The Human Eye and Vision
• The structure of the eye
– Iris
– Cornea
– Lens
• Focusing
– Cornea
– Accommodation
• The Retina
– Photoreceptors
– Processing time
– Sensitivity
Rods and Cones
• Because of their different functions, rods and cones are
present in varying densities in the retina. The blind spot
is due to the connection of the optic nerve
Light Sensitivity
• Remember we talked about rods and cones
• Cones:
– Sensitive to bright light, photopic conditions
– Densely packed in the fovea
– Only a few cones per nerve fiber
• Rods:
– Sensitive to low light, scotopic conditions
– Widely distributed across the retina
– Up to 1000s of rods per nerve fiber (think of this as
many many drops falling into the same pipe, one drop
can’t be detected, but many drops generate some
water flow that can be measured)
Dark Adaptation
Object must be
very bright to be
seen
Dim objects can
be seen
Concept Question
The most important means by which you can see
light intensities varying by over 13 orders of
magnitude is
a) the variable opening of your iris which acts like a
diaphragm
b) your retina's ability to change its sensitivity to light
c) your optic nerve
d) your cornea letting in more light
e) your photoreceptors turning on and off faster or
slower
Color Effects
• The rods and cones are sensitive to different
wavelengths (colors) of light. Recall our discussions of
resonance.
Rods
Cones
Color Effects
• Rods are only sensitive to green and blue light,
and not sensitive at all to red and yellow light.
• In low light conditions, red objects will appear
very dim, because the rods are not sensitive to
the light from those objects
• This causes the relative brightness of different
colored objects to change when viewed in
different lighting conditions
Chapter 6: Optical Instruments
• Eyeglasses
– nearsightedness
– farsightedness
– contact lenses
• Magnifying Glasses
Near and Far Points
• The eyelens has two extreme points, fully relaxed
and fully “bulged”, called fully accommodated.
When the lens is fully accommodated, which object
is in focus on the retina?
A. A distant star
B. A tree outside in your yard
C. Your cell phone screen when texting
Far Points
• When the lens is fully relaxed, a normal eye cornea
and lens will focus distant objects (at infinity) on the
retina
• This is known as the “far point” of the eye
Near Points
• When the lens is fully accommodated (bulged), the
eye will focus an object at about 25 cm (10 inches)
away onto the retina
• This is known as the “near point” of the eye
25 cm (10 inches)
Imperfect Vision
• Let’s consider light coming into the eye from a distant
object, approximated as parallel rays. In a normal
eye, these rays focus on the retina when the eyelens
is fully relaxed
• If the cornea is not properly shaped, these rays will
not focus on the retina
parallel rays focus past the retina
parallel rays focus in front of the retina
Myopia (Nearsightedness)
Myopia
• Myopia occurs when the cornea is too powerful.
• When the eyelens is fully relaxed, the far point is
not at infinity, but closer
• This results in distant objects appearing blurry
far point is less than infinity
Hyperopia (Farsightedness)
• Hyperopia is the opposite problem, when the
cornea is not powerful enough, and parallel rays
are not focused by the time they reach the retina.
• The eyelens can partially accommodate to
increase the power of the cornea-lens system,
and focus these rays on the retina
eyelens partially accommodated to increase lens power
Hyperopia
• Because the eyelens has to partially accommodate to
focus rays from distant objects, its range will not be
sufficient to focus near objects on the retina
25 cm
more than 25 cm
This results in a near point that is more distant than the standard 25 cm
Power of a Lens
• It’s going to be easier to think about corrective lenses
using lens power rather than focal length, so let’s
review what this means
• Remember:
• The more a lens bulges, the shorter its focal length,
and the larger its ray-bending power
Power of a Lens
When the eyelens is fully relaxed, the power of the
cornea plus the eyelens is 60 diopters in a normal
eye.
If the eyelens then fully accommodates, does the
power of the cornea plus eyelens
A. increase
B. stay the same
C. decrease
Power of a Lens
• When fully accommodated, the power of the
cornea plus eyelens increases by about 4
diopters.
• Your eyeglass or contact lens prescription is given
in diopters, the power of the lens needed to
correct the imperfect curvature of your cornea
• Converging lenses have a positive power (positive
focal length) and diverging lenses have a negative
power (negative focal length)
Corrective Lenses
• Myopic (nearsighted) eyes have a cornea plus
lens that is too powerful
– They will require a negative (diverging) lens to
compensate
• Hyperopic (farsighted) eyes have a cornea plus
lens that is not powerful enough
– They will require a positive (converging) lens to
compensate
Multiple Lenses: Review
Multiple Lenses
Lens 1
Lens 2
Image from Lens 1
only, effective
image for Lens 2
f1
f2
f1
f2
If we add a second lens, we can find the image produced
by the combination of lenses by using the image from
Lens 1 as an effective image for Lens 2
Multiple Lenses
Lens 1
f1
f2
Lens 2
f1
f2
• We know where rays from the original object have to hit
Lens 2 because we know where the image is. We can use
this to find the special rays for Lens 2, and the final image.
