Videos
SP212
Ch. 34 - Images
http://demonstrations.wolfram.com/
RayDiagramsForSphericalMirrors/
http://demonstrations.wolfram.com/
TracingRaysReflectedFromASphericalMirror/
http://demonstrations.wolfram.com/
AParabolicMirror/
Maj Jeremy Best USMC
Physics Department, U.S. Naval Academy
April 11, 2016
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Find the Physics
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Images: Real and Virtual
This image encompasses three specific physics principles
from 212. What are they?
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We will discuss two types of images in this chapter, real
and virtual.
An example of a virtual image is the image formed
by an ordinary flat mirror. It looks like there’s a
person standing behind the mirror, but no one’s
actually there
An example of a real image is the image formed by
a projector like here or the movies. If you can
project it: it’s REAL!!
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Tricky Images
Plane Mirrors
We are all familiar with ordinary flat (plane) mirrors.
Here is how the image is formed. Each individual ray
obeys the law of reflection we learned last chapter.
The object distance, p
is positive
the image distance, i is
negative for a virtual
image
We see that i = −p
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Corner Reflectors
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Extended Objects
We will often deal with extended objects, conventionally
drawn as arrows.
Reflected ray is always
parallel to the incident
ray.
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Spherical Mirrors
Spherical Mirrors
For spherical mirrors, we find that
f = (1/2)r
Plane mirrors can be interesting, but things get much
more fun when we bend the mirror into a spherical
surface with radius of curvature r . We find that
incoming parallel rays (from an object at infinity) all
converge (for a concave mirror) or at least seem to
converge (for a convex mirror) at a single point called
the focal point of the mirror. The distance from there
to the center is the focal length. All distances are
measured from the center of the mirror.
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Where f and r are positive for concave mirrors, and
negative for convex mirrors
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Images from Spherical Mirrors
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Magnification
One simple equation relates the three quantities we have
discussed, the object distance, p, the image distance i,
and the focal length f .
We define the magnification of a mirror as the ratio of
the height of the image, h0 to the height of the object, h:
h0
|m| =
h
1 1 1
2
+ = =
p i
f
R
Real images form on the same side of the mirror as the
object, virtual images form on the opposite side (in the
mirror)
i is positive for real images, and negative for virtual
images
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Negative magnifications mean the image is inverted ,
and we find
m=
−i
p
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Concave Virtual Images
Ray Diagrams
We can also find images from spherical mirrors by using
carefully drawn ray diagrams . Use the following rules:
A ray that is parallel to the axis reflects through the
focal point f
A ray that initially passes through the focal point f
reflects parallel to the axis
A ray that passes through the center of curvature C
reflects back along itself
A ray that reflects from the mirror at the axis (point
c) is reflected symmetrically about the axis.
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Light Rays Example
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Convex Ray Tracing
Ray heading to the focus hits the mirror and comes
off parallel.
Parallel ray hits the mirror and reflects as if it
started at the focus.
Ray heading to the center of curvature returns along
the same path.
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Convex
Concave Ray Tracing
Parallel ray hit the mirror and heads to the focus.
Ray through focus hits the mirror and comes off
parallel.
Ray through center of curvature returns to center of
curvature.
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Concave and Convex
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Ray Diagrams
See page 932 in HRW:
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Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
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Example Problem
Spherical Refracting Surfaces
A concave shaving mirror has a radius of curvature of 35
cm. It is positioned so that the image of the face is 2.5
times the size of the face.
How far is the mirror from the face?
Is the image real or virtual?
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Spherical Refracting Surfaces
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Spherical Refracting Surfaces
The following general properties apply to refracting
surfaces:
Real images form on the side of the surface opposite
the object, virtual images on the same side
When the object faces a convex refracting surface,
the radius of curvature is positive.
When an object faces a concave refracting surface,
the radius of curvature is negative.
