LIGHT

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LIGHT THIN LENSES
Name ________________ Class _________________
Index ________________
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Learning objectives
At the end of this unit you should be able to
1. Describe the action of converging lens and
diverging lens on a beam of light. 2. Define the
term focal length of a converging lens. 3. Draw
a ray diagram to illustrate the formation of real
and virtual images of an object by a converging
lens.
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Types of converging lens

• A converging (or convex) lens is thicker in
• the middle than at the edge.

(a) biconvex (b) plano-convex (c)
concavo-convex
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Technical Terms
The principal axis of a lens is a line passing
through the optical centre, C, of the lens and
perpendicular to the plane of the lens.
principal axis
Optical centre, C
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The optical centre, C, of a lens is the point
midway between the lens surfaces on its principal
axis. Rays passing through the optical centre are
not deviated.
principal axis
Optical centre, C
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The principal focus, F, of a thin converging lens
is the point on the principal axis, to which an
incident beam parallel to the principal axis is
made to converge.
F focus
F
F
C
Focal length
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The focal length, f, of a lens is the distance
between the optical centre and the principal
focus, F.
F
F
C
Focal length f
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The focal plane of lens is the vertical plane
which passes through the principal focus and
perpendicular to the principal axis.
Focal Plane
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The object distance, u, is the distance between
the optical centre and the object. The image
distance, v, is the distance between the image
and the optical centre. Since light can pass
through a lens either the left or right side, a
lens has two principal foci.
Object distance u
Image distance v
object
F F
image
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Construction of rays of a converging lens
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Standard rays (For construction of ray diagram)
The ray must parallel to the principal axle
step 1 step2 step 3
F
C
F
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Construction rules

• Incident ray through the optical centre, C
• Incident ray parallel to the principal axis
• Incident ray directed towards principal focus, F

object
F
F
C
Image
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Formation of image by a converging lens

• Converging lens of focal length f
• Object distance u
• Image distance v ( 6 Cases)

Given
(continue on next slide)
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Case 1
u gt 2f
Nature of image real, inverted and
diminished Uses In a camera, in your eye at
this moment
u
v
object
image
2F F F
2f
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Case 2
u 2f
Nature of image real, inverted and same
size Uses Photocopier
u
v
object
2F F F
2F
image
2f
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Case 3
Nature of image real, inverted and
magnified Uses slide projector, film projector,
objective lens of microscope
fltult2f
u
v
object
F F
image
f
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Case 4
No image is formed. (Image is formed at
infinity). Depending on usage Uses spotlights,
eyepiece of telescope
uf
u
object
F F
f
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Case 5
Nature of image virtual, upright and
magnified Uses magnifying glass, spectacles for
correcting long-sightedness
0ltultf
image
object
u
F F
f
v
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Case 6
Object at infinite position
Image nature real, inverted and diminished
image Uses objective lens of telescope
v
image
2F F F
f
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Worked example 1
Given focal length of convex lens, f, object
distance, u and its size. Find by graphically the
size and the nature of its image produced.
object
F F
The image obtained Real, inverted
and magnified. Image distance, v gt f
image
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Worked example 2
Given focal length of convex lens, f, image
distance, v and its size. Find graphically the
size and the position of the object.
object
F F
image
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Worked example 3
Given the size and position of distance of an
object and its image . Find by graphically the
focal length, f, and the position of the lens.
focal length f
object
F
image
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Formation of virtual images by a convex lens
(Case 5)

• When an object is placed within the focal length
  of a convex lens, the image formed is virtual,
  upright and magnified.
• This principal is used in a magnifying glass.

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Virtual Image
The image formed by this way is a virtual image,
please explain?
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To find the focal length of a convex lens

• Approximate method
• Place a screen at the back of a convex lens.
  Adjust the position of the lens until a clear
  image of distance object is obtained on the
  screen. The distance between the lens and the
  screen gives the focal length of the convex lens.

