Announcements
Review
Chromatic Dispersion
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Optical Instruments
Sections 25.1 - 25.3
Optical Instruments
The Camera
Final Questions
Announcements
Review
Chromatic Dispersion
Aberrations
The Camera
Reading Assignment
Read sections 25.4 - 25.5
Homework Assignment 8
Homework for Chapter 23 at due at the beginning of class today
Homework Assignment 9
Homework for Chapter 25 (due at the beginning of class on Wednesday, October 27)
Q: 3, 6, 14
P: 16, 24
Optical Instruments
Final Questions
Announcements
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Chromatic Dispersion
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Final Questions
Question
A diverging lens has a focal length of 10.0 cm. An object is placed 30.0 cm from the lens. Find the image distance
and describe the image.
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Question
A diverging lens has a focal length of 10.0 cm. An object is placed 30.0 cm from the lens. Find the image distance
and describe the image.
Answer
Because the lens is a diverging lens, its focal length is negative
Because the lens is diverging, we expect it to form an upright, reduced, virtual image for any object position
Using the thin lens equation 1/p + 1/q = 1/f and solving for q we find that
q
1
1
=
=
−7.50 cm
−
q
p
−1
=
1
1
−
−10.0 cm
30.0 cm
−1
The magnification of the image is
M =−
q
p
−7.50 cm
=−
30.0 cm
= +0.250
This result confirms that the image is virtual, smaller than the object, and upright
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The human eye
The human eye focuses light and produces sharp images (much like a lens or a camera, though much more
complex)
Only three types of color-sensitive cells are present in the retina (red, green, and blue cones)
If the red and green cones are stimulated simultaneously, the brain interprets what is seen as yellow
If all three types of cones are stimulated simultaneously, white light is seen
White light
The color white is the perception that is evoked by light that stimulates all three types of color sensitive
cone cells in the human eye
The sun and incandescent lightbulbs are sources of white light
Reflection, transmission, and absorption
When light strikes an object, it may either (1) by reflected by the surface of the object, (2) be transmitted
through the object (refraction) or (3) be absorbed by the object
The color of the objects that we see are largely due to the way these objects reflect or transmit light to our
eyes
The color of an object is in the light that shines upon it and is ultimately reflected or transmitted to our
eyes
For example, if an object absorbs all of the frequencies of visible light except for the frequency associated
with green light, then the object will appear green
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Chromatic dispersion
An important property of the index of refraction n is that, for a given material, the index varies with the
wavelength of the light passing through the material
This behavior is called chromatic dispersion
Because n is a function of the wavelength, Snell’s law of refraction indicates that light of different
wavelengths is refracted at different angles when incident on a material
The index of refraction generally decreases with increasing wavelength (in other words, violet light refracts
more than red light does when passing into a material)
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Lens aberrations
Our analysis of mirror and lenses assumes that rays make small angles with the principal axis and that the
lenses are thin
When these approximations do not hold, imperfect images (aberrations) are formed
There are three types of aberrations in optics: spherical, chromatic, and astronomical
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Lens aberrations
Our analysis of mirror and lenses assumes that rays make small angles with the principal axis and that the
lenses are thin
When these approximations do not hold, imperfect images (aberrations) are formed
There are three types of aberrations in optics: spherical, chromatic, and astronomical
Spherical aberration
Spherical aberration is caused by spherical lenses or mirrors
Spherical aberration occurs because the focal points of rays far from the principal axis of a spherical lens
(or mirror) are different from the focal points of rays passing near the axis
Spherical aberration results in a blurry image
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Optical Instruments
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Chromatic Dispersion
Aberrations
The Camera
Final Questions
Announcements
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Chromatic Dispersion
Aberrations
The Camera
Final Questions
Lens aberrations
Our analysis of mirror and lenses assumes that rays make small angles with the principal axis and that the
lenses are thin
When these approximations do not hold, imperfect images (aberrations) are formed
There are two types of aberrations in optics: spherical and chromatic
Spherical aberration
Spherical aberration is caused by spherical lenses or mirrors
Spherical aberration occurs because the focal points of rays far from the principal axis of a spherical lens
(or mirror) are different from the focal points of rays passing near the axis
