Download Chapter 34 – Geometric Optics and Optical Instruments

Chapter 34 – Geometric Optics and Optical Instruments
I.
Introduction – find the position of the image due to reflections and refractions
II.
Reflections from Plane Surfaces
A.
Ray diagram showing where the image of an object is located
object
y
Optic Axis
s
reflecting
surface
Observations:
1.
image is called a virtual image – the light appears to diverge from the image.
(a real image is one to where the light converges)
B.
2.
image distance = object distance
3.
image size = object size
Lateral Magnification, m
m =
C.
image size
object size
Image appears to undergo a left to right reversal, but no top to bottom reversal. Why?
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III. Reflection from a Spherical Surface
A.
Types of spherical reflecting surfaces (spherical mirrors)
1.
Concave mirror (converging)
C
2.
Convex mirror (diverging)
C
B.
Location of image for a spherical mirror
object
y
C
V
R
s
2
1.
Lateral magnification
m
image size

object size
2.
Mirror equation
3.
Focal point and focal length
a.
Focal point, F – position of the image when the object is at infinity
Focal length, f – the image distance when the object is at infinity
b.
Graphical interpretation of the focal point and focal length
1)
concave mirror
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2)
C.
convex mirror
Graphical method of locating images - three (four) rays whose paths are known
1.
ray parallel to the optic axis > reflects back through the focal point
2.
ray through the center of curvature, C > reflects back through the center of curvature
3.
ray through focal point > reflects back parallel to the optic axis
4.
ray to vertex > reflects back ( = ’)
concave mirror, I:
concave mirror, II:
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concave mirror, III:
convex mirror:
D.
Using the Mirror Equation:
1 1 2 1
  
s s' R f
and
m
s'
s
Sign convention – the signs associated with object distances, images distances, etc. are based on
where the object, image, etc. is located relative to the incident and reflected rays. MEMORIZE THIS!
+s: real object – object on same side as incoming light rays
-s: virtual object – object not on same side as incoming light rays
+s’: real image – image on same side as outgoing light rays
-s’: virtual image – image not on same side as outgoing light rays
+R: concave mirror – center of curvature, C, on same side as outgoing light rays
-R: convex mirror – center of curvature, C, not on same side as outgoing light rays
+f: focal length – focal point, F, on same side as outgoing light rays
-f: focal length – focal point, F, not on same side as outgoing light rays
+m: upright (erect) image
-m: inverted image
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E.
Examples
1.
A 3 cm high object is located at a position 80 cm away from a concave mirror of 20 cm radius.
Find the position and size of the image.
2.
A shaving mirror is a concave mirror of 80 cm radius. A person’s nose is located 20 cm in front
of the mirror. Where is the image located and what is its magnification?
3. A person is standing 50 cm in front of a 20 cm convex shaped doorknob. Where is the image of
the person located and what is the magnification?
4.
Can these equations be used for a plane mirror?
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IV. Refractions at spherical surfaces
n1
object
n2
y
C
Optic
Axis
R
s
A.
Lateral magnification
m
B.
image size
object size
Refraction equation
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C.
Sign Convention – same as for mirrors (page 34-5)
+s (real object): object on same side as incoming light rays
+s’ (real image): image on same side as outgoing light rays
+R: C on same side as outgoing light rays
+m: upright or erect image
D.
Examples
1.
How deep does a coin on the bottom of a two feet deep pond appear to be?
2.
A fish is at the center of a spherical fishbowl whose radius is R. Where does the fish appear to
be and how large is the fish? Assume you are a distance of 2R from the surface of the fishbowl.
3.
What does the fish in question 2 see?
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V.
Multiple optical surfaces
A.
Analysis
object
surface 1
surface 2
In general, the image for one optical surface becomes the object for the next optical surface.
B.
Examples:
1.
A glass rod 40 cm long and index 1.50 has one end that is convex of radius 20 cm and the other
end has a convex surface of radius 30 cm. An object is placed 100 cm in front of the 20 cm
convex surface. Where, what size, and what orientation is the final image?
n = 1.50
100 cm
40 cm
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2.
A one centimeter high object is placed a distance 4R to the left of a glass sphere of radius R and
index 1.50. The right half of the sphere is coated with a reflecting material. Where, what size,
and what orientation is the final image?
3.
Two identical spherical mirrors with radius R
are separated by a distance equal to their focal
length, f = R/2. An object is placed on the
surface of one of the mirrors. After
undergoing two reflections, where will the
image be located, and what kind of image is it?
If a small hole is made in the middle of the top
mirror, will the image exist?
hole
f = R/2
object
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V.
Thin lenses – the thickness of the lens is small compared to the radii of curvature of the surfaces.
A.
Types of thin lenses
B.
1.
Converging: double convex, plano-convex, converging meniscus
2.
Diverging: double concave, plano-concave, diverging meniscus
Derivation of thin lens equation. The lens has radii R1 and R2, thickness t, and index n.
R1
R2
n
O1
I1 -> O2
s1
I2
s1’
s2
s2’
t
Surface 1
Surface 2
Note: If s’ for surface 1 is positive, then s for surface 2 is negative; or if s’ for surface 1 is negative, then
s for surface 2 is positive. That is s2 = - s1’.
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1.
Write the refraction equations for the two surfaces, and derive the thin lens equation.
Surface 1:
Surface 2:
2.
The focal point of a lens is the image position when the object is at infinity.
Rewrite the lens equation including the focal length.
3.
What is the magnification of a thin lens?
4.
Graphical interpretation of the focal point:
a.
Converging lens:
b.
Diverging lens:
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C.
Graphical method to find the position of images – three rays:
1.
2.
3.
ray parallel to the optic axis > travels through the focal point
ray through the vertex of lens > travels straight through the lens
ray through the other focal point > travels parallel to the optic axis
Converging lens:
Converging lens:
Diverging lens:
D.
Examples:
1.
Find the focal length of a thin, plano-convex lens with a radius of 30 cm and made of glass on
index n = 1.50. Is the focal length the same if the lens is reversed?
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2.
Find the focal length of a diverging meniscus lens with radii of 20 cm and 30 cm. The index of
the glass is n = 1.50.
3.
Where must a converging lens of focal length f be placed between an object and screen a
distance D apart so that the image is focused on the screen? (conjugate foci)
lens
object
screen
x
D
4.
An object is placed 40 cm in front of a converging lens with a focal length of 20 cm. A diverging
lens with a focal length of 30 cm is placed 25 cm behind the converging lens. Find the position
of the final image, its magnification, and its orientation.
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VI. Lens Aberrations – problems that produce blurred images of objects when light passes through lens.
A.
Spherical aberration – light far from the optic axis focuses at a different point from light traveling
close to the optic axis.
B.
Chromatic aberration – light of different wavelengths focuses at different points.
white light
white light
C.
Astigmatism – the curvature of the lens is different in different planes.
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VII. Optical Instruments – the basics
A.
Pinhole Camera
B.
Camera
C.
Projector
D.
Eye
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E.
Magnifier
F.
Microscope
G.
Telescope
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