Lab
Reflections of a Triangle
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The
purpose
of this experiment is to study the physical law of reflection from a plane surface by locating the virtual image of a triangular object "behind" a mirror.
Strategy
The method of ray sighting will be used to locate the image of each vertex.
Procedure
Carefully fold a clean sheet of unlined paper down its center and place a piece of mirror along the fold. On the paper, draw and shade in a large scalene triangle in such a manner that no two vertices coincide along any given perpendicular to the interface and no vertex is closer to the interface than 2 cm. Label the vertices A, B, and C.
Set a push pin or a sharpened pencil at vertex A. Take a ruler and "sight" the image of vertex A in the mirror. When the edge of the ruler is perfectly aligned with the image of A, draw a line on the paper marking this edge and label it A
_{1}
. Then move the ruler and "sight" the image of vertex A again in the mirror. Once more, mark the edge of the ruler when the image of A is perfectly aligned and label it A
_{2}
. These lines will later be used to triangulate A' (the virtual image of A). Move the push pin or sharpened pencil to vertices B and C and repeat the procedure with these vertices. Mark these sighing lines B
_{1}
, B
_{2}
, C
_{1}
, and C
_{2}
. After your have made all of your sightings, remove the mirror.
Extend the sighting lines B
_{1}
and B
_{2}
to triangulate B'. At the positions where these lines "cross" the interface, draw in two new "solid" lines back to the original vertex B. Place arrows on the solid lines to show that they are actually the incident and reflected rays from B. At each point of contact on the interface, carefully construct a normal and measure both the incident and reflected angles for B
_{1}
and then those for B
_{2}
. Place your answers in a table called Data Table I. Calculate a percentage difference for each set of angles.
Data Table I
ray
incident
angle
reflected
angle
percent
difference
B
_{1}
B
_{2}
On your paper, connect A', B', and C' to form the image of the original scalene triangle. Shade in this triangle using a different color from the original triangle. Measure the perpendicular distances from each of the original vertices and from each of the image vertices to the interface. Place your answers in a table called Data Table II. Calculate a percentage difference for each set of distances.
Data Table II
vertex
perpendicular
distance
percent
difference
A
A'
B
B'
C
C'
On your papers, calculate the area of each triangle. Remember that area = ½bh. In each case, let the side CB (or C'B') be the length of the base and measure the height as the perpendicular distance from its opposite vertex A (or A'). Place your answers in Data Table III.
Data Table III
base
height
area
triangle
(cm)
(cm)
(cm
^{2}
)
ABC
A'B'C'
Conclusions
Part I:
When you were taking your distance measurements for Data Table II, which each set of vertices (AA', BB', and CC') fell on the same perpendicular, or normal, to the mirror?
AA'
BB"
CC"
Should all three? Why or why not? Explain your decision
Based on these results, did your mirror lie exactly along the interface or was it twisted towards one vertex?
exactly along the interface
twisted towards A
twisted towards B
twisted towards C
Explain your decision.
Part II:
How does the area of the original triangle ABC compare to the area of the triangle A'B'C'?
area
_{ABC}
= area
_{A'B'C'}
area
_{ABC}
> area
_{A'B'C'}
area
_{ABC}
< area
_{A'B'C'}
Based on your areas, was the mirror perpendicular to the table or tilted slightly forward or backward?
perpendicular
tilted forward towards ABC
tilted backward towards A'B'C'
Explain your decision.
Refer to the following information for the next five questions.
(1)
The angle of incidence is measured from the ____ to the ____; while the angle of reflection is measured from the ____ to the ____.
(2)
The angle of incidence should ____ the angle of reflection.
(3)
The perpendicular distance from any object to the reflecting surface must be ____ to the perpendicular distance of its corresponding image to the reflecting surface.
(4)
All plane mirror images are ____ images because they lie behind the mirror in positions that cannot be reached by the actual rays of light.
(5)
The size of the image is ____ to the size of the object.
(1)
(2)
(3)
(4)
(5)
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