Download A Question Simple Magnifier Magnification by a Lens

11/29/2011
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Simple Magnifier
A simple magnifier consists of a
single converging lens
This device is used to increase the
apparent size of an object
The size of an image formed on
the retina depends on the angle
subtended by the eye
A Question
Unpolarized light of intensity I goes
through an ideal polarizer. What is
the intensity of the transmitted light?
A: 3I / 2 .
B: I / 2 .
C: I / 4 .
D: Depends on θ.
Magnification by a Lens
With a single lens, it is possible to
achieve angular magnification up
to about 4 without serious
aberrations
With multiple lenses,
magnifications of up to about 20
can be achieved
The multiple lenses can correct for
aberrations
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Compound Microscope,
cont
Compound Microscope
A compound
microscope consists
of two lenses
Gives greater
magnification than a
single lens
The objective lens has
a short focal length,
ƒo<1 cm
The ocular lens
(eyepiece) has a focal
length, ƒe, of a few
cm
The lateral magnification of the microscope is
q
L
Ml = − l ≈ −
pl
ƒo
The angular magnification of the eyepiece of
the microscope is
25 cm
m =
e
ƒe
The overall magnification of the microscope is
the product of the individual magnifications
m = Ml me = −
L  25 cm 


ƒo  ƒe 
L is much greater than either focal length
The approach to analysis is the same as
for any two lenses in a row
Magnifications of the
Compound Microscope
The lenses are separated by a distance L
The image formed by the first lens becomes
the object for the second lens
The image seen by the eye, I2, is virtual,
inverted and very much enlarged
Other Considerations with
a Microscope
The ability of an optical microscope
to view an object depends on the
size of the object relative to the
wavelength of the light used to
observe it
For example, you could not observe
an atom (d ≈ 0.1 nm) with visible
light (λ≈ 500 nm)
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Telescopes
Two fundamental types of telescopes
Mount Wilson
Refracting telescope uses a combination of
lenses to form an image
Reflecting telescope uses a curved mirror
and a lens to form an image
Telescopes can be analyzed by
considering them to be two optical
elements in a row
The 100 inch (2.5 m)
Hooker reflecting
telescope at Mount
Wilson Observatory near
Los Angeles, California.
The image of the first element becomes the
object of the second element
http://en.wikipedia.org/wiki/Gran_Telescopio_Canarias
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http://www.jwst.nasa.gov/images_artist13532.html
http://hubble.nasa.gov/
Refracting Telescope
The two lenses are arranged
so that the objective forms a
real, inverted image of a
distant object
The image is near the focal
point of the eyepiece
The two lenses are
separated by the distance ƒo
+ ƒe which corresponds to
the length of the tube
The eyepiece forms an
enlarged, inverted image of
the first image
Angular Magnification of a
Telescope
The angular magnification depends on
the focal lengths of the objective and
eyepiece
m=
ƒ
θ
= o
θo ƒe
Angular magnification is particularly
important for observing nearby objects
Very distant objects still appear as a small
point of light
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Problem 25.36
Galileo devised a simple terrestrial telescope that
produces an upright image. It consists of a converging
objective lens and a diverging eyepiece at opposite
ends of the telescope tube. For distant objects, the
tube length is the objective focal length less the
absolute value of the eyepiece focal length.
(a) Does the user of the telescope see a real or virtual image?
(b) Where is the final image?
(c) If a telescope is to be constructed with a tube 10.0 cm
long and a magnification of 3, what are the focal lengths of
the objective and eyepiece?
Disadvantages of
Refracting Telescopes
Large diameters are needed to
study distant objects
Large lenses are difficult and
expensive to manufacture
The weight of large lenses leads to
sagging which produces
aberrations
Problem 25.36-II
Note: We solve part (b) before answering part (a) in this problem.
(b) The objective forms a real, diminished, inverted image of a very
distant object at q1 = fo.
This image is a virtual object for the eyepiece at pe = - |fe | , giving qe-1
=0
(a) Parallel rays emerge from the eyepiece, so the eye observes a virtual
image.
(c) The angular magnification is m = fo/|fe |= 3, giving fo = 3|fe|. Also,
the length of the telescope is L = fo+fe =3.00|fe| − |f e| =10.0 cm,
giving fo = -5.00 cm and fe = 15 cm.
Reflecting Telescope
Helps overcome some of the
disadvantages of refracting telescopes
Replaces the objective lens with a mirror
The mirror is often parabolic to overcome
spherical aberrations
In addition, the light never passes
through glass
Except the eyepiece
Reduced chromatic aberrations
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Reflecting Telescope,
Newtonian Focus
The incoming rays
are reflected from
the mirror and
converge toward
point A
At A, a photographic
plate or other
detector could be
placed
The ability of an optical system to
distinguish between closely spaced
objects is limited due to the wave
nature of light
If two sources of light are close
together, they can be treated as noncoherent sources
Because of diffraction, the images
consist of bright central regions flanked
by weaker bright and dark rings
Reflecting Telescopes
Largest in the world are 10 m diameter
Keck telescopes on Mauna Kea in Hawaii
Largest single mirror in US is 5 m diameter
on Mount Palomar in California
Refracting Telescopes
A small flat mirror,
M, reflects the light
toward an opening in
the side and passes
into an eyepiece
Resolution
Examples of Telescopes
Largest in the world is Yerkes Observatory
in Wisconsin
Has a 1 m diameter
Rayleigh’s Criterion
If the two sources are separated so that
their central maxima do not overlap,
their images are said to be resolved
The limiting condition for resolution is
Rayleigh’s Criterion
When the central maximum of one image
falls on the first minimum of another image,
they images are said to be just resolved
The images are just resolved when their
angular separation satisfies Rayleigh’s
criterion
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Barely Resolved (Left) and
Not Resolved (Right)
Just Resolved
If viewed through a slit
of width a, and applying
Rayleigh’s criterion, the
limiting angle of
resolution is
θmin =
λ
a
For the images to be
resolved, the angle
subtended by the two
sources at the slit must
be greater than θmin
Resolution with Circular
Apertures
The diffraction pattern of a circular
aperture consists of a central,
circular bright region surrounded
by progressively fainter rings
The limiting angle of resolution
depends on the diameter, D, of the
aperture
θmin = 1.22
λ
Resolving Power of a
Diffraction Grating
If λ1 and λ2 are nearly equal
wavelengths between which the grating
spectrometer can just barely
distinguish, the resolving power, R, of
the grating is
R≡
λ
λ
=
λ2 − λ1 ∆λ
All the wavelengths are nearly the same
D
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Resolving Power of a
Diffraction Grating, cont
A grating with a high resolving power
can distinguish small differences in
wavelength
The resolving power increases with
order number
R = Nm
N is the number of lines illuminated
m is the order number
All wavelengths are indistinguishable for the
zeroth-order maximum
Another question
Eye glasses for a nearsighted person
require:
A: converging lenses;
B: diverging lenses;
C: either ones depending on the
type of nearsightedness.
m = 0 so R = 0
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