Lenses

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Lenses
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Refraction of Light

• When light travels through a surface between two
  different media, the light will be refracted if
  the angle of incidence is greater than zero.
• If light is passing into a more dense media, it
  will bend towards the normal.

www.hyperphysics.phy-astr.gsu.edu
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Law of Refraction (Snells Law)

• The ratio of the sine of the angle of incidence
  to the angle of refraction is a constant.
• n1 sin?1 n2 sin?2
• Where
• n1, n2 index of refraction
• ?1 Angle of incidence
• ?2 Angle of refraction
• speed of light in a vacuum c
• speed of light in the material v

n
www.sol.sci.uop.edu
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Light Passing Through Glass
Air
Air
Glass
Reflected Ray
Refracted Ray
?4
?2
?3
?1
Incident Ray
Note ?1 ?4 ?2 ?3
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Lenses and Their Uses

• Eyeglasses first made around the 13th century.
• Galileo used them as a telescope to discover the
  moons of Jupiter and the phases of Venus.
• Other applications include microscopes, overhead
  projectors and cameras.
• A special type of lens, called the fresnel lens,
  is used in lighthouses, traffic lights, rear
  windows of motor homes and overhead projectors.

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Definition of a Lens

• What is a lens?
• A lens is made of a transparent material such as
  glass or plastic such that the index of
  refraction is greater than that of air.

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Types of Thin Lenses

• What types of lenses are there?
• Convex (Converging) A lens that is thicker in
  the middle than at the edges. Converging lenses
  cause incident parallel rays to converge at a
  point.
• Concave (Diverging) A lens that is thinner in
  the middle than at the edges. Diverging lenses
  cause parallel rays of light to diverge when
  leaving the lens.
• Fresnel A lens comprised of rings of glass
  prisms positioned above and below a lamp to bend
  and concentrate light into a bright beam.

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Converging and Diverging Thin Lenses

• Convex/Converging Lens
• Concave/Diverging Lens

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Focal point
3
Principle Axis
F
2F
F
2F
2
Focal point
1
2
3
F
F
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Image Formation by Converging Thin Lens
1
Real Image
3
Principle Axis
F
F
2F
2F
2
Object

• An object placed more than 2X the focal distance
  before the lens will produce an inverted and
  smaller real image.
• This type of lens is similar to those used in
  cameras.

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Image Formation by Converging Thin Lens
Real Image
1
3
Principle Axis
F
2F
F
2F
2
Object

• An object placed between F and 2F will produce an
  inverted and larger real image.
• This type of lens is similar to those used in
  projectors.

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Image Formation by Converging Thin Lens
1
Principle Axis
F
F
2F
2F
2
Object
Virtual Image

• An object placed between F and the lens will
  produce an upright and larger virtual image.
• This type of lens is similar to a magnifying lens.

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Image Formation by Diverging Thin Lens
1
2
3
F
F
Virtual Image
Object

• A diverging lens always produces a virtual image
  that is upright and smaller than the object.
• This type of lens is used in glasses to correct
  for myopia (near sighted).

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Image Formation for Converging and Diverging Thin
Lenses

• Image formation for diverging lenses.
• Image formation for converging lenses.

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The Thin Lens Equations

• 1 1 1
• do di f
• Where
• do and di are the distances of the object
  and image from the mirror, respectively.
• f focal length.
• Image height, hi di
• Object height, ho do

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Example 1
Image
hi
Principle Axis
F
F
2F
2F
hi
Object
f
do
di

• An object is placed at a distance of 6 cm from a
  converging lens. The focal length of the lens is
  2 cm. The distance of the image to the lens is
• a. 1.0 cm b. 1.5 cm c. 3.0 cm d. 4.5 cm
  e. 6.0 cm

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Example 2 3

• An object is placed between the focal point and
  twice the focal length of a converging lens. The
  image formed will be
• a. real and upright b. real and inverted
• c. virtual and upright d. virtual and
  inverted
• e. located at the focal length
• An object is placed at a distance of 20 cm from a
  converging lens. The resulting image appears at
  a distance of 80 cm from the lens. The image is
  magnified by a factor of
• a. 0.25 b. 4.0 c. 8.0 d.
  12.0 e. 16.0

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Sign Conventions for Thin Lenses

• Focal Length
• f is positive for a converging lens.
• f is negative for a diverging lens.
• Object Distance
• do is if the object is to the left of the lens
  (real object).
• 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 to the left.
• 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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Key Ideas

• Snells Law / Law of Refraction Light will bend
  toward the normal when transitioning from a media
  with a low index of refraction (e.g. air) to a
  media with a higher index of refraction.
• Paraxial light rays parallel to the principle
  axis of a converging lens will come to a point
  called the focus.
• Paraxial light rays parallel to the principle
  axis of a diverging lens will appear to have
  originated from a point called the focus.
• Diverging lenses always form virtual images.

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Key Ideas

• The thin lens equation can be used to determine
  the distance an image forms from a lens and is
  the same as that used for spherical mirrors.
• Ray diagrams can be used to determine where
  images will form.