Transcript lecture25

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Announcements
 Physics 2135 spreadsheets for all sections, with Exam 3 scores,
will be available on the Physics 2135 web site.
 Preliminary exam average is about xx.x% (xx sections out of 13
reporting). Comment. Scores ranged from a low of xx to a high of
xxx (x students). I will fill in the xx’s during the “live” lecture and in its “.ppt” file.
 Physics 2135 Exam 3 will be returned in recitation tomorrow.
Please check that points were added correctly. Review the course
handbook and be sure to follow proper procedures before
requesting a regrade. Get your regrade requests in on time!
(They are due by Thursday of the week after the exam is returned
in recitation.)
 Caution: it’s the points in the spreadsheet that count, not the
percent. Your points can go down if you miss boardworks!
Announcements
Physics 2135 schedule for the rest of the semester:
April 20 & 21: Lenses
April 25 & 26: Double Slit Interference
April 27 & 28: Thin Film Interference
May 2 & 3: Diffraction
May 4 & 5: Final Review
Wednesday, May 11, 3:00 pm:
50 point all multiple choice End Material Test
(you do not need to take it to earn 8 free points—assuming I owe you free points)
200 point all problem Final Exam
You may take one, or both, or neither
 Special Homework #10 is due tomorrow. Download and print
it if you lost it. Special Homework #11 is also due!
Today’s agenda:
Death Rays.
You must know when to run from Death Rays. Maybe skip for now.
Refraction at Spherical Surfaces.
You must be able to calculate properties of images formed by refraction at spherical
surfaces.
Thin Lenses: Concave and Convex Lenses, Ray Diagrams,
Solving the Lens Equation.
You must understand the differences between these two kinds of lenses, be able to draw
ray diagrams for both kinds of lenses, and be able to solve the lens equation for both kinds
of lenses.
Lens Combinations, Optical Instruments.
You should be aware of this useful information, which will not be presented in lecture.
News Flash!
Archimedes invents Death Ray that sets enemy
ships on fire!
Fishbane* and Mythbusters say it’s impossible!
*Author of text used
through spring 2006.
News Flash!
MIT students set wooden “ships” on fire with
death rays! Details here!
Demo: the Missouri S&T death ray.
Maybe some day there will be a video.
Today’s agenda:
Death Rays.
You must know when to run from Death Rays.
Refraction at Spherical Surfaces.
You must be able to calculate properties of images formed by refraction at spherical
surfaces.
Thin Lenses: Concave and Convex Lenses, Ray Diagrams,
Solving the Lens Equation.
You must understand the differences between these two kinds of lenses, be able to draw
ray diagrams for both kinds of lenses, and be able to solve the lens equation for both kinds
of lenses.
Lens Combinations, Optical Instruments.
You should be aware of this useful information, which will not be presented in lecture.
Refraction at Spherical Surfaces
Convex surface:
1
2
axis
C
R
F
f
na nb>na
Geometry: a light ray parallel to
the axis passes through F.
 nb 
f =
 R >R
 nb - na 
An extended object will form an image inside the nb medium.
1
Ray 1: parallel to the axis, through F.
Ray 3: through C.
2
axis
R
s
C
F
f
na nb>na
This image is real and inverted.
s’
Concave surface:
R
F
C
axis
f
na
Geometry: a light ray parallel to
the axis seems to have come
from F.
nb>na
 nb 
f =
 R >R
 nb - na 
An extended object will form an image inside the na medium.
Ray 1: parallel to the axis, through F.
Ray 3: through C.
R
F
C
axis
f
na
nb>na
The image is virtual and upright.
There are three different places to put the object. The different images
formed are always virtual and upright.
We can use geometry to derive an equation relating the image
and source positions, and an equation for the magnification.
axis
C
R
s
F
f
na
nb
na nb nb - na
+ =
s
s'
R
s’
na s'
y'
m= =y
nb s
The same equations work for concave surfaces.
R
F
C
s
f
s’
na
na nb nb - na
+ =
s
s'
R
axis
nb
na s'
y'
m= =y
nb s
Approximations Were Used!
The equations in this section are excellent approximations if
both the angles of incidence and refraction are small.
Sign Conventions
 R is positive when it is in the medium into which the light
propagates. R is negative when it is in the medium from which
the light radiates.
 The image distance is positive when the image is in the
medium into which the light propagates, and negative if it is in
the medium from which the light radiates (virtual image).
 The object distance is positive when the object is in the
medium from which the light radiates (the usual case—a real
object), and negative if on the side opposite to the light
source (a virtual object).
These are really “the same” as for mirrors.
Example: a Jurassic mosquito is discovered embedded in an
amber sphere which has an index of refraction of 1.6. The
radius of curvature of the sphere is 3.0 mm. The mosquito is
located on the principal axis and appears to be imbedded 5.0
mm into the amber. How deep is the mosquito really?
na nb nb - na
+ =
s
s'
R
The object is in the
amber, so na=1.6 and
nb=1.
The image is in the medium
from which the light radiates
so s’=-5.0 mm.
nb=1
na=1.6
R
s
s’
R is negative because it is in the medium from which the
light radiates. R=-3.0 mm.
1.6
1
1-1.6
+
=
s
-5.0
-3
s = 4 mm
nb=1
na=1.6
R
s
s’
Example: a Jurassic mosquito is discovered embedded in an
amber sphere which has an index of refraction of 1.6. The
radius of curvature of the sphere is 3.0 mm. The mosquito is
located on the principal axis and appears to be imbedded 5.0
mm into the amber. What is the magnification?
-na s'
m=
nb s
nb=1
na=1.6
s=4 mm and s’=-5.0 mm.
na=1.6 and nb=1
- 1.6  -5  8
m=
= =2
4
1 4 
R
s
s’
Today’s agenda:
Death Rays.
