Goal: To understand multiple lens systems'

1
Goal To understand multiple lens systems.

• Objectives
• 2 lens combos
• The eye

2
2 lenses

• We have learned how to do the equations for the
  first lens, but what happens when you have 2
  lenses?
• The image from the first lens becomes the object
  for the second lens.
• The separation distance between lenses is denoted
  as s.
• Everything is normal after that.
• So, 1/p2 1/q2 1/f2
• And p2 s q1

3
Sample

• Lets make sure we still know the lesson from
  yesterday
• You have 2 lenses. We will do the 2nd lens in
  the 2nd sample.
• An object is 10 cm from lens one.
• The focal length is 3 cm.
• What is the image distance (i.e. q1)?

4
Sample

• Lets make sure we still know the lesson from
  yesterday
• You have 2 lenses. We will do the 2nd lens in
  the 2nd sample.
• An object is 10 cm from lens one.
• The focal length is 3 cm.
• What is the image distance (i.e. q1)?
• q1 -f1p1 / (f1 p1)
• -30 / -7 cm 4.3 cm

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Sample 2

• 1/p2 1/q2 1/f2
• And p2 s q1
• For the previous question, if the separation
  distance between lenses is 20 cm then what is p2?

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Sample 2

• 1/p2 1/q2 1/f2
• And p2 s q1
• For the previous question, if the separation
  distance between lenses is 20 cm then what is p2?
• q1 4.3 cm
• So, p2 20 cm 4.3 cm 15.7 cm

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Sample 3

• Now that we have p2 as 15.7 cm, if the focal
  length for the 2nd lens is 10 cm then what is the
  image distance for the 2nd lens?

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Sample 3

• Now that we have p2 as 15.7 cm, if the focal
  length for the 2nd lens is 10 cm then what is the
  image distance for the 2nd lens?
• q2 - f2p2 / (f2 p2)
• -2015.7 / (10-15.7) cm 317 / 5.7
• 55.6 cm

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Magnification

• Each lens will have a magnification.
• How do you think this will work with 2 lenses?
• A) M M1 M2
• B) M M1 M2
• C) M M1 M2
• D) M M1 / M2

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Magnification

• Each lens will have a magnification.
• How do you think this will work with 2 lenses?
• C) M M1 M2
• So, you multiply them
• In other words (since M -q/p)
• M q1q2 / p1p2
• In other words, the first lens expands the image
  by some factor then the 2nd lens expands the
  blown up image by another factor.

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Sample

• We will put all this together
• We have 2 lenses.
• An object is placed 6 cm from the first lens.
• The focal length of the first lens is 2 cm.
• The 2nd lens is 7 cm from the first lens.
• The focal length of the 2nd lens is 3 cm.
• What is the total magnification of the system (to
  find this you will have to find q1, q2, M1, and
  M2)?

12
Sample

• An object is placed 6 cm from the first lens.
• The focal length of the first lens is 2 cm.
• q1 -f1p1 / (f1-p1) -2 6 / (2 6)
• q1 3 cm
• M1 -q1 / p1 -2 / 6 -0.33 (note that
  magnifications do not have units!)
• The 2nd lens is 7 cm from the first lens.
• The focal length of the 2nd lens is 3 cm.
• What is the total magnification of the system?
• p2 s q1 7 cm 3 cm 4 cm
• q2 -f2p2 / (f2-p2) -3 4 / (3 4)
• q2 12 cm
• M2 -q2 / p2 -12 / 4 -3
• M M1 M2 -1/3 -3 1 (yeah I know this was
  mean)

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The Eye

• Okay time for some cool stuff and some concepts.

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But what happens

• If the eye is not correctly shaped?
• Myopia (nearsightedness) you can focus on
  nearby objects but not distant ones.
• This is because the eyes lens forms the image
  just in front of the retina.
• You compensate for this by using a divergent
  lens.
• Can you start fires with a lens like this?

15
Hyperopia

• This is farsightedness.
• This time you have exactly the opposite problem.
• The lens doesnt bend the light enough so the
  focus is just beyond the retina.
• To fix this you use a convergent lens.
• Note you COULD start a fire with this kind of
  lens!

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Presbyopia

• At some point a persons eyes can loose
  flexibility.
• You start to have trouble focusing on nearby
  objects.
• While you are not better at seeing far away ones
  as you would be with farsightedness, to read
  something near by you need reading glasses.
• The reading glasses would be similar to the
  glasses used for farsightedness.

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The math

• There is some math for using glasses.
• There are two values to worry about the near
  point and the far point.
• The near point is the nearest you can clearly see
  something.
• The far point is the farthest you can clearly see
  something.

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Refractive power

• P is the refractive power of a lens.
• P 1 / f and is in units of Diopters (D).
• D has units of 1/meters
• Note that P also 1/q 1/p
• And if you have multiple lenses close together
• P P1 P2

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How to know what to use

• Correcting nearsideness
• You want p to be infinity
• The far point distance is what you use for q, but
  use a negative number (because it is a divergent
  lens, and divergent lenses have negative values
  of q and yes that means they have negative
  values of focal length).
• Sample if your far point was 40 cm then what
  power of lens would you need to correct it?

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Correcting farsightedness

• q is the near point (and is negative).
• p is the distance you want to be able to see
  clearly
• NOTE this is for contact lens. The distances
  are measured from the lens, so if the lens is 2
  cm from the eyes then you have to subtract 2 cm
  off of both p and from the magnitude of q (so,
  the magnitude of q goes down).

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Sample

• A pair of eyeglasses are 2 cm from the eye.
• If the closest someone can see is 0.5 meters and
  they wish to be able to see things clearly at 0.1
  meters then what power of glasses do they need?

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Sample

• A pair of eyeglasses are 2 cm from the eye.
• If the closest someone can see is 0.5 meters and
  they wish to be able to see things clearly at 0.2
  meters then what power of glasses do they need?
• P 0.2 0.02 0.18 m
• Q -0.5 0.02 -0.48m
• So, P 1/q 1/p 3.5

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Conclusion

• We have learned how to solve for distances in
  multiple lens systems
• We learned that the magnifications for each lens
  multiply together.
• We learned about the eye and different eye
  conditions.
• We learned how to correct vision problems and how
  to calculate the power required to do so.