focal point to observe what
happens to the lens and the image that is formed.
– Notice how they use three rays instead of two
Thin Lens Equation
• The distance of the object from the lens, do, the
distance of the image from the lens, di, and the
focal length of a lens, f, can all be related using
the Thin Lens Equation.
1
1 1


f do di
• Go to page 455 – 457 of the textbook to see
examples of calculations involving the thin lens
equation.
Draw Ray Diagrams
• Go to the word document for this lesson
and print out the ray diagram pages.
• Complete the ray diagrams for the
concave and convex lenses.
– You only need to do rays for the tip of the
arrow, just like you learned in the previous
slides.
Quick Lab
• Go to page 459 and perform the Quick
Lab
• Read the instructions carefully.
• Answer questions 10 and 11.
Questions from the Textbook
• Answer Questions 1, 2, 5, 6, 8 and 10 on
page 462 of the textbook.