Download Reflection

Introduction to Optics
Lecture 11
(See Giancoli Chapter 23)
Ray Optics
Reflections and Mirrors
Phenomena involving reflection
Silas Laycock, UML, General Physics II. Spring 2014.
Lecture slides not to be disseminated on the internet or shared
beyond this class
Primary colors
•  The primary colors are Red, blue and
yellow
•  Green light+ Red light = Yellow light
•  Blue light + yellow light = green light
Optics: Summary
•  The Ray Model of Light
•  Image formed by a pinhole
•  Reflection; Image Formed by a Plane Mirror
•  Formation of Images by Spherical Mirrors
•  Index of Refraction
•  Refraction: Snell’s Law
•  Total Internal Reflection; Fiber Optics
•  Thin Lenses; Ray Tracing
•  The Thin Lens Equation; Magnification
•  Lens power and diopter
•  Combinations of Lenses (extra)
There are 3 basic ways to gather light and
focus it to make an image.
Pinhole - Simple geometry
Mirror - Reflection
Lens - Refraction
Pinhole Camera Image Formation
(the pinhole camera is the “perfect” optical system)
•  Pinhole images can form whenever
light passes though a small hole.
•  Sunlight falling between the leaves
of trees often causes a dappled
appearance on the ground. Each of
the small round dapples (patches of
light) is a perfect focused image of
the Sun!
•  In this picture a solar eclipse was in
progress so the patches are all
crescent shaped.
This pinhole image of a living
human (!) was made using
gamma rays
The Law of Reflection
Law of reflection: the angle of reflection
(that the ray makes with the normal to a
surface) equals the angle of incidence.
23.2 Reflection; Image Formation by a
Plane Mirror
When light reflects from a rough surface, the law
of reflection still holds, but the angle of
incidence varies. This is called diffuse reflection.
The size of this sun patch depends on the roughness of the sea surface
ConcepTest 23.1
Reflection
1) the Moon is very large
When watching the Moon over
2) atmospheric conditions are
just right
the ocean, you often see a long
3) the ocean is calm
streak of light on the surface of
4) the ocean is wavy
the water. This occurs because:
5) motion of the Moon
ConcepTest 23.1 Reflection
1) the Moon is very large
When watching the Moon over
the ocean, you often see a long
streak of light on the surface of
the water. This occurs because:
2) atmospheric conditions are
just right
3) the ocean is calm
4) the ocean is wavy
5) motion of the Moon
When the water surface changes, the angle of
incidence also changes. Thus, different spots
on the water can reflect the Moon into your
eyes at different times.
Follow-up: Where else does this occur?
Reflection; Image Formation by a Plane
Mirror
With diffuse reflection, your eye sees
reflected light at all angles. With specular
reflection (from a mirror), your eye must be in
the correct position.
Munch’s “Girls on the Pier” Painting
Reflection; Virtual Images
What you see when you look into a plane (flat)
mirror is an image, which appears to be behind
the mirror.
Notice how many ways mirror images differ from
a direct view of the scene
ConcepTest 23.2b Mirror II
1) same as your height
You stand in front of a
mirror. How tall does the
2) less than your full height but
more than half your height
mirror have to be so that
3) half your height
you can see yourself
4) less than half your height
entirely?
5) any size will do
ConcepTest 23.2b
Mirror II
1) same as your height
You stand in front of a
mirror. How tall does the
2) less than your full height but
more than half your height
mirror have to be so that
3) half your height
you can see yourself
4) less than half your height
entirely?
Trace the light rays from the
image’s foot to the mirror and
then to the eye. Since we know
that θi = θr , you need a mirror
only half your size.
5) any size will do
ConcepTest 23.2c Mirror III
1) No.
Does this depend
on your distance
from the mirror?
2) Yes.
3) Depends on the mirror.
4) Depends on the person.
ConcepTest 23.2c Mirror III
1) No.
Does this depend
on your distance
from the mirror?
The further you step back, the
smaller the incident and
reflected angles will be. But the
rays will still be reflected at the
same points, so the ray from the
foot will still be reflected at midheight.
2) Yes.
3) Depends on the mirror.
