Converging Lenses

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Converging Lenses

• If we think of a double convex lens as consisting
  of prisms, we can see how light going through it
  converges at a focal point (assuming the lens is
  properly shaped).

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Diverging Lenses

• A double concave lens can also be modeled by
  prisms

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Converging and Diverging Lenses
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Terminology of ConvexLenses
On diagram, we show that light ray bends once on
the optic axis
In reality, light bends twice at the air / glass
boundaries
Optic axis
Principal axis
Optical centre
Principal Focus
Secondary Focus
Focal Length
Focal Length
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Concave Lens Terminology
Concave Lens is diverging. The Principal focus is
virtual, in front of the lens.
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Principle Rays Converging Lens
Lens has two focal points because light can go
both ways and still focuses on one spot
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Principle Rays Converging Lens (Convex)
Incident Ray Reflected Ray
Parallel to principal Axis Through the focal point
Through the focal point Parallel to principal Axis
On the vertex of the lens Goes straight through and does NOT change direction
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Principle Rays Diverging Lens
Concave lens also has secondary focus, behind the
lens. On diagrams, light rays also bend on the
optic axis.
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Principle Rays Diverging Lens (Concave)
Incident Ray Reflected Ray
Parallel to principal Axis Through the focal point
Aiming the secondary focal point Parallel to principal Axis
On the vertex of the lens Goes straight through and does NOT change direction
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Ray Diagram - Converging Lens

• Location of the image of an object located at 2F

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Ray diagrams Converging Lens

• Location the image of an object located in front
  of F

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Ray Diagram - Diverging Lens

• Your turn Locate the image of an object located
  
• between F and 2F for a
  diverging lens

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Image Types Convering Lens

• The convex lens forms different image types
  depending on where the object is located with
  respect to the focal point
• S size can be enlarged or reduced
• A attitude can be inverted or upright
• L image can be infront or behind the lens
• T image can be real or virtual

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Image Types Diverging Lens

• The concave lens forms same type of image no
  matter where object is located
• S reduced
• A upright
• L in front of the lens
• T virtual

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Summary Image Characteristics formed by Concave
and Convex Lenses
Concave Lens (Diverging) Concave Lens (Diverging) Concave Lens (Diverging) Concave Lens (Diverging) Concave Lens (Diverging)
Object Location SIZE ATTITUDE LOCATION TYPE
Arbitrary Smaller Upright Same side of lens as object Virtual
Convex Lens (Converging) Convex Lens (Converging) Convex Lens (Converging) Convex Lens (Converging) Convex Lens (Converging)
Object Location SIZE ATTITUDE LOCATION TYPE
In front of F Larger Upright Same side of lens as object Virtual
Between F and 2F Larger Inverted Opposite side beyond 2F Real
At 2F Equal Inverted Opposite side at 2F Real
Beyond 2F Smaller Inverted Opposite side between F and 2F Real
As object moves away from convex lens, real image
moves closer to lens When object is located at F,
no image is formed (verify with ray diagram)
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The Thin-Lens Equation Sign Convention

• Distances positive for real
• negative for virtual
• Heights positive above axis
• negative below axis

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The Thin-Lens Equation
do the distance from the mirror to the object
di the distance from the mirror to the image
f the focal length
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Sign conventions LENS Equation
Focal Length f Object Distance do Image Distance di
Converging Lens (Convex) Object is in front of mirror Image is REAL (opposite side of object)
- Diverging Lens (Concave) N/A. do is always positive Image is VIRTUAL (same side as object)
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Magnification Equation for LENS
-
If M gt 1, image is larger than object
(enlarged) If M lt 1, image is smaller than
object (reduced) M gt 0 for up-right images M lt
0 for inverted images