Imaging with a single lens

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Topics

• Imaging with a single lens
• Aperture and its effect on depth of field
• Measuring the focal length with the
  auto-collimation method
• Spherical Aberration and the Foucault knife test
• Total internal reflection Determining the index
  of refraction of a liquid with Abbes Method.
• Building a beam expander.

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Thin Lens
Quantity Sign Sign
-
so Real object Virtual object
si Real image Virtual image
f Converging lens Diverging lens
yo Erect object Inverted object
yi Erect image Inverted image
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IV.A Imaging by a single lens
Lens
Screen
Lens
Screen
Figure out the exact position of the filament!
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IV.B Depth of Field

• Depth of field in photograph
• The range of distances over which the image is
  sharp.
• Can be controlled with aperture.
• Depth of field is a trade-off for time of
  exposure in photography
• Smaller aperture greater depth of field but
  requires longer exposure time.
• Larger aperture less depth of field but
  requires less exposure time.

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yo
Fo
Fi
yi
xo
f
xi
f
si
so
Screen placed away from image plane Blurry image
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yo
Fo
Fi
yi
xo
f
xi
f
si
so
Screen placed away from image plane but using an
aperture..
Aperture
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IV.C Auto-collimation method
Make sure the image appearing here is a sharp
image of the aperture, NOT an image of the
filament!
Lens
Aperture
Mirror
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IV.D Spherical aberration
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IV.D Foucault knife test explained
Note The different colors used are just for the
purpose of easier visual tracking. They do not
represent different colors. Assume all rays have
the same color.
1
6
2
5
3
4
4
3
5
6
2
1
Perfect Lens
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IV.D Foucault knife test explained
Foucault knife at position 1 (in front of focus)
Screen
1
6
2
5
3
4
4
3
5
6
2
1
Perfect Lens
Screen
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IV.D Foucault knife test explained
Foucault knife at position 2 (at focus)
Screen
1
6
2
5
3
4
4
3
5
6
2
1
Perfect Lens
Screen
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IV.D Foucault knife test explained
Foucault knife at position 3 (behind the focus)
Screen
1
6
2
5
3
4
4
3
5
6
2
1
Perfect Lens
Screen
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IV.D Foucault knife test explained
In this example of a lens with spherical
aberration, we assume for simplicity two
different focal points One for outer rays
(1,6) and one for inner rays (2,3,4,5)
1
5
2
4
3
6
4
1
5
6
3
2
Lens with spherical aberration
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IV.D Foucault knife test explained
Foucault knife at position 1 (in front of
inner focus)
Screen
1
2
3
4
5
6
Lens with spherical aberration
Screen
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IV.D Foucault knife test explained
Foucault knife at position 2 (in front of
inner focus)
Screen
1
2
3
4
5
6
Lens with spherical aberration
Screen
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IV.D Foucault knife test explained
Foucault knife at position 3 (between inner
and outer focus)
Screen
1
2
3
4
5
6
Lens with spherical aberration
Screen
This should be enough instruction for you to
complete!
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IV.D Setting up your Foucault knife test
18mm lens
Razor blade
Screen
Light Source
Short ends towards each other
Razor blade
View from the front
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IV.E Total internal reflection
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IV.E Determine the refractive index of prism by
measuring the critical angle
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IV.E Determine the refractive index of prism by
measuring the critical angle
Note We call the angle on the left the
critical angle here. That is a bit different
notation compared to the previous example of
critical angle.
Task Derive the relationship between nprism and
Qcritical.
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IV.E Careful when deriving nprism (Qcritical)
There are two possibilities requiring you to
count the critical angle positive or negative
Case A
Case B
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IV.E The result will be (please derive)
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IV.E Measuring the critical angle

• Use the angular translator and position prism
  such that the laser hits the prism exactly at the
  rotational axis of the rotation stage.
• Reorient prism such that when the rotation stage
  is at 0 degrees the laser light is back-reflected
  (make sure back-reflection goes back into laser).
• Use the screen on the arm of the rotation stage
  to vie outgoing light ray.

Top view
Laser
Screen
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IV.E Measuring the critical angle

• Use the screen on the arm of the rotation stage
  to vie outgoing light ray.

Top view
Laser
Screen
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IV.E Measuring the index of refraction of a
liquid using two prisms
Before adding the liquid
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IV.E Measuring the index of refraction of a
liquid using two prisms
After adding the liquid
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• Reorient to find the new critical angle.
• Determine nliquid from the new critical angle.
• Do not assume that the critical angle is small.
• Use numerical value of nprism from the previous
  result.
• Derive in steps
• Knowing nprism and the new critical angle,
  calculate a using Snells law.
• Calculate d from trigonometric relationship.
• Calculate nliquid from nprism and d using
  Snells law.

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IV.E Beam expansion/contraction using a Kepler
style telescope
Parallel Light Diameter Dout
Parallel Light Diameter Din
Eyepiece Lens
Objective Lens
How are Dout , Din , fo , and fe related? Use
trigonometry!
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IV.E Beam expansion/contraction using a Galileo
style telescope
Parallel Light Diameter Din
Parallel Light Diameter Dout
Objective Lens
Eyepiece Lens
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Advanced Optics Set Components

• In the manual called Advanced Optics Set on
  page 3 there is a list of components. Check to
  make sure all of them are in your set. Note that
  most sets only have one prism. You will need to
  borrow a second prism from the TA as needed.
• On page 4 of that manual at the bottom, there is
  a list of offsets for each component. Example
  Lenses have an offset of 6.5mm. Keep that in mind
  when reading out the location using the marker on
  the component holder.

6.5 mm