You must know when to run from Death Rays.
Refraction at Spherical Surfaces.
You must be able to calculate properties of images formed by refraction at spherical
surfaces.
Thin Lenses: Concave and Convex Lenses, Ray
Diagrams, Solving the Lens Equation.
You must understand the differences between these two kinds of lenses, be able to draw
ray diagrams for both kinds of lenses, and be able to solve the lens equation for both kinds
of lenses.
Lens Combinations, Optical Instruments.
You should be aware of this useful information, which will not be presented in lecture.
Thin Lenses
A lens in this section is taken to be a single object made of
transparent material of refractive material n>1.
There are two surface boundaries.
Light from an object incident on
the first surface forms an image,
which becomes the object for the
second surface.
A thin lens is one for which the
distance from the object to each of
the two surfaces is the “same”
(and the distance from the image
to each surface is the “same”).
This would NOT
qualify as a thin lens.
I will make my lenses look “hollow,” like this.
There are several surface combinations from
which we can make lenses. Here are three
(there are more).
Converging and Diverging Lenses
Thin lenses can be converging or diverging.
The converging lens is thicker in the center. The diverging
lens is thicker at the edges.
There are focal points on both sides of each lens.
The focal length is the same whether light passes
from left to right or right to left.
There are two surfaces at which light
refracts. Our equations (provided later)
“automatically” take care of this.
In your diagrams, simply draw the incident
ray up to the center of the lens, then draw
the refracted ray in its final direction.
Ray Diagrams for Diverging Lenses
Ray 1 is parallel to the axis and refracts as if from F.
Ray 2 heads towards F’ before refracting parallel to the axis.
Ray 3 passes straight through the center of the lens.
O
F
I
F’
The image is virtual and upright. It is smaller than the object.
Converging and Diverging Lenses
The image formed by a converging lens may be real, inverted,
and either smaller or larger than the object. It may also be
virtual, upright, and larger than the object. See this web page.
The image formed by a diverging lens is always virtual,
upright, and smaller than the object. See the same web page.
Do these lens properties remind you of anything else you’ve
studied recently?
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=48.0
Handy quick reference card from Dr. Hale:
http://web.mst.edu/~hale/courses/Physics24/Quick.Reference.Cards/mirror.lens.table.pdf
Homework Hint
If Problem 34.32 is assigned:
the image is 80 times larger than the object.
The object is very close to the lens compared to the image.
A ray diagram will be difficult to draw!
Do your best; maybe just make a diagram suggesting
how the rays converge “far” from the lens.
Lens combination problem: suggested as a Final Exam
problem last spring. See what you think of it.
Today’s agenda:
Death Rays.
You must know when to run from Death Rays.
Refraction at Spherical Surfaces.
You must be able to calculate properties of images formed by refraction at spherical
surfaces.
Thin Lenses: Concave and Convex Lenses, Ray Diagrams,
Solving the Lens Equation.
You must understand the differences between these two kinds of lenses, be able to draw
ray diagrams for both kinds of lenses, and be able to solve the lens equation for both kinds
of lenses.
Lens Combinations, Optical Instruments.
You should be aware of this useful information, which will not be presented in lecture.
The Lensmaker’s Equation
s’
s
s’
 1
1 1
1 
+ = n-1   
s s'
 R a Rb 
The Lensmaker’s Equation
s
 1
1
1 
=  n-1   
f
 R a Rb 
1 1 1
+ =
s s' f
y'
s'
M= = y
s
Sign Conventions for The Lens Equation
1 1 1
+ =
s s' f
y'
s'
M= = y
s
The focal length f is positive for converging lenses and
negative for diverging lenses.
The object distance s is positive if the object is on the side of
the lens from which the light is coming; otherwise s is
negative.
The image distance s’ is positive if the image is on the
opposite side of the lens from where the light is coming;
otherwise s’ is negative. (If s’ is negative, is the image real?)
The image height y’ is positive if the image is upright and
negative if the image is inverted relative to the object.
Example: an object is located 5 cm in front of a converging
lens of 10 cm focal length. Find the image distance and
magnification. Is the image real or virtual?
It’s just a coincidence that
the image is located at F’.
F’
F
O
1 1 1
1
1
1
= - =
=s' f s +10 +5
10
s' = -10
M= -
s'
-10
==2
s
5
Image distance is 10 cm, image is on side of lens light is
coming from, so image is virtual. M=2 so image is upright.
Summary of Sign Conventions
Mirrors
Lenses
The focal length f is positive for
converging lenses and negative for
diverging lenses.
When the object, image, or focal
point is on the reflecting side of the
mirror, the distance is positive.
The object distance s is positive if the
object is on the side of the lens from
which the light is coming; otherwise s is
negative (and the object is virtual).
When the object, image, or focal
point is “behind” the mirror, the
distance is negative.
The image distance s’ and radius of
curvature R are positive if the image is
on the side of the lens into which the
light is going; otherwise negative.
The image height is positive if the
image is upright, and negative if the
image is inverted relative to the object.
The image height is positive if the
image is upright, and negative if the
image is inverted relative to the object.
Summary of Sign Conventions
Here’s a more compact way of expressing the sign
conventions all at once.
Object Distance. When the object is on the same side as
the incoming light, the object distance is positive (otherwise
is negative).
Image Distance. When the image is on the same side as
the outgoing light, the image distance is positive (otherwise
is negative).
Radius of Curvature. When the center of curvature C is on
the same side as the outgoing light, R is positive (otherwise
is negative).
“Image Distance. When the image is on the same side as
the outgoing light, the image distance is positive (otherwise
is negative).”
If the image distance is negative, can the image be real?