4) Depends on the person.
Formation of Images by Spherical Mirrors
Spherical mirrors are shaped like sections of
a sphere, and may be reflective on either the
inside (concave) or outside (convex).
Try this yourself, next time you have a spoon in your hand.
Compare to what you see in a shaving/makeup mirror.
Is the Convex image ALWAYS erect, and the Concave ALWAYS
inverted?
______ Mirrors always produce an erect image,
______ mirrors can produce an inverted
image or an erect image depending on the
viewing distance.
A.  Convex, Concave
B.  Flat, Convex
C.  Concave, Convex
23.3 Formation of Images by Spherical
Mirrors
Rays coming from a faraway object are
effectively parallel.
23.3 Formation of Images by Spherical
Mirrors
Parallel rays striking a spherical
mirror converge at a point, called
the Focus, or focal point.
The law of reflection does not
depend on the wavelength of
light, so mirrors produce perfect
color images (no chromatic
aberration)
If the curvature of the mirror is
large, the point becomes spread
out. This is called spherical
aberration.
Radius of Curvature and Focal Length
Focal Length of a Spherical Mirror
•  A deeper curve gives a shorter focal length
•  Using geometry, we find that the focal length is half the radius of
curvature:
•  Spherical aberration can be avoided by using
a parabolic reflector; which are only a little
more difficult/expensive to make.
•  Typically used in Telescopes, Camera lenses
Lab equipment, shaving/make-up Mirrors, and
this solar fire-lighter for campers!
•  Mirrors are preferred to lenses in many
applications because of their perfect color
rendition, greater maximum size, and
substantially lower cost.
23.3 Formation of Images by Spherical
Mirrors
We use ray diagrams to determine where an
image will be. For mirrors, we use three key
rays, all of which begin on the object:
1.  A ray parallel to the axis; after reflection it
passes through the focal point
2.  A ray through the focal point; after reflection
it is parallel to the axis
3.  A ray perpendicular to the mirror; it reflects
back on itself
The Mirror Equation
Focal Length is the most important characteristic of an any optical element. It is
the distance from the mirror (or lens) surface at which a distant object is brought
to focus.
The More strongly curved the surface, the more it bends the light rays.
Steep curve = short focal length
(23-2)
Geometrically, one can derive an equation that
relates the object distance, image distance, and
focal length of the mirror:
Magnification by Mirrors and simple lenses
Magnification is the ratio of image height to
object height. (this is an “obvious” definition)
(23-3)
Less obvious but more useful: This ratio is the
same as the ratio of Image distance to Object
distance!
A negative sign indicates that the image is
inverted.
-1 < m < 1 means the image is smaller than the
object.
Magnification = -0.5 means what?
A.  Image is twice the height of the object, and
upside down.
B.  Image is half the height of the object.
C.  Image is half the height of the object, and
upside down.
D.  Image is half the area of the object.
23.3 Formation of Images by Spherical
Mirrors
If an object is outside the center of curvature of a
concave mirror, its image will be inverted,
smaller, and real.
23.3 Formation of Images by Spherical
Mirrors
If an object is inside the focal point, its image
will be upright, larger, and virtual.
Convex Mirrors
•  A Convex Mirror has no Focal
point.
•  Hence it Cannot form a Real
image
•  Virtual Images only.
• All the mathematical rules for
mirrors still apply.
•  For a convex mirror, the image
is always upright, and smaller.
•  Convex mirrors can compress
a large view into a small image.
•  Often used to provide a view of
a whole room, or a street.
23.3 Formation of Images by Spherical
Mirrors
Problem Solving: Spherical Mirrors
1.  Draw a ray diagram; the image is where the rays
intersect.
2.  Apply the mirror and magnification equations.
3.  Sign conventions: if the object, image, or focal point is
on the reflective side of the mirror, its distance is
positive, and negative otherwise. Magnification is
positive if image is upright, negative otherwise.
4.  Check that your solution agrees with the ray diagram.
Example Calculation: Meatloaf vs Toyota/Ford etc…..
“Objects in the mirror are closer
than they appear”
“Objects in the rearview mirror
may appear closer than they are.”