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,

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

fdd io

111

The lateral magnification, m, of a mirror is defined as the height of the image divided by the height of the object:

o

i

o

i

d

d

h

hm

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.