LECTURE 15
OPTICAL INSTRUMENTS
Instructor: Kazumi Tolich
Lecture 15
2
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Reading chapter 27.1 to 27.6
¤ Optical
Instruments
n Eyes
n Cameras
n Simple
magnifiers
n Compound microscopes
n Telescopes
¤ Lens
aberrations
Quiz: 1
3
¨
If your near point distance is 𝑁, how close can you
stand to a mirror and still be able to focus on your
(beautiful) image? Answer in terms of 𝑁, i.e., what is 𝑥
in 𝑥𝑁?
Quiz: 15-1 answer
4
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¨
¨
¨
¨
0.5 𝑁
The near point, 𝑁, is the closest point to the eye
that the lens is able to focus (~ 25 cm for normal
eyes).
If you are a distance 0.5 𝑁 in front of a mirror,
your image is a distance 0.5 𝑁 behind the mirror.
Therefore, you can clearly see your image if the
distance from you to your image is 𝑁.
The far point is the farthest point at which the eye
can focus (∞ for normal eyes).
Cameras
5
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¨
The camera lens moves closer to or farther away
from the film in order to focus.
The amount of light reaching the film is
determined by shutter speed and the 𝑓-number:
𝑓-­‐‑number =
./012 234567
891:363; /. 1<3;6=;3
=
>
?
Quiz: 2
6
¨
A camera’s 𝑓-number is reduced from 2.8 to 1.4. Does the light
entering the camera (the exposure) increase, decrease, or remains the
same, assuming the shutter speed is unchanged?
A.
B.
C.
Increase
Decrease
Remains the same
Quiz: 15-2 answer
7
¨
Increase
¨
𝑓-­‐‑number =
./012 234567
891:363; /. 1<3;6=;3
=
>
?
Decreasing the 𝑓-number will increase the diameter.
¨ This will increase the area through which light enters and thus
increases the exposure.
¨
Quiz: 3
8
¨
In the famous novel Lord of the Flies, one of the boys is
nearsighted, and his glasses are used to start a fire. Is this a
feasible story?
A.
B.
Yes
No
Quiz: 15-3 answer/Corrective lenses
9
¨
¨
¨
¨
¨
No
Concave (diverging) lenses would have
not been able to focus the rays of the
sun.
Nearsightedness is corrected with a
diverging lens.
Farsightedness is corrected with a
converging lens.
The strength of corrective lenses is
usually quoted as refractive power.
refractive power = 1
𝑓
Example: 1
10
¨
A nearsighted person cannot
focus clearly on objects that are
more distant than 2.25 m from
her eye. What refractive power
lenses are required for her to
see distant objects clearly?
Apparent size
11
¨
The apparent size of an object is determined by the actual size of the
image on the retina.
Magnifying glass
12
¨
The angular magnifications of a magnifying glass (𝑓 < 𝑁) are by
𝑀=
𝑀=
LM
L
LM
L
=
N
>
(image at infinity)
=1+
N
>
(image at near point)
Example: 2
13
¨
In your botany class, you
examine a leaf using a convex
12-D lens as a simple magnifier.
What is the angular
magnification of the leaf if the
image formed by the lens is at
infinity? Assume your near point
distance is 𝑁 = 25 cm.
Compound microscope/Demo: 1
14
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¨
¨
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The object is placed just outside of the focal length of
the objective.
The objective forms a real, enlarged, and inverted
image of the object.
The image formed by the objective falls at the focal
length of the eyepiece.
The total magnification is the product of the
magnification of each lens:
𝑀6/612 = 𝑚/QR3069S3 𝑀3T3<9303 = −
𝑑9 𝑁
𝑓/QR3069S3 𝑓3T3<9303
Quiz: 4
15
¨
A compound microscope has an objective lens with a focal
length of 2.2 cm and an eyepiece with a focal length of
5.4 cm. If the image produced by the objective is 12 cm from
the objective, what magnification does this microscope
produce for a normal eye with its near point of 25 cm?
Quiz: 15-4 answer
16
¨
-25
¨
𝑀6/612 = −
WX N
>YZ[\]^X_\ >\`\aX\]\
=−
bc 0: cd 0:
c.c 0: d.f 0:
= −25
Refracting telescopes
17
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¨
¨
Refractive telescopes work by creating a real, inverted, and diminished
image of an object that is much closer than the object.
An eyepiece at its focal length away from the image is used as a simple
magnifier to view that image.
The total angular magnification of the telescope is
𝑀6/612 =
LM
L
=
>YZ[\]^X_\
>\`\aX\]\
Quiz: 5
18
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Two telescopes have identical eyepieces, but telescope A is
twice as long as telescope B. Compare the total angular
magnifications of the telescopes.
Quiz: 15-5 answer
19
𝑀6/612, j < 𝑀6/612, k
¨ The objective lens and the eyepiece must be separated by the
sum of the focal lengths, 𝑓/QR3069S3 + 𝑓3T3<9303 .
¨
¨
¨
Since the scopes have identical eyepieces, telescope A must
have a greater 𝑓/QR3069S3 .
𝑀6/612 =
>YZ[\]^X_\
>\`\aX\]\
Example: 3
20
¨
An astronomical telescope has a
total angular magnification of 7.0.
The two lenses are 32 cm apart.
Find the focal length of each lens.
Demo 3
21
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Galilean Telescope: Eyepiece is a diverging lens placed before the focal point of the objective lens. The
resulting magnified image is upright.
Keplerian Telescope: Eyepiece is a converging lens placed after the focal point of the objective lens. The
resulting magnified image is inverted.
Reflecting Telescope
Lens aberration
22
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Spherical aberration occurs when light striking the
lens far from the axis does not focus properly. It
can be fixed by grinding the lens to a nonspherical shape.
Chromatic aberration occurs when different colors
of light focus at different points.
Chromatic aberration can be improved by
combining two or more lenses that tend to cancel
each other’s aberrations. This only works perfectly
for a single wavelength, however.