Optics

1
Summary for Converging lens
Image real, inverted, reduced (magnified for l
lt 2f )
Virtual, upright, magnified
2
Lens magnification Diverging lens
Virtual, upright, reduced
To Summarize for both types of lenses
3
What happens to the image if we put in an
aperture?If we remove the lens?
Top and bottom of image is less bright.
Bottom half of image is less bright
4
Who has seen the lens?!
I
O
I
O
5
Who has seen the lens?!
O
I
I
O
6
Lens aberrations, spherical
Ideally, the surface of a lens should be
parabolicThose are very difficult to make,
though! Spherical shape is rather close to a
parabola for paraxial rays, which are close to
the axis of the lens.The rays, which come at
greater angles (further away from the axis)
converge in a different, closer point.The mage
of the point O gets blurry
7
Lens aberrations, chromatic
Regular glass materials are dispersive indices
of refraction are different for different
colors.Rays of different colors are refracted
through different angles and converge in
different points the image gets
blurry!Remedies try to use a single color
illumination or a composite lens compensating for
the dispersion.
8
High end microscope objective collect light from
wide angles and compensate for all possible
aberrations
9
Imagine a camera with a single lens with a focal
distance f 35 mm.By how much and in what
direction should the lens be moved to move its
focus from an object, which is far-far away to an
object at a distance of 1.5 m?
Far-far away means l ?, and l f 35 mm.
New distance l 1.5 m l ?
10
A movie projector. Where is the film with
respect to the focal point?
11
The diameter of an eyeball is about 23 mm in
diameter.It focuses light emanating from
different objects onto the retina to produce
sharp images. Most of the focusing job is done
by the cornea, which acts as a fixed lens with a
focal distance of 23 mm.The lens is only doing
some fine tuning to move the focusing from
objects which are far-far away to objects which
are close.
12
By changing the focal distance of the lens! We
always have l ? 23 mm.
A healthy human eye can clearly see (focus)
objects at distances from infinity to about 25
cm. How is that achieved?
Far-far away means l ?, and f l ? 23 mm.
An object at l 25 cm means
The adaptive lens driven by the eye muscles
changes the focal distance of the eye by only
10. But this is quite a lot!..
13
Myopic (shortsighted) eye the lens is always
too strong, that is too much converging and if
the object is far away it creates its image in
front of the retina.So, the light pattern on
the retina becomes blurry, out of focus.The eye
can be helped by a negative, diverging lens,
which creates virtual images of far away objects
closer to the eye.Rephrasing it the diverging
lens the too much converging lens in the eye
make a composite lens of the right converging
power.
The power of the corrective lens is P1/f
(diopters, m-1)
14
Hyperopic (farsighted eye) the lens is
sometimes not quite strong enough. If an object
is close it focuses behind the retina.So, the
light pattern on the retina becomes blurry, out
of focus.The eye can be helped by a positive,
converging lens, which creates magnified virtual
images of close objects further away from the
eye.Rephrasing it the additional converging
lens the not strong enough converging lens in
the eye make a composite lens of the right
converging power.
15
Optics in Review
Electromagnetic waves (light) all propagate in
vacuum at c3x108 m/sec In a transparent medium
with refractive index n, the speed is vc/n.
With an angle of incidence between two different
transparent mediums, q1, Snells Law
Mirrors and Lenses
What is the difference between the lens and
mirror equations?
16
Meter Stick
If you look into the corner of the cube at 45o
(as shown) what mark on the meter stick do you
see if
(a) The tank is empty?
40cm doh!
(b) The tank is half full?
(c) The tank is full?
17
Critical Angle
When light is propagating in glass with n1.52,
what is the critical angle when the glass is
immersed in (a) water (n1.33)?
(b) Benzene (n1.50)?
(c) diiodomethane (n1.738)?
18
Displaced laser beam
Find the displacement of a laser beam that is
approaching a 5cm thick layer of ice with an
angle of incidence of 30o when ice has an index
of refraction of n1.3.
The angle of refraction, q2, is found
from Snells law
The diagonal through the slab is given by
The displacement is found from
19
Image Formation with a Mirror
A candle is 36cm from a concave mirror with a
focal length 15cm.
(a) Where is the image?
(b) What is the magnification?
(c) Is the image real or virtual, upright or
inverted?
The image is in front of the mirror, hence real.
The magnification Is negative, hence inverted.
20
Image Formation with a Mirror
The image of an object in a 27cm focal length
concave mirror is upright and magnified by a
factor of 3. Where is the object?
From the magnification factor of 3 we know that
From the lens equation
The image is 18cm front of the mirror which is
inside the focal point!
21
Image Formation with a Mirror
At what two distances could you place an object
from a 45cm focal length concave mirror in order
to obtain an image that is 1.5 times the
objects size?
First from the magnification we know that
From the lens equation
First
The image is behind the mirror and virtual. Is it
upright or inverted?
M is positive so the image is upright!
22
Image Formation with a Mirror
At what two distances could you place an object
from a 45cm focal length concave mirror in order
to obtain an image that is 1.5 times the
objects size?
First from the magnification we know that
From the lens equation
Second
The image is in front of the mirror and real. Is
it upright or inverted?
M is negative so the image is inverted!
23
Image Formation with a Lens
A light bulb is 56cm from a convex lens. The
image appears on a screen 31cm on the other side
of the lens.
(a) What is the focal length of the lens?
(b) What is the magnification factor of the image?
Is the image inverted?
YES!
24
Image Formation with a Lens
A lens has a focal length of 35cm.
(a) Find the type and height of the image when a
2.2cm high object is placed f10cm from the
lens.
The image is real, behind the lens, and inverted.
25
Image Formation with a Lens
A lens has a focal length of 35cm.
(b) Find the type and height of the image when a
2.2cm high object is placed f-10cm from the
lens.
The image is virtual, in front of the lens, and
upright.
26
Image Formation with a Lens Fine Print
You have a magnifying lens has a focal length of
30cm. How far from the page should you hold the
lens in order to see the print enlarged 3X?
First note that the image is on the same side of
the lens as the object, the page! This means
that the image distance is negative. Hence
From the lens equation
This result means that the lens is 20cm above
the page and the image is 40cm below the
page, and the image is upright.