Chapter
6 Lectures Physics 1230
Light and Color
Optical
Instruments
I
Eyeglasses & contact lenses
a
Normal & abnormal eyes: definitions &
terminology.
1
Normal eye accommodates
from 25 cm to ´ (infinity).
o
Abnormal eye requires glasses or contacts to have this
range of good vision.
2
Relaxed eye defined:
o
When focused at infinity the eyelens is flattest and
the cillial muscles are relaxed.
o
For a normal
relaxed eye, rays from ´ focus
on the retina (Fig. 6.1a)
3
Far point.
o
Defined as the farthest object-to-eye distance
at which an object can be seen clearly.
o
For normal eye far point is ´.
4
Near point.
o
Defined as the closest object-to-eye distance at
which an object can be seen clearly.
o
For normal eye near point is 25 cm.
5
Myopia = nearsightedness.
o
Near is clear, far is blurred.
o
Cornea bulges too much.
o
Focal length too short: power = 1/f (in meters) is too large.
o
Power of lens is a measure of bulge and ray-bending
ability.
o
Too much bending
of rays
o
Image from ´ is
formed by relaxed eye in front of retina (Fig. 6.1b)
o
Far point closer than ´.
o
Near point also closer than 25 cm (for normal
accommodation).
6
Hyperopia = farsightedness.
o
Far is clear, near is blurred.
o
Cornea doesn't bulge enough.
o
Too little ray bending.
o
Focal length too long (power is too low)
o
Image from ´ is
formed by relaxed eye in back of retina (Fig. 6.1c).
o
Near point is further than 25 cm if accommodation power
is normal.
7
Presbyopia = poor accommodation
o
May prevent otherwise normal eye from focusing on near
objects.
b
Normal accommodation Þ 4 diopter change.
1
Recall how to add powers of lenses 1 and 2 (touching) to get
power of combined lens system.
o
Powers of 2 lenses add when they are in contact to give
power of combined lens.
o
P1
+ P2 = Pcombo
2
Think of normal eye = fictitions pair of lenses
o
Lens 1 is the relaxed eye focused on infinity.
o
Lens 2 represents the effect of accommodation.
o
For fully accommodated eye, 2nd lens converts rays from
pt 25 cm away into parallel rays, sent to relaxed eyelens.
o
Note, 2nd lens must have 25 cm focal length, or power of 4 D (4 diopters).
3
Power of fully accommodated normal eye = [power of 4 D] + [power of relaxed eyelens].
o
Normal eye is focused at near point when fully accommodated
4
Partial versus full accommodation,
o
To focus on objects between 25 cm and ´,
2nd lens must have power between 0 and 4 D.
o
Hence, "normal" accommodation = 4 D change.
5
Demo with large lenses of fully relaxed versus fully
accommodated eye.
o
Use 35 cm lens as relaxed eyelens.
o
Focus point light source from far away on screen.
o
Use 25 cm lens with aperture as second lens.
o
Point light source 25 cm in front of shorter lens
produces parallel rays which are focused on screen 35 cm behind longer lens.
o
This is fully accommodated eye.
c
Prescription glasses to correct for myopia
(nearsightedness)
1
Relaxed eye has too much power
o
(As evidenced by a relaxed focal length shorter than
the lens-retina distance).
o
Far pt. is closer than ´.
2
Diverging lens needed
o
fig. 6.2.
o
Negative power of diverging lens adds to positive power
of eyelens, reducing power of system.
3
What is correct power (your prescription) for diverging lens? Visual construction:
o
Diverging lens should make incoming parallel rays appear
to come from the eye's actual far point.
o
Virtual image of object at ´ needed at far point
o
By definition of focal length of diverging lens, f = -[far point distance].
o
Example: far point of 50 cm requires -2 D prescription.
4
Correct power in terms of adding powers:
o
Combined relaxed eyelens & diverging lens should be
correct (reduced) value for image at ´
to reach retina.
o
Normal relaxed eye lens system has power of about 60 D
o
In above example, myopic eye had power of 62 D, for the
following reason:
o
Adding powers of lenses in contact, 62 - 2 = 60 D.
5
Demo of correction for myopia.
o
Use incandescent light in box as object.
o
Let 24 cm lens with stop be eye, located 63 cm from
object.
o
Show normal image with screen 36 cm behind.
o
Myopic person = screen (retina) placed 87 cm behind
lens. Show out of focus image.
o
Place -500 mm diverging lens over "eye" to
bring image on retina into focus.
o
Combo power is 4 D - 2 D = +2 D.
d
Prescription for hyperopia (farsightedness)
1
Hyperopic eye has too low a power in relaxed state.
o
Suppose power of relaxed hyperopic eye is 57 D.
2
What does accommodation do for this hyperopic person?
o
57 D eye can see object at infinity by accommodating by
3 D (Fig. 6.3a).
o
57 D eye cannot bring an object at 25 cm into focus (Fig.
6.3b), because it cannot accommodate enough.
3
Where is near point for this hyperopic person?
o
Maximum accommodation for this person is 61 D, assuming
normal accommodation.
o
The effective fictitious pair of lenses are 60 D and 1
D (1 D beyond normal relaxed eye)..
o
The 1 D lens has a focal length of 1 meter.
o
Therefore, 1 m is the near point for this hyperopic
person (Fig 6.3c).
o
No additional accommodation can be achieved for this
person without glasses.
4
What is the correct prescription for this person?
o
Full accommodation to 60 D + 4 D requires an additional
3 D of power.
o
Hence, person needs 3 D converging lens as eyeglass or
contact lens.
II
Magnifying glass
a
Apparent size of
an object or image
1
Object (or image) appears large when it subtends a large angle
o
Show with arrow 2 ft from my eye (sweep out angle).
o
Estimate angle at 45¡ or 60¡.
o
Define subtend.
2
Object (or image) appears small when it subtends a small
angle.
o
Ask seated student to estimate size in terms of angle.
o
Angle will be much smaller.
3
Angle from top to bottom is a good measure of apparent size.
o
Equally good measure for object or for real or virtual
image of an object.
4
Image on retina is
larger when angle subtended by object (or image outside the eye) is larger.
o
Show by drawing central (#2) rays from top & bottom
of object to retinal image..
b
Magnifying glass lets you bring in-focus objects closer
(fig 6.7)
1
Without magnifying
glass (Fig.6.7a):
o
Only need follow central ray to intersection with
retina to obtain size of retinal image.
o
Normal eye sees largest retinal image when object is at
near point.
2
With magnifying glass
(Fig 6.7b):
o
Object is at focal point of magnifying glass (less than
25 cm. near pt.)
o
Virtual image at infinity formed by magnifying glass is
easilly seen by relaxed eye (extend back rays).
o
Note larger angle is subtended.
o
Note larger retinal image.
3
Magnifying power of a magnifying glass
o
Defined as ratio of retinal image size with glass to
without glass.
o
With glass means
object is at focal length (relaxed eye of Fig. 6.7b)
o
Same as ratio of object distances for two cases.
o
Magnifying power ¼ 25/(f
in cm.)
o
Hence, shorter f means more magnification.
4
To obtain even larger retinal image (Fig. 6.7b):
o
Place object closer
than focal pt. of magnifying glass.
o
Want virtual image formed by mag. glass at eye's near
near pt.
o
Virtual image can be seen by fully accommodated normal
eye.
o
Largest angle is subtended here.
o
Largest retinal image is produced.