#$&*
*#&!
@&
I'm not sure I've located all your tests, but this is almost certainly the result of an electronics glitch, which I should have straightened out by tomorrow. So if you've completed the tests, there's nothing to worry about. I'll be turning in grade updates tomorrow.
*@
#$&*
*#&!
@&
OK, the dates are the key. You'll get your final grade tomorrow. You've done very well in the course.
*@
course Phy 232
8/5 8 am
Experiment 26: Ray Tracing for a Circular Lens and a Circular MirrorUsing a hand-held laser and a circular mirror cut from a soft-drink can we observe the focal point at which parallel rays incident on the mirror converge. We also observe the paths of rays through circular lenses and the focal points of the lenses. The lenses have been constructed from broken pieces of clear Christmas tree ornaments mounted on clear cassette cases and filled with water.
Trace the paths of parallel rays reflected from a circular mirror
Using any reasonably sharp steel knife (it should not damage a tempered steel knife to cut aluminum, but just in case don't use your best cutlery), cut a section like the one shown on the videotape from a soft drink can.
Determine the radius of the can.
• Using this radius with either a compass or a pencil and a piece of string, sketch a segment of a circle with this radius to match the section cut from the can.
• Be sure to clearly mark the center of the circle you used to sketch this segment.
• Sketch the segment on a piece of lined notebook paper and position the segment so that when the piece of the can is positioned on the segment you will be able to direct parallel rays toward it as indicated on the video clip.
Position the section on the paper, and if necessary adjust it as necessary so that its curvature matches that of the circular segment you sketched.
• Direct four beams at the section of the can (hereafter referred to as the mirror) and trace their paths toward and away from the mirror.
• The first beam should be a central beam, which is reflected from the mirror along the same path with which it approached the mirror.
• The second beam should be parallel to the central beam and approximately 1/8 of the container's radius to the right of the central beam.
• The third beam should be parallel to the central beam and approximately 2/8 (i.e., 1/4) of the container's radius to the left of the central beam.
• The fourth beam should be parallel to the central beam and approximately 3/8 of the container's radius to the right of the central beam.
• Mark the center of each beam as it leaves the pointer at a distance of about 15 cm from the mirror, at the point where it strikes the mirror, and at the most distant point you can reasonably locate after the beam is reflected from the mirror.
Trace the paths of parallel rays entering a circular container full of liquid (a circular lens).
Using similar techniques to those used above, using a lined piece of paper (e.g., ruled notebook paper) to ensure that the beams are parallel, trace the paths of four beams through a transparent circular container filled with colored water or lightly colored soft drink, as specified below.
• The container should have a section with smooth sides and a very circular cross-section (i.e., that section should make a nice uniform circular cylinder), and should have the approximate diameter of a soft drink container (20 oz. or larger--the larger the container the better your accuracy will be). Many glass jars, soft-drink bottles, etc. make good containers for this experiment. A petri dish might have been included with your kit and if so you may use it or any container of the above description.
• At and near the points where the beams will enter and leave the container, the container should form a smooth, uniform vertical cylinder.
• On your paper indicate the outline of the container. Report what you did to accurately represent the container.
• It is very important that the four beams all be parallel, so take particular care to ensure that this is the case, and be sure to report how you managed this.
• The first beam should be a central beam, which passes through the container without any change of direction.
• The second beam should be parallel to the central beam and approximately 1/8 of the container's radius to the right of the central beam.
• The third beam should be parallel to the central beam and approximately 2/8 (i.e., 1/4) of the container's radius to the left of the central beam.
• The fourth beam should be parallel to the central beam and approximately 3/8 of the container's radius to the right of the central beam.
• Mark the center of each beam as it leaves the pointer at a distance of about 10 cm from the container, as it enters the container, as it leaves the container and at a point approximately 10 cm beyond where it leaves the container.
Observe the focal point of the lens
By placing a 'screen' (e.g., the cassette case with the copy of the ruler taped to it) at the appropriate position behind the circular lens used in the preceding procedure, determine the distance at which the emerging beam appears to remain stationary as the laser is moved back and forth in front of the lens.
• Take care to keep the laser pointed in a consistent direction so that the beams striking the lens are all parallel.
• Observe how the dot on the screen will move in the opposite direction to your movement of the laser when the screen is far from the lens, and how it will move in the same direction when close to the lens.
• The distance at which the dot on the screen remains stationary will be the point at which the direction of movement of the dot changes.
• Mark this distance on your paper.
Analyze the various paths
Sketch the paths of the four beams to and from the mirror.
For the mirror, determine whether the angle of each incoming beam with the normal to the mirror is the same as that of the reflected beam.
• At each point where the beam strikes the mirror, sketch a radial line segment (i.e., a straight line segment from the center of the circle to the point).
• Sketch at each point a short line segment tangent to the mirror (the tangent will be perpendicular to the radial line segment).
• The radial line segment is perpendicular, or normal, to the mirror at each point.
• Determine the angle between the incoming beam and the normal, and between the reflected beam and the normal.
&&&&
Incoming beam and normal = 42 degrees
Reflected beam and normal = 46 degrees
#$%&
• Determine whether these two angles are equal.
&&&&
The angles are close to the same. I used the paper to try and determine the angles and position the light beams at the appropriate spots.
#$%&
For the mirror, determine as accurately as possible the point at which the reflected rays converge.
&&&&
Converge around 2 cm on a can of a radius of roughly 3.5 cm
#$%&
• The rays closest to the central ray of a truly circular mirror will converge almost perfectly; those furthest from the central ray will converge less perfectly.
• Determine the ratio between the point of convergence and the radius of the circle.
&&&&
3:5
#$%&
For the circular lens, sketch the paths of of the four rays and determine whether the path of the fourth ray is consistent with Snell's Law.
Sketch the paths of the four rays.
• For each ray, sketch the normal line as the ray enters and as it leaves the circle, and sketch the tangent line to the circle at each of these points.
• For a point on a circle, the normal line is a radial line from the center; the tangent line at this point is perpendicular to the normal line.
• Determine whether each ray is in fact deflected toward the normal as it moves from a lower to a higher index of refraction, and away from the normal as it moves may higher to the lower index of refraction.
&&&&
It appears that each ray is deflected toward the normal as it moves from a lower index to a higher index, and each ray moves away as it moves from higher to lower index of refraction
#$%&
• For the fourth ray, determine as accurately as possible the angle with normal before and after the ray enters the circle, and before and after it leaves the circle.
• Determine whether these angles are consistent with an index of refraction of 1.34 for water, 1.00 for air.
For the circular lens, determine the distance of the focal point from the lens.
Determine as accurately as possible where the four rays converge.
• The four rays should converge at a point 'behind' the lens. Determine the distance behind the lens at which the rays converge.
&&&&
They converge around 2 cm
#$%&
• Determine the ratio between this distance and the radius of the circle.
&&&&
3:5
#$%&
Compare the position of the point of convergence to the position of the focus as you observed it by moving the laser back and forth in front of the lens.
• Should the point of convergence and the focus be the same?
• &&&&
Yes because the focus is the point where all of the rays converge together.
#$%&
• Which do you think is the more accurate determination of the focal point?
&&&&
R = 4FP cm
#$%&
"