Download Lecture 25 - UF Physics

Lecture Objectives
After this class you will be able to:
1. Apply the Law of Reflection
2. Locate and state the properties of an image
3. Determine the focus of a concave mirror, given its
radius of curvature
4. Make ray diagrams for a concave mirror to locate an
image and state its properties.
5. Use the mirror equation with correct rules for signs.
6. Calculate Image Magnification
7. Do the #3-6 for a convex mirror.
0. Polarization
Polarization of Light Waves
• Each atom produces a
wave with its own
orientation of
• All directions of the
electric field vector are
equally possible.
• This is an unpolarized
wave.
• Natural Light is
unpolarized.
Central dot represents light
travelling out of the plane
Linear Polarization
• An unpolarized beam
can be polarized by
– Selective absorption
– Scattering
– Reflection
Unpolarized
Polarized
Polarization by Selective Absorption
θ
I = I0 cos2θ
Intensity after polaroid
Intensity before polaroid
For unpolarized light, a polaroid sheet reduces its intensity
to half (sunglasses).
Polarization by Selective Absorption
Io
I
I = Io cos2 θ
What happens at ө = 90◦?
A Sequence of Polarizers
Polaroids: Selective Absorption
• E. H. Land discovered a material that polarizes
light through selective absorption.
– He called the material Polaroid.
– The molecules readily absorb light whose electric
field vector is parallel to their lengths and transmit
light whose electric field vector is perpendicular to
their lengths.
Polarization by Scattering
• Horizontally and vertically polarized waves are emitted.
Polarization by Reflection
• When an unpolarized light beam is reflected from a
surface, the reflected light is
– Completely polarized
– Partially polarized
– Unpolarized
• It depends on the angle of incidence.
– For one particular angle, the beam is completely polarized.
Dual Nature of Light
• Light has a number of physical properties, some
associated with waves and others with particles.
• In considering reflection we will consider the light as
a wave.
Reflection and Refraction
When light traveling in one medium encounters
a boundary leading to a second medium:
• reflection, part of the light bounces off the
second medium.
• refraction, the light passing into the second
medium bends.
• Often, both processes occur at the same time.
Following the Reflected and Refracted
Rays
• Which rays are
reflected rays and
which are refracted?
Following the Reflected and Refracted
Rays
• Ray  is the incident ray.
• Ray  is the reflected ray.
• Ray  is refracted into the
Lucite.
• Ray  is internally reflected
in the Lucite.
• Ray  is refracted as it
enters the air from the
Lucite.
Geometric Optics – Using a Ray Approximation
• The ray approximation is used to represent
beams of light.
• A ray of light is an imaginary line drawn along
the direction of travel of the light beams.
Diffuse Reflection
• Diffuse reflection is
reflection from a rough
surface.
• The reflected rays travel
in a variety of
directions.
Specular Reflection
• Specular reflection is
reflection from a
smooth surface e.g. a
mirror
1. Law of Reflection
θi= θr
2. Plane Mirror
Properties of the image can be determined by
geometry.
Notation for Mirrors and Lenses
• The object distance (p) is the distance from the object to
the mirror or lens.
• The image distance (q) is the distance from the image to
the mirror or lens.
– Images are formed at the point where rays actually intersect or
appear to originate.
• The lateral magnification (M) of the mirror or lens is the
ratio of the image height to the object height.
Types of Images
• Real images are formed at the point the rays
of light actually intersect.
• Virtual images are formed at the point the
rays of light appear to originate.
– The light appears to diverge from that point.
– Virtual images cannot be displayed on screens.
3. Spherical Mirrors
• A spherical mirror has the shape of a segment of a
sphere.
• A concave spherical mirror has the silvered surface of
the mirror on the inner, or concave, side of the curve.
• A convex spherical mirror has the silvered surface of
the mirror on the outer, or convex, side of the curve.
Concave Mirror, Notation
• The mirror has a radius
of curvature of R.
• Its center of curvature is
the point C.
• Point V is the center of
the spherical segment.
• A line drawn from C to
V is called the principal
axis of the mirror.
• The focus is at half the
distance of C
4. Ray Diagrams
• A ray diagram can be used to determine the position
and size of an image.
• They are graphical constructions which tell the
overall nature of the image.
• They can also be used to check the parameters
calculated from the mirror and magnification
equations.
The Rays in a Ray Diagram
• Ray 1 is drawn parallel to the principle axis and is
reflected back through the focal point, f.
Credit: Nerd Island Studios
The Rays in a Ray Diagram
• Ray 2 is drawn through the center of curvature and is
reflected back on itself.
The Rays in a Ray Diagram
• Ray 3 is drawn through the focal point and is
reflected parallel to the principal axis.
More About Images
• To find where an image is formed, it is always
necessary to follow at least two rays of light as
they reflect from the mirror.
Ray Diagram for Concave Mirror,
p > 2f, Image is real, inverted and smaller.
• The image is real, inverted and smaller than the
object.
Ray Diagram for Concave Mirror,
2f > p > f, Image is real, inverted and larger.
• The image is real, inverted and larger than the
object.
Ray Diagram for a Concave Mirror, p < f,
Image is virtual, upright and enlarged
• The image is virtual, upright and larger than the
object.
Notes About the Rays
• The rays actually go in all directions from the
object.
• The three rays were chosen for their ease of
construction.
• The image point obtained by the ray diagram
must agree with the value of q calculated from
the mirror equation.
Example 26.1
An object is placed at the center of curvature of
a concave mirror. Where is the image formed?
Describe the image.
Simulation
Example 26.1 Solution
Image properties:
• Real
• Inverted
• Same size.