• Homework Set 5:
Due Wednesday, March, 17
From Chapter 5:
P2, P8, P10, P11,
From Chapter 6:
P1, P2, P6, PM2,
Single-Lens Instruments
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Eyeglasses: Spherical Corrections
Eyeglasses: Cylindrical Corrections
Contact Lenses
Magnifying Glass
Eyeglasses: Spherical
Corrections
• Normal focus:
– Ciliary muscles relax: see light ray
from infinity. This is the far point of
the vision.
– Muscles tense: shorten the focal
length, see object clearly about
25cm away. This is the near point of
the vision.
• We can think of the eye as
effectively consisting of two lenses:
– First is used when see infinity
(power ~ 60 D).
Lens I
– Second is used when see 25cm. One
needs an additional 1/f=1/0.25=4 D
lens to convert rays from 25cm
away object into parallel rays. The
total focusing power is now ~ 64 D.
Lens I
Lens II
Thus, during accommodation, the change of
power is from 60D to 64 D.
• When a relaxed eye has too much
focusing power, the image is in front
of the retina (myopia). It cannot see
parallel rays from infinity. However,
it can see things close by
• For example, if when relaxed, an eye
has focusing power of 61D, it is
effectively made of two lenses with
focusing power of 60D and 1D. The
first one is what is needed to see
objects far away, and the second one
has a focal length of 1m. If an object
is just one meter away, the second
lens converts its light-rays into
parallel rays. Thus 1m is the far point
that this eye can see!
• If the far point is at 100 cm, then
one needs a diverging lens to convert
the light ray from infinity to a light
ray from 100 cm away. The focal
length of the lens then must be –
100cm.
The power of the lens is –1 = – 1D
correction.
• When a relaxed eye has too little
power (less than 60 D, say 58 D),
then it has maximum focusing power
of 62D. When focusing on an object
25cm away, the image is behind the
retina (hyperopia).
• When at 62D, it can be viewed as two
lenses 60D+2D. Thus it can only see
things clearly at ½ m =50 cm away.
We say the near point is 50cm. Need
a prescription of +2D (converging
lens) to correct.
• When aged, the eye does not
accommodate well (does not have a
full range of 4D).
For example, one might has a
focusing range (61D-63D). Then one
has the so-called presbyopia, a
bifocal correction is needed.
A summary
Normal vision
See infinity
60
62
See 25cm away
64
Focusing
power
Myopia
Hypropia
Presbyopia
• Astigmatism
is a vision condition that occurs when
the front surface of your eye, the
cornea, is slightly irregular in shape.
– curved in one direction but not the
other. Or the extent of curving is
different in different directions.
This irregular shape prevents light from
focusing properly on the back of your
eye, the retina.
– the focal length of the astigmatic eye is
different for rays on one plane than for
those in a perpendicular plane.
• As a result, your vision may be blurred at all
distances. People with severe astigmatism will
usually have blurred or distorted vision, while
those with mild astigmatism may experience
headaches, eye strain, fatigue or blurred
vision at certain distances.
• Almost all levels of astigmatism can be
optically corrected with properly prescribed
and fitted eyeglasses and/or contact lenses.
– Cylindrical lens: curved in one direction but not
the other. Or the extent of curving is
different in different directions.
• Corneal modification is also a treatment
option for some patients.
Contact Lens
• Since the contact lenses are worn in
contact with the cornea, the image
has the same size as if the lenses
are absent. (This is not the case with
the normal glasses.)
• Very easy for correcting
astigmatism because the front
surface of the contact lenses are
always spherical.
Magnifying glass
• A converging lens with a focusing
power.
• Can be used to convert rays from its
focal point into parallel rays, and
then can be viewed with a relaxed
Lens I
eye.
Lens II
How to use a Magnifying
Glass
• A wrong way to held a magnifying
glass: holding it at arm’s length.
– The image does look bigger than the object, but
not the biggest.
• The correct way is to held it next to
your eye and place the object at the
focal point of the magnifying glass.
– So there no magnification, but the image is the
BIGGEST! The same principle is used for closeup photography.
Magnifying power
• The magnifying power is the ratio between
the sizes of the images when the object is
f-cm away and when it is 25-cm away.
Magnification = 25/f (cm)
If f=10cm, the magnifying lens has
magnifying power of 2.5.
• One can get as a large image as possible
using a magnifying glass with very short
focal length.