Download Physics 263 Experiment 6 Geometric Optics 1 Refraction

Physics 263
Experiment 6
Geometric Optics
In this laboratory, we will perform several experiments on “geometric” optics. A pictorial
diagram of the various components to be used is shown in Figure 5.
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Refraction
When light with a well-defined direction passes between two transparent media, the light
is bent (refracted). The Law of Refraction states that
n1 sin θ1 = n2 sin θ2
(1)
where n1 is the index of refraction of medium 1, θ1 is the angle between the light direction
and the normal to the plane, in medium 1 etc. This, and the apparatus setup is shown
in Figure 1.
Figure 1: Light refraction.
Procedure
1. Place the ray box, label side up, on a white sheet of paper on the table. Slide the
ray mask until only one white ray is showing.
2. Place the rhombus on the table and position it so the ray passes through the parallel
sides as shown in Figure 1.
3. Mark the position of the parallel surfaces of the rhombus and trace the incident and
transmitted (refracted) rays. Mark where the ray enters and leaves the rhombus.
4. Remove the rhombus and on the paper draw a line connecting the points where the
ray entered and left the rhombus. Draw the normal to the surface.
5. Measure the angles of incidence and refraction with a protractor. Record the data
in a spreadsheet.
6. Repeat this procedure for a total of three different angles of incidence.
7. plot sin θ1 vs. sin θ2 and determine the slope. Since medium 1 is air, n1 ≈ 1.00, so
the slope is n2 , the index of refraction of the acrylic plastic.
2
Total Internal Reflection
Generally, when light hits the interface, there is some reflection as well as refraction. If
the light moves in the denser (higher n) medium toward the interface, then total internal
reflection may occur. This happens if the angle of incidence is greater than the critical
angle for the medium. At this angle, the angle of refraction is 90◦ . If the “outside”
medium is air, then Equation 1 gives
sin θc =
1
n
(2)
The cases of angle of incidence less than and greater than the critical angle are shown
in Figure 2.
Figure 2: Total internal reflection.
2
The apparatus setup is shown in Figure 3
Figure 3: Light refraction.
Procedure
1. Place the ray box, label side up, on a white sheet of paper on the table. Slide the
ray mask until only one white ray is showing.
2. Position the rhombus as shown in Figure 3. Do not shine the ray through the
rhombus too near the triangular tip.
3. Rotate the rhombus until the emerging ray just barely disappears. Just as it disappears, the ray separates into colors. The rhombus is correctly positioned if the red
has just disappeared.
4. On the paper, mark the surfaces of the rhombus. Mark exactly the point on the
surface where the ray is internally reflected. Also mark the entrance point of the
incident ray, and the exit point of the reflected ray. Determine the critical angle.
5. Calculate the critical angle from Equation 2 and compare it with the measured
value.
3
Focal Length of a Thin Lens
For an image produced by a thin lens,
1
1
1
=
+
f
do di
(3)
where f is the “focal length”, di is the distance from the lens to the plane of the image,
and do is the distance from the lens to the object. These distances are shown in Figure 4
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Figure 4: The setup for testing the thin lens equation.
The focal length is a fixed property of the lens; it is determined by the radii of curvature
of the surfaces, and the lens index of refraction. If the object and image distances are
different from those constrained by Equation 3, the image will be blurry.
If the object distance is very large (do ≈ ∞), then Equation 3 also predicts that the
image distance is equal to the focal length. This is a convenient way of measuring the
focal length of a positive (f > 0) lens.
Procedure
1. On the optical bench, position the lens between a light source (the object) and a
screen.
2. Move the lens to a position where an image of the object is formed on the screen.
Measure the image distance and the object distance.
3. Repeat the above procedure for a least 3 additional, different object distances. Enter
the data into a spreadsheet. Plot 1/do vs. 1/di . Use trend-line information to find
the focal length. Compare this with the nominal value.
4. Estimate the focal length of the lens by measuring the image distance for a distant
object (eg. a light at the other side of the room.) Compare this with the other
values.
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Figure 5: The various pieces of apparatus used in this experiment.
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