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Types of diverging lens
A diverging (or concave) lens is thicker in at
the edge than at the middle.
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Action of diverging lens on a beam of light
If the lens is concave, a beam of light passing
through the lens is diverged (spread) the lens
is thus called a negative or diverging lens. The
beam after passing through the lens appears to be
emanating from a particular point on the axis in
front of the lens the distance from this point
to the lens is also known as the focal length,
although it is negative with respect to the focal
length of a converging lens.
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The Thin-Lens Equation and the Magnification
Equation
Thin Lens Equation 1/do 1/di
1/f Magnification Equation m hi/ho - di/do
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Summary of sign conventions for lenses Focal
length f is for a converging lens. f is for a
diverging lens. Object distance do is if the
object is to the left of the lens (real object),
as is usual. do is - if the object is to the
right of the lens (virtual object). Image
distance di is for an image (real) formed to
the right of the lens by a real object. di is -
for an image (virtual) formed to the left of the
lens by a real object Magnification m is for an
image that is upright with respect to the
object. m is - for an image that is inverted with
respect to the object.
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Example A 1.70m tall person is standing 2.50m in
front of a camera. The camera uses a converging
lens whose focal length is 0.05m. (a) Find the
image distance (the distance between the lens and
the film) and determine whether the image is real
or virtual. (b) Find the magnification and the
height of the image on the film. Solution (a)
To find the image distance di, we use the
thin-lens equation with do 2.50m and f 0.05m
1/di 1/f 1/do 1/0.05 1/2.50 19.6
m-1 di
0.051m Since the image distance is a
positive number, a real image is formed on the
film (b) The magnification follows from the
magnification equation m -
di/do - (0.051/2.50) -0.0204 The image
is 0.0204 times as large as the object, and it is
inverted since m is negative. Since the object
height is ho 1.70m, the image height is hi
mho (-0.0204)(1.70) -0.0347m
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• Example An object placed 7.10m to the left of a
  diverging lens whose focal length is f -5.08cm
  (a diverging lens has a negative focal length).
  (a) Find the image distance and determine whether
  the image is real or virtual. (b) Obtain the
  magnification.
• Solution
• The thin-lens equation can be used to find the
  image distance di
• 1/di 1/f 1/do 1/(-5.08) 1/7.10 -0.338
  cm-1
• di -2.96 cm
• The image distance is negative, indicating
  that the image is virtual and located to the left
  of the lens.
• (b) Since di and do are known, the magnification
  equation shows that
• m - di/do - (-2.96/7.10) 0.417
• The image is upright (m is ) and smaller (m lt
  1) than the object.

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Application of Converging Lenses
A camera consists of converging lens and light
sensitive film mounted in a light-tight box. The
lens can be moved to or fro so that a real,
inverted, diminished and sharp image is focused
on the film. The intensity of light that falls
onto the film is controlled by a shutter and a
variable aperture diaphragm. The shutter controls
the length of time that the film is exposed to
light. The diaphragm controls the aperture that
allows light to pass through.
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A projector essentially uses converging lenses to
produce a real and magnified image. The condenser
lenses direct the light through the slide or film
to a projection lens. The projection lens is
moved to and fro until a real, magnified and
sharp image is focused to the screen. Since the
image formed on the screen is inverted, the slide
or film has to be put upside down. The real image
formed on the screen is then the right way up.
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A magnifying glass produces a virtual, upright
and magnified image. The image appears to be
larger and more distant than the object but it
cannot be projected on a screen.
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References

• http//www.odec.ca/projects/2005/dong5a0/public_ht
  ml/lenses.html
• http//www.antonineeducation.co.uk/physics_a2/opti
  ons/Module_6/Topic_2/ray_di
• ag_7.gif
• http//www.mvlc.info/images/lighting_glossary_file
  s/image007.gif
• http//bloggingwoolf.files.wordpress.com/2008/12/m
  agnifying-glass.jpg
• http//www.colorado.edu/physics/phys1020/phys1020_
  sp05/labs/Lab4_Optics_files
• /image004.png