Which summary is false?
A. For a converging lens:
If do < f, the image is virtual, upright and enlarged
(di < 0 and m > 1).
B. For a converging lens:
If f < do < 2f, the image is real, inverted and enlarged
(di > do and m < –1).
C. For a converging lens:
If do > 2f, the image is real, inverted and reduced
(0 < di < do and –1 < m < 0).
D. For a diverging lens:
For any do, the image is virtual, upright and reduced
(i.e. di < 0 and 0 < m < 1).
E. None of the above.
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Oregon State University PH 212, Class #17
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A Challenge
Suppose you’re trying to use a single converging lens to
focus the image of some object on a screen in a room,
under the following conditions:
The room is small; most objects are larger than the
room—and far from the room.
The image distance—from the lens to the screen—is
fixed (you can’t change it): di
You can choose any converging lens focal length you
wish, within a certain range: fmin ≤ f ≤ fmax
At what nearest and farthest distances, do.min and do.max,
could you place an object in front of the lens and still
focus its image on the screen?
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Oregon State University PH 212, Class #17
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This is the challenge of the human eye.
The dimensions of the interior of the eyeball
determine the image distance: di ≈ 2 cm
The curvature of the cornea/lens system (which can
change—but only within the limits of the muscles and
lens tissue) determine the minimum and maximum
focal lengths, fmin and fmax.
Together, those factors determine the minimum and
maximum object distances, do.min and do.max, at which
we can achieve focused images of those objects.
These limiting object distances, do.min and do.max, are
called, respectively, the near point and far point of
the eye. They define your eye’s focal range.
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Oregon State University PH 212, Class #17
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Figure 24.6-2
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Oregon State University PH 212, Class #17
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Figure 24.8
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Oregon State University PH 212, Class #17
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For “normal” (average, unaided) eyes, the far point is
nearly infinite: do.max ≈ . That is, di ≈ fmax.
In a nearsighted eye (myopia), fmax is shorter than
normal: di > fmax The eyeball is too long (the most
relaxed lens is still too curved). The screen is too far
from the lens for the lens’ maximum focal length, so
the far point is nearer than normal—not nearly infinite.
In a farsighted eye (hyperopia), fmin is longer than
normal: di < fmin. The eyeball is too short (the most
curved lens is not curved enough). The screen is too
close to the lens for the lens’ minimum focal length) so
the near point is farther away than normal.
For “normal” (average, unaided) eyes, the near point is
about 25 cm. Note what this says about a normal eye’s
minimum focal length, fmin.
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Oregon State University PH 212, Class #17
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Aiding the Eyes: Multiple-Lens Systems
(1) Allowing our eyes to focus:
We can correct the physical flaws of our eyes (the
mismatched image distances and focal ranges) by
using another lens to effectively change the object
distance. How? We use the image of one lens
(eyeglasses) as the object for the second lens (our eye).
We focus on that image instead of the original object.
It’s all a matter of where that image is placed.
For a near-sighted eye, we use a diverging lens to place
a (virtual) image of a distant object nearer—at that
eye’s far point. For a far-sighted eye, we use a
converging lens to place a (virtual) image of a nearby
object farther away—at that eye’s near point.
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Oregon State University PH 212, Class #17
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Figure 24.10
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Oregon State University PH 212, Class #17
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Figure 24.9
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Oregon State University PH 212, Class #17
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