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With refracting surfaces, light rays are bent at the
surface according to Snell’s Law. We will always consider
our object to be inside the material with index of
refraction n1 . This may be the larger or smaller of the
indicies.
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If the object is embedded in the material with index of
refraction n1 , the images distance i, radius of curvature r
and object distance p are related:
n1 n2
n2 − n1
+
=
p
i
r
Watch your signs!!!!!
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Crazy Cat
Cat Mirage Explained
What is going on in this picture?
Real images form on the side of the surface opposite
the object, virtual images on the same side
When the object faces a convex refracting surface,
the radius of curvature is positive.
When an object faces a concave refracting surface,
the radius of curvature is negative.
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Videos
http://demonstrations.wolfram.com/
RayDiagramsForLenses/
http://demonstrations.wolfram.com/
RayTracingWithLenses/
http://demonstrations.wolfram.com/
RayDiagramsForMicroscopeAndTelescope/
http://demonstrations.wolfram.com/
ConstructingASimpleOpticalSystem/
https://phet.colorado.edu/en/simulation/
geometric-optics
Lenses on Youtube great
http://youtu.be/8gyGfiiC3ms
http://youtu.be/X2-Rv_aVr40
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Thin Lenses
A lens is a piece of transparent material with two
refracting surfaces.
Some lenses cause rays initially parallel to the central
axis to converge , and some cause these rays to
diverge. Lenses follow the same relation as mirrors:
1 1 1
+ =
p i
f
i is still positive for real images and negative for virtual
images, but now real images form on the opposite side of
the lens from the object, virtual images form on the
same side!
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The Lensmaker’s Equation
When a thin lens of index of refraction n is immersed in
air, the lensmaker’s equation applies:
1
1
1
= (n − 1)
−
f
r1 r2
Which relates the focal length to the radii of the two
sides (r1 is closer to the object). If the lens is not in air
(suppose it’s submerged in water), replace n with
n/nmedium
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The Lensmaker’s Equation, Better
Where converging lenses are +,+, diverging lenses are
−,−, and combo lenses are built from the pieces of those
two reference systems
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Images from Thin Lenses
OK, that’s the equation on your sheet, but I’m going to
overrule it. Instead, use this:
1
1
1
= (n − 1) ± ±
f
r1 r2
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Converging lenses can form both real and virtual images
Real images appear on the opposite side of the lens
from the object, when the object is outside the
focal point.
Virtual images appear on the same side of the lens
as the object, when the object is inside the focal
point.
Diverging Lenses only form virtual images
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Magnification of Lenses
Lenses follow the same magnification rules as Mirrors.
m=
−i
p
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Ray Diagrams
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Ray diagrams
Lenses have different rules for drawing ray diagrams
A ray initially parallel to the central axis will pass
through the focus
A ray initially through the focus will emerge parallel
to the central axis
A ray directed toward the center of the lens passes
through undeflected
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Multiple Lens Systems
Multiple lens systems are an extension of one lens
systems.
First, ignoring lens 2, find the location of the image
from lens 1, I1 . Note where it is, whether it is real
or virtual, inverted, etc.
Now, ignoring lens 1, use image I1 as the object for
lens 2 (at distance p2 ) to find the image I2
If image I1 lies to the right of lens 2, its object distance
p2 , is negative. The total magnification of the system is
M = m1 m2 .
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Summary of Ch34
Mirrors
IMAGE
Object Location Image Location Type
Orientation Magnification
Plane
Concave
Concave
Convex
Anywhere
Outside of F
Inside of F
Anywhere
Lenses
Object Location Image Location Type
Converging Outside of F
Converging Inside of F
Diverging
Anywhere
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Opposite
Same
Opposite
Opposite
Opposite
Same
Same
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Virtual
Real
Virtual
Virtual
Real
Virtual
Virtual
Upright
Inverted
Upright
Upright
0
Negative
Positive
Negative
Orientation Magnification
Inverted
Upright
Upright
Depends on Dist
Positive
Negative
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