Download REFLECTION AND REFRACTION OF LIGHT

REFLECTION AND REFRACTION OF LIGHT
This laboratory exercise is one quantitative investigation of the reflection and refraction
of light off optical interfaces. An optical interface is a boundary between two transparent
media of different indices of refraction. Reflection makes mirrors, refraction eyeglasses
and microscopes.
Laser
Pointer
S θi1
Incident ray
n
w
Reflected ray
θr
I
θt1
Refracted ray
θi2
x
E
Quadrille
Paper
θt2
Transmitted ray
d
1. Tape a sheet of quadrille paper onto the table. Record the label of your
sample, a rectangular slab of transparent material, so later you can check
the value of its index of refraction n against the manufacturer’s. Center
this slab on the paper and tape it down. With pen or pencil mark its
position onto the quadrille paper: draw a line against each of the four sides
at their base. By positioning the laser pointer at various places in the upper
left quadrant and aiming it at the slab, you can vary the angle of incidence
θi1. Position the laser at the edge of the quadrille paper.
2. Hold an index card in the path of the laser beam, so you can see where the
laser hits. Every few centimeters between S (the mouth of the laser) and I
(the point of impact on the slab) mark with a pencil the path of the light on
the quadrille paper. [Hold the index card straight up, position it so one of
its vertical edges just clips the ray of light, then mark the quadrille paper at
the foot-corner of the index card.] Draw the best straight line through the
marks. Does light travel in a straight line in the uniform medium of still
air? Depending on the optical quality of your sample, you may or may not
be able to see the laser beam traversing it: less than perfectly transparent
materials, such as dusty air, may scatter enough light sideways to make
the beam visible. Look down through the top of the sample, see if you can
see the beam inside the slab, to ascertain if it travels in a straight line
through this material as well.
WARNING: NEVER LOOK A LASER BEAM IN THE EYE. NEVER
POINT A LASER BEAM AT ANYONE’S EYE.
PERMANENT
BLINDNESS MAY RESULT.
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3. With the help of the index card locate I, the point of incidence on the
interface, and another point several centimeters downstream of the
reflected ray (upper right quadrant). Mark these two points on the
quadrille paper and draw a straight line through them: the reflected ray.
Measure the angle of reflection θr and compare it to the angle of incidence
θi1. Hint: You can measure angles with the protractor provided, or by
reading off the relevant lengths on the quadrille paper and using
trigonometry. It would even be better to do both and compare, at least
once.
We adopt the universal convention of measuring angles of all rays with
respect to the local normals to the interfaces, the two dotted lines through I
and E.
Estimate visually the intensity of the light reflected from the slab
compared to the intensity of the incident ray: would you say it is less than
10%, about half, or more than 90%?
4. Repeat step 3 on the ray of light transmitted through the sample that exits
from point E (lower right quadrant). Compare the angle of exit θt2 to the
angle of incidence θi1. Would you say the amount of light transmitted is
less than 10%, about half, or more than 90% of the incident light? Is this
estimate consistent with the one you made in step 3? Explain.
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HOMEWORK 1. Use high-school geometry to show that θt1 = θi2.
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HOMEWORK 2. Theoretically, the angle of reflection θr always equals the angle of
incidence θi1. Theoretically, is the angle of exit θt2 always equal to the angle of
incidence? Explain.
5. By measuring w, the width of the slab, and d, the distance along the
interface between the points of incidence (I) and exit (E), deduce the angle
of refraction θt1. If your sample scatters enough light sideways to be seen
looking down into it, then you can measure the angle of refraction directly
with a protractor without measuring d.
6. Repeat the measurements of the angles of reflection and refraction at three
other values of the angle of incidence. Plot θr against θi1 and compare to
the law of reflection. Plot sin θt1 against sin θi1 and compare to Snell’s
law. From the latter plot deduce the index of refraction n of your
material and compare to the value quoted. Take the index of refraction of
air to be 1.
7. Remove the sample. Prolong the line of step 1, the record of the incident
ray. Measure x, the (perpendicular) distance between the incident and
transmitted rays, at two different places along the rays: are these two rays
parallel to each other? Have you not already checked this claim earlier?
Compare x to your answer to Homework 3.
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HOMEWORK 3. The slab is perfectly rectangular. Use high-school geometry and
Snell’s law to show that the transmitted ray keeps the direction of the incident ray, only
displaced sideways by a distance x. Calculate this displacement x in terms of the
refractive index of the sample, its width, and the angle of incidence. Is rectangularity of
the sample a condition a) necessary but not sufficient, b) sufficient but not necessary, c)
necessary and sufficient, d) neither necessary nor sufficient, of parallelism between the
incident and transmitted rays?
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HOMEWORK 4. Given the equipment available: laser pointer, rectangular sample,
protractor/ruler, index card, design your own experiment to observe total internal
reflection and to measure the angle of total internal reflection. Hint: Total internal
reflection occurs only when light goes from a denser medium (the sample) into one of
lower index (air). The difficulty is that the laser pointer cannot be inserted into the
sample.
8.
θi1 (˚)
0
Do the experiment you have concocted in Homework 4. From the result
calculate the index of refraction n and compare to the value obtained
earlier.
θr
θt2
θt1
d
3
sin θi1
sin θt1