Lenses and Mirrors

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• Lenses and Mirrors

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Lenses and your EYE
.
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Review of LensesPreflight 18.8
Focal point determined by geometry and Snells
Law n1 sin(q1) n2 sin(q2)
n1ltn2
P.A.
Fat in middle Converging Thin in middle
Diverging Larger n2/n1 more bending, shorter
focal length. n1 n2 gt No Bending, f infinity
Lens in water has larger focal length!
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Mirage- Light travels faster through the hot ,
less dense air.
Hot Air
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note that in (b) far away object with converging
lens gives inverted image, (c) near object with
converging lens gives erect image, (d) diverging
lenses give erect images.
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Various Lenses
Double Convex
Double Concave
Plano Convex
Plano Concave
Convex Meniscus
Concave Meniscus
Convex lenses are positive converging
lenses. Concave lenses are negative diverging
lenses.
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Lenses -- Wave Picture
A converging lens bends light toward the axis
Focal point is a place on the axis where all rays
directed parallel to the axis arrive
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Convex (Converging) Lens
Focal Point
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Converging Lens-Ray Diagrams
Bend the ray at the middle of the lens
In parallel-out through focus
In through focus-out parallel
Also straight through the center of the lens
h0
hi
f
f
The image will also appear on a screen placed at
the image location.
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Converging Lens Principal Rays
F
P.A.
Object
F
1) Rays parallel to principal axis pass through
focal point.
2) Rays through center of lens are not refracted.
3) Rays through F emerge parallel to principal
axis.
Image is real, inverted and enlarged
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A converging lens is used to project a real image
onto a screen. A piece of black tape is then
placed over the upper half of the lens.
Java
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Equations
Thin lens equation
Magnification equation
What do and - mean???
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Lens Equation
F
Image
P.A.
Object
F

• do distance object is from lens
• Positive object in front of lens
• Negative object behind lens

Example

• di distance image is from lens
• Positive real image (behind lens)
• Negative virtual image (in front of lens)

• f focal length lens
• Positive converging lens
• Negative diverginer lens

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Converging Lens-Ray Diagrams and Math
d0 12 cm, f 4 cm find di, m, hi
f
f
d0
For lenses di is positive on the right.
The image will also appear on a screen placed at
the image location.
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Equations
Thin lens equation
f always for converging lens (- for
diverging)d0 always (except sometimes in
two-lens systems)di if opposite side (- if
same side as d0)m if image upright (- if image
inverted)h if upright (- if inverted)
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Lenses -- Wave Picture
A converging lens bends light toward the axis
A diverging lens bends light away from the axis
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Lenses
A diverging lens bends light away from the axis
Now the Focal point is a place on the axis where
all rays directed parallel to the axis seem to
come from
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Diverging Lens-Ray Diagrams
Bend the ray at the middle of the lens
In parallel-out as if from left focus
In as if toward right focus-out parallel
Also straight through the center of the lens
f
f
For lenses (both types) di is positive on the
right.Here di will be a negative number.
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Diverging Lens-Ray Diagrams and Math
d0 12 cm, f -4 cm find di, m, hi
f
f
For lenses (both types) di is positive on the
right.Here di will be a negative number.
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Virtual and Real Images
Real
Virtual
A screen placed at the image will not produce an
image.
A screen placed at the image will produce an
image.
All image forming rays actually pass through the
image.
At most only one image forming ray will pass
through the image.
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Convex Lens
Ray Diagramming
f
Principal axis

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Lenses
Double Convex (Converging) Lens
Focal Point
Focal
Length
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Double Concave (Diverging) Lens
Focal Point
Focal
length
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R
focal
length
Central
Center of Curvature
Axis
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Real Object
Inverted Real Image
f
f
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Noninverted Virtual Image
Real Object
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Virtual, non-inverted Image
f
f
Real Object
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Virtual, non-inverted Image
Real Object
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note that in (b) far away object with converging
lens gives inverted image, (c) near object with
converging lens gives erect image, (d) diverging
lenses give erect images.
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f f ' for thin lenses
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(No Transcript)
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See useful java applets Image Formation by a
Converging Lens Image Formation by a Diverging
Lens
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Ray tracing for a converging lens
This could be used in a camera. Big object on
small film
This could be used as a projector. Small slide on
big screen
Thin lens equation
This is a magnifying glass
Magnification
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Question?