Corrective Lenses
Lens 1
f1
f2
Lens 2
Retina
f1
f2
• Here the eye lens system produces an image behind the retina.
• If we add a lens in front, like glasses or contacts, the combination of
the two lenses will produce an image correctly located at your retina
Multiple Lenses: Power
Lens Power
A myopic eye is too powerful, say it has a power of
63 diopters. What power of lens should we put next
to it to get a combined power of 60 diopters
(normal eye)
A.
B.
C.
D.
-2 diopters
-3 diopters
2 diopters
3 diopters
Lens Power
If we have a hyperopic eye of power 58 diopters
wearing corrective lenses of power 2 diopters, what
is the focal length of the combined set of lenses?
A. 1.5 cm (0.015 m)
B. 1.7 cm (0.017 m)
C. 2 cm (0.02 m)
Corrective Lenses: Myopia
To correct myopia (nearsightedness), a diverging lens
creates an intermediate image of a distant star at your
far point so that your eye can see it even though the
star is beyond your far point.
Corrective Lenses: Myopia
To correct myopia (nearsightedness), a diverging lens
creates an intermediate image of a distant star at your
far point so that your eye can see it even though the
star is beyond your far point.
far point
image of distant object
Corrective Lenses: Hyperopia
To correct farsightedness your contact lens creates an
(intermediate) image of a book 25 cm away at your near
point so that your farsighted eye can see it even though
the book is closer than your near point
near point
25 cm
Corrective Lenses: Hyperopia
To correct farsightedness your contact lens creates an
(intermediate) image of a book 25 cm away at your near
point so that your farsighted eye can see it even though
the book is closer than your near point
near point
25 cm
focal point of corrective lens
Determining Prescription
Determining Prescription
Determining Prescription
You are near sighted and your far point is 1 meter
away. What is your prescription?
A.
B.
C.
D.
E.
+1 diopter
-1 diopter
+2 diopters
-2 diopters
+3 diopters
Determining Prescription
You are far sighted and your near point is 1 meter
away instead of 25 cm. What is your prescription?
A.
B.
C.
D.
E.
+1 diopter
-1 diopter
+2 diopters
-2 diopters
+3 diopters
Presbyopia: Bifocals
• It is possible to have both a near point that is
more distant than 25 cm and a far point that is
closer than infinity.
• In this case, you need bifocals, which have two
lenses in them, one to correct each imperfection
The top part of the lens (the
picture shows a pair of bifocals
upside down) corrects the far
point
The bottom part of the lens
corrects the near point
Contact Lenses
Contact lenses are just a thinner and smaller version
of glasses that rest directly on the cornea, with a
thin layer of fluid in between.
Magnifying Glasses
F
F
Recall this configuration (also on the exam) that produces
an upright, magnified image.
Magnifying Glasses
F
F
Where should we put the lens to get the biggest image on
our retina?
If we move the object closer to the magnifying glass, the
image gets smaller.
Magnifying Glasses
F
F
You would think we would want to put the object close to
the focal point of the lens, which would make the biggest
image. But we want the biggest image on our retina
Image Size on the Retina
• The size of an object on your
retina is related to the angle
between the axis and the ray
passing through the center of
the lens
• A large angle means a large
image on the retina.
• Here we see an example that
you all know intuitively: that
objects look smaller when
they are farther away
this angle is large so the object is large
this angle is small so the object is small
Image Size on the Retina
• So to make the image as large as possible on the
retina, we want the object to be as close as
possible to the eye
• But we can only focus objects as closer as our
near point (25 cm in a normal eye, closer for
nearsighted people)
• A magnifying glass allows you to bring objects
closer to your eye and still keep them in focus
Magnifying Glasses
Placing an object at the focal point of the magnifying
glass will produce an image at infinity, which your eye can
focus on (its far point) with the eyelens in its fully relaxed
state
Magnifying Glasses
You get a slightly larger image on the retina if you
move the object such that the magnifying glass
produces an image at your near point.
Magnifying Power
Magnification
Magnification
A magnifying glass has a focal length of 10cm. What
is its magnification?
A.
B.
C.
D.
E.
1X
1.5X
2X
2.5X
3X