Transcript Light: Geometric Optics

1. Two long straight wires carry identical currents in opposite
directions, as shown. At the point labeled A, is the direction of
the magnetic field left, right, up, down, into the page or out of
the page?
A.
2. A magnet produces a magnetic field that points vertically
upward. Along what line does the force on a proton act if it
enters this region with a horizontal velocity toward the south?
3. A copper ring is oriented perpendicular to a uniform magnetic
field. The ring is quickly stretched such its radius doubles over a
short time. As the ring is being stretched, is the magnitude of the
net magnetic field in the center of the loop greater than, equal to,
or less than the magnitude of the uniform field? Explain.
4. Can you accelerate the stationary particle with magnetic field?
An electric field? Explain.
Light: Geometric Optics
The Ray Model of Light
The ray model of light assumes
that light travels in straight-line
path called rays.
Reflection
For flat surfaces, it is found that the
incident and reflected rays lie in the
same plane with the normal to the
surface.
Law of Reflection
The angle of incidence equals the angle of
reflection.
Diffuse reflection
Specular reflection
Image Formation by a Plane
Mirror
For a plane mirror the image distance
(distance from mirror to image) equals
the object distance.
Real and Virtual Images
How tall must a full-length mirror be?
A woman 1.60m tall stands in front of a
vertical plane mirror. What is the minimum
height of the mirror, and how high must its
lower edge be above the floor, if she is to be
able to see her whole body? Assume her eyes
are 10 cm below the top of her head).
Formation of Images by
Spherical Mirrors
For an object infinitely far away (the sun or starts), the rays
would be precisely parallel.
If a mirror is small compared to its
radius of curvature, so that the reflected
rays make only a small angle upon
reflection, then the rays will cross each
other at a single point, or focus.
The principal axis of a mirror is defined as the
straight line perpendicular to the curved
surface at its center.
The point F, where the rays parallel to the
principal axis, come to a focus, is called
the focal point of the mirror.
The distance between focal point and the
center of the mirror is called the focal
length, f, of the mirror.
Another way of defining the focal point is
to say that it is the image point for an
object infinitely far away along the
principal axis.
Finding the Image Position for a
Curved Mirror
-ray 1 is drawn parallel to the axis; therefore it must pass
along a line through F;
-ray 2 is drawn through F, as result is must reflect into parallel
to the principal axis ray;
-ray 3 is chosen to be perpendicular to the mirror, and so is
drawn so that it passes through C, the center of curvature; it
will be reflected back on itself.
Mirror Equation
1
1 1
 
d o di f
The lateral magnification, m, of a mirror is
defined as the height of the image divided by
the height of the object:
hi
di
m

ho
do
The Sign Convention
-the image height hi is positive if the image is
upright, and negative if inverted, relative to the
object;
-di and do are both positive if image and object are
on the reflecting side of mirror, but if either image
or object are behind the mirror, the corresponding
distance is negative.