Download Example: The near point of a given eye is N=25cm. Treating the eye

Example:
The near point of a given eye is N=25cm.
Treating the eye as it were a single thin lens a
distance 2.5cm from retina. Find the focal
length of the lens when it is focused on an
object
a) At the near point
b) At infinity
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
The goal is simply to make the
image on the retina larger.We
want to put the image at the
near point of the eye to make it
as large on the retina as the eye
can accommodate.
The Size of a
Magnified Image
Image at infinity
„
When an object is placed at
the near point, the angle
subtended is maximum
„
„
The near point is about 25 cm
When the object is placed
just inside the focal point of
a converging lens, the lens
forms a virtual, upright, and
enlarged image
Image at near point
We use converging lenses
with f < N
Angular Magnification
„
Angular magnification is defined as
Image at infinity
Angle with lens
h/ f N
θ′
M= =
=
=
θ Angle without lens h / N f
„
The angular magnification is a maximum
when the image formed by the lens is at the
near point of the eye
Therefore, .
„
q = - 25 cm
„
Calculated by
1
1
1
=
+
f d o di
1
1 1
= −
do
f di
N N N
= −
do
f di
m
N N
M = − max
f di
Image at near point
The closer an image is to the eye, the greater
the magnification. Since the closest an image
can be to the eye and still be in focus is the
near point,
N N N
25cm
= +1
= 1 + M M== N  −
f
−
N
f
 f do 
Magnification by a Lens
„ With
a single lens, it is possible to
achieve angular magnification up to
about 4 without serious aberrations
„ With one or two additional lenses,
which correct the aberrations, a
magnification of up to about 20 can be
achieved
Example:
A biologist with a near-point distance of N=26cm
examines an insect wing through a magnifying
glass whose focal length in f=4.3cm. Find
angular magnification when the image
produced by the magnifier is
a) At infinity
b) At the near point
THE COMPOUND MICROSCOPE
A compound microscope uses two
lenses in combination – an objective
and an eye piece (ocular) – to produce a
magnified image
The object to be viewed is placed just
outside the focal lenght length of the
objective lens
We must supply light in order to illuminate the
sample. Typically the light source must have
heat absorbing filters in place so that the energy
of the beam does not boil away the liquid-like
biological sample. In advanced scopes, on may
also use polarized light in order to see details
that ordinary white light will not be able to
resolve.
Compound Microscope
„
The lenses are separated by a distance L
„
„
The approach to analyze the image
formation is the same as for any two
lenses in a row
„
„
L is much greater than either focal length
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
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
Magnifications of the
Compound Microscope
„ The
lateral magnification of the objective is
m =−
„ The
di
di
≈−
do
f objectve
angular magnification of the eyepiece of
the microscope is
M eyepiece =
N
f eyepiece
Overall magnification
„ The
overall magnification of the
microscope is the product of the individual
magnifications
M total = mobjective M eyepiece = −
di
N
f objectve f eyepiece
The magnifications quoted for microscopes
assume a near-point distance of 25 cm
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 (we will see this
in the next chapter interference/diffraction)
„
For example, you could not observe an
atom (d ≈ 0.1 nm) with visible light (λ ≈
500 nm)
Telescopes
„
Two fundamental types of telescopes
„
„
„
Refracting telescope uses a combination of lenses to
form an image (invented Galileo and by Kepler)
Reflecting telescope uses a curved mirror and a lens
to form an image (invented by Newton)
Telescopes can be analyzed by considering them
to be two optical elements in a row
„
The image of the first element becomes the object of
the second element
Refracting Telescope
The two lenses are arranged so
that the objective forms a real,
inverted image of a distance
object
„ The image is near the focal
point of the eyepiece
„ The two lenses are separated
by the distance ƒobj + ƒeye
which corresponds to the
length of the tube
„ The eyepiece forms an
enlarged, inverted image of the
first image
„
Note: θ≈h’/fe and θ0 ≈h’/f0
Angular Magnification of a
Telescope
„
The angular magnification depends on the
focal lengths of the objective and eyepiece
θ ' hi / f e ƒo
m=
=
=
θ
hi / f o ƒe
„
Angular magnification is particularly important
for observing “nearby” objects (sun, moon,…)
„
Very distance objects still appear as a small point
of light
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
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
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
A small flat mirror, M,
reflects the light toward an
opening in the side and
passes into an eyepiece
Examples of Telescopes
„
Reflecting Telescopes
„
„
„
Largest in the world are 10 m diameter Keck telescopes
on Mauna Kea in Hawaii
Largest single-mirrored telescope in US is the 5 m
diameter instrument on Mount Palomar in California
Refracting Telescopes
„
Largest in the world is Yerkes Observatory in Wisconsin
„
Has a 1 m diameter
Hubble Telescope