• Which way should you move object so image is
  real?
• Closer to lens
• Further from lens
• Diverging lens cant create real image.

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Preflight

• A beacon in a lighthouse is to produce a parallel
  beam of light. The beacon consists of a bulb and
  a converging lens. Where should the bulb be
  placed?
• Outside the focal point
• At the focal point
• Inside the focal point

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Preflight

• A converging lens is placed in water. Its focal
  length
• Stays the same
• Increases
• Decreases

Ratio of refractive indices has gone down.
Therefore, less bending, which implies longer
focal length.
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Preflight

• A converging lens is used to project a real image
  onto a screen. A piece of black tape is then
  placed over the upper half of the lens. Which of
  the following is true?
• Only the lower half of the object will show on
  the screen
• Only the upper half of the object will show on
  the screen
• The whole object will still show on the screen.

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Combination of Thin Lenses
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THIN LENS EQUATION For a thin lens (thickness ltlt
focal length), the relationship between image
distance, object distance and focal length is
given by the thin lens equation
The lateral magnification of the image is given
by
f gt 0 converging lens f lt 0 diverging lens o gt
0 real object same side of lens as incident
light o lt 0 virtual object opposite side of
lens from incident light i gt 0 real image
opposite side of lens from incident light i lt
0 virtual image same side of lens as incident
light hi, ho positive for above axis, negative
for below m gt 0 erect image same side of axis as
object m lt 0 inverted image opposite side of
axis from object m lt 1 image smaller than
object m gt 1 image larger than object.
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Multiple Lenses
Image from lens 1 becomes object for lens 2
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2
Example
f1
f2
Lens 1 creates a real, inverted and enlarged
image of the object.
Lens 2 creates a real, inverted and reduced image
of the image from lens 1.
The combination gives a real, upright, enlarged
image of the object.
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f R/2
Differences in conventions from lenses i gt
0 real image same side of mirror as incident
light i lt 0 virtual image opposite side of
mirror from incident light
See useful java applet Image Formation by a
Diverging Mirror Student Tutorial Disk Lenses
and Mirrors
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Spherical Aberration
Rays that are further from the optical axis of a
lens or mirror with spherical surfaces are
focused more strongly that those near the
axis. This effect can be minimized by using a
combination of lenses, restricting the light to
the center section of the lens or mirror (e.g.-
decreasing the aperture of a camera), or by using
aspherical (parabolic) surfaces.
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Chromatic Aberration
Since the index of refraction decreases slightly
with increases in wavelength, light towards the
red end of the spectrum is refracted less than
the blue end. This effect is called dispersion.
In effect, the lens acts in the same manner as a
prism, separating light into a spectrum of
colors. This will cause the focal length of the
lens to be different for different colors of
light and thus images will be focused properly
for one color only. This effect can be
compensated for by using combinations of lenses.
Mirrors do not exhibit chromatic aberration
because they work by reflection. This is the
reason why nearly all astronomical telescopes are
reflectors (Newtonian) instead of refractors
(Galilean.)
See Useful Java Applet Light Dispersion through
a Glass Prism
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Chapter 23 - Selected Topics
ncenter 1.406 nedge 1.386
nair 1
n 1.336
n 1.336
n 1.376
The majority of refraction occurs at the
air/cornea interface. The lens mainly functions
to perform accommodation for nearby objects.
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Normal vision, distant object
Normal vision, near object
Nearsighted, uncorrected
Nearsighted, corrected
Farsighted, uncorrected
Farsighted, corrected
Opticians generally express lens strength in
diopters