#$&*
course Phy 232
Focusing Light#$&*
course Phy 232
This experiment uses a cylindrical container and two lamps or other compact light sources. Fill a cylindrical container with water. The cylindrical section of a soft-drink bottle will suffice. The larger the bottle the better (e.g., a 2-liter bottle is preferable to a 20-oz bottle) but any size will suffice.
Position two lamps with bare bulbs (i.e., without the lampshades) about a foot apart and 10 feet or more from the container, with the container at the same height as the lamps. The line separating the two bulbs should be perpendicular to the line from one of the bulbs to the cylindrical container. The room should not be brightly lit by anything other than the two bulbs (e.g., don't do this in front of a picture window on a bright day).
The direction of the light from the bulbs changes as it passes into, then out of, the container in such a way that at a certain distance behind the container the light focuses. When the light focuses the images of the two bulbs will appear on a vertical screen behind the cylinder as distinct vertical lines. At the focal point the images will be sharpest and most distinct.
Using a book, a CD case or any flat container measure the distance behind the cylinder at which the sharpest image forms. Measure also the radius of the cylinder.
As explained in Index of Refraction using a Liquid and also in Class Notes #18, find the index of refraction of water.
Then using a ray-tracing analysis, as describe in Class Notes, answer the following:
1. If a ray of light parallel to the central ray strikes the cylinder at a distance equal to 1/4 of the cylinder's radius then what is its angle of incidence on the cylinder?
Theta(I)=theta(r)-4.98
@&
4.98 has no units.
You do not document how you obtained this result.
Theta(r), which apparently indicates the refracted angle, is not relevant to this question. It becomes relevant for the next question, where it again must be justified.
*@
@&
This would be the angle of incidence if the beam struck the cylinder along the central ray.
The ray is incident at any point on the plane tangent to the cylinder at that point.
*@
2. For the index of refraction you obtained, what therefore will be the angle of refraction for this ray?
Theat(I)=theta(r)=4.98
3. If this refracted ray continued far enough along a straight-line path then how far from the 'front' of the lens would it be when it crossed the central ray?
(2 - n) / (2n - 2) * R->2-1/2*1.33-2*R=3 R=4.98
@&
4.98 appears once more but with no units, and its former meaning has no apparent relationship to its present meaning.
(2 - 1/2) * 1.33 - 2 is not equal to 3 or to 4.98. It is difficult to understand your meaning here.
*@
4. How far from the 'front' of the lens did the sharpest image form?
The image forms at the focal point which is found by solving (2 - n) / (2n - 2) * R->2-1/2*1.33-2*R=3 R=4.98
5. Should the answer to #3 be greater than, equal to or less than the answer to #4 and why?
It should be equal because this is the focal point.
6. How far is the actual refracted ray from the central ray when it strikes the 'back' of the lens? What is its angle of incidence at that point? What therefore is its angle of refraction?
It is sin(theta(r)).087 in=, angle of incidence= angle of refration=4.98
7. At what angle with the central ray does the refracted ray therefore emerge from the 'back' of the lens?
Theta(i)=theta(r)=4.98
8. How far from the 'back' of the lens will the refracted ray therefore be when it crosses the central ray?
The image will be focal distance-diameter of cylinder. (6-3)=3 inches
@&
"
@&
You need to explain your results and how they are obtained.
Please revise as instructed below.
&#Please see my notes and submit a copy of this document with revisions, comments and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).
Be sure to include the entire document, including my notes. &#
*@