Spherical aberration results in a blurry image
Chromatic aberration
Lenses refract light differently based on their wavelength
As white light passes through a lenses, the individual colors (red, orange, yellow, etc.) will not focus on the
same point
Violet, with a short wavelength bends more than red and focuses closer to the lens than red
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The camera
A camera is an optical instrument that consists of a light-tight chamber, a converging lens that produces a
real image, and a light-sensitive film on which the image is formed
In a digital camera, the film is replaced by a charge-coupled device (CCD) which digitizes that image
A camera is focused by varying the distance between the lens and the CCD
The shutter, which is positioned behind the lens, is a device that is opened for selected time intervals
(exposure times)
You can photograph moving objects by using short exposure times
You can photograph dark scenes (low light levels) by using long exposure times
1 s, 1 s, 1 s, and 1 s
Typical exposure times are 30
60
125
250
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The eye
Like a camera, the eye focuses light and produces a sharp image
The eye focuses on an object by quickly varying the shape of the pliable lens (accommodation)
The near point is the closest distance for which the lens can accommodate to focus light on the retina
This distance usually increases with age (at age 20, its about 25 cm)
The far point is the greatest distance for which the lens of the relaxed eye can focus light on the retina
A person with normal vision can see very distant objects (we approximate this distance as infinite)
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Hyperopia (farsightedness)
Hyperopia (or farsightedness) is a defect of vision caused by an imperfection in the eye causing difficulty
focusing on near objects
A farsighted person can usually see faraway objects clearly (but not nearby objects)
The near point of a farsighted person is much farther away than normal
The refracting power in the cornea and lens of a farsighted person is insufficient to focus the light from
nearby objects
Farsightedness can be corrected by placing a converging lens in front of the eye
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Final Questions
Hyperopia (farsightedness)
Hyperopia (or farsightedness) is a defect of vision caused by an imperfection in the eye causing difficulty
focusing on near objects
A farsighted person can usually see faraway objects clearly (but not nearby objects)
The near point of a farsighted person is much farther away than normal
The refracting power in the cornea and lens of a farsighted person is insufficient to focus the light from
nearby objects
Farsightedness can be corrected by placing a converging lens in front of the eye
Myopia (nearsightedness)
Myopia (or nearsightedness) is a defect of vision caused by an imperfection in the eye causing difficulty
focusing on distant objects
A nearsighted person can usually see nearby objects clearly (but not faraway objects)
The far point of a farsighted person is not infinity
Rays from distant objects converge to focus in front of the retina; they then continue past that point,
diverging before they final reach the retina
nearsightedness can be corrected by placing a diverging lens in front of the eye
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Final Questions
Question
The accommodation limits for a nearsighted person’s eyes are 18.0 cm and 80.0 cm. When he wears glasses, he
can see faraway objects clearly. At what minimum distance is he able to see objects clearly? (Assume that the
glasses are very close to his eyes.)
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Question
The accommodation limits for a nearsighted person’s eyes are 18.0 cm and 80.0 cm. When he wears glasses, he
can see faraway objects clearly. At what minimum distance is he able to see objects clearly? (Assume that the
glasses are very close to his eyes.)
Answer
To correct nearsightedness, the man should place diverging lenses (his glasses) in front of his eyes
With his glasses on, when he looks at a faraway object (infinitely far away), we want the virtual image
formed by the glasses to be 80.0 cm away (why? )
Using the thin lens equation 1/f = 1/p + 1/q where p = ∞ and q = −80.0 cm, we find that the focal
length f of the diverging lens in his glasses is f = −80.0 cm
Now that we know the focal length of the lens in his glasses, we can find the minimum distance at which
he can see objects clearly
When an object is at some minimum distance pmin , we want the virtual image formed by the glasses to be
18.0 cm away
Therefore, using the thins lens equation and solving for pmin we find that
pmin
=
=
1
1
−
f
q
−1
=
1
1
−
−80.0 cm
−18.0 cm
−1
23.2 cm
Notice that in correcting his nearsighted problem, the glasses also increased his near point
Optical Instruments
Announcements
Review
Chromatic Dispersion
Aberrations
The Camera
Reading Assignment
Read sections 25.4 - 25.5
Homework Assignment 8
Homework for Chapter 23 at due at the beginning of class today
Homework Assignment 9
Homework for Chapter 25 (due at the beginning of class on Wednesday, October 27)
Q: 3, 6, 14
P: 16, 24
Optical Instruments
Final Questions