Optics Lab:
Mirrors and Lenses
Theodore Gotis
Oakton Community College
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I. Introduction and Objectives
II. Equipment Needed
Ray Box
Plane Mirror
Concave Mirror
Convex Mirror
Concave Lens
Convex Lens
Prism
Water Tray
Compass
Protractor
Ruler
III. Theory
Ray diagrams
Focal length
Radius of curvature
Law of reflection
Snell’s Law (Refraction)
Total Internal Reflection
IV. Experimental Procedure
A. Plane Mirrors
1. Use a ruler to draw a straight line on one side of a sheet of paper, then draw a
perpendicular line through the center of the first line.
2. Line up the front edge of the plane mirror with the straight line so that the
perpendicular is at the center of the mirror.
Figure 1: Plane Mirror
Ray Box
Incident Ray

Concave Mirror
Reflected Ray
Plane Mirror
Perpendicular to
the Plane Mirror
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3. Using the concave mirror from your mirror and lens kit, cover up all but one of the
rays coming from the ray box.
4. Now aim this single beam of light at an angle  between 30and 60 from the
perpendicular to the plane mirror, and trace the incident and reflected beams of light with
a pencil.
5. Using a protractor, measure the angle  between the incident ray and the perpendicular
to the plane mirror. Do the same for the reflected ray.
6. Now repeat Steps #4-6 for two more incident beams of light between 10 and 80
Data Table 1: Plane Mirror
Angle of Incident Ray
Angle of Reflected Ray
7. Write an equation on the line below describing the relationship between the angles of
the incident beam and reflected beam of light from the perpendicular to the plane mirror.
(Yes, it is as simple as you think.)
____________________=______________________
B. Spherical Mirrors (Funhouse Mirrors)
CONCAVE MIRROR
Concave spherical mirrors behave very much like the mirrors used in reflecting
(Newtonian) telescopes, they direct rays of light to a focus in front of the mirror.
Reflecting telescopes actually use parabolic mirrors to assure that all the rays are directed
to the same focus. Spherical aberration occurs when all the rays are not directed to the
same focus. Guess which type of mirror is known for spherical aberration, spherical
mirrors or parabolic mirrors?
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1. Trace the shape of a concave mirror on one side of a sheet of paper using the mirror
provided. Then line up the mirror on the curve you traced just as you did with the plane
mirror.
2. Place the lens that it is convex on one side and flat on the other at the front of the ray
box so that the rays leaving the box are parallel to one another. Then aim the rays at the
concave mirror so that all the rays converge at the same focus. (Remember that you need
to focus the rays in the center portion on the mirror because in general not every ray
running parallel to the principal axis will be reflected through the same focal point. This
is only true where the arc length of the mirror is smaller than the radius of curvature.)
Figure 2: Concave Mirror
Ray Box
Concave Mirror
Perpendicular
3. Trace all incident and reflected rays, indicating the direction of the rays using arrows.
Do all the rays intersect at the same focus (or do you see spherical aberration)?
4. Use a ruler to measure the focal length of the mirror.
5. Use a compass to determine the radius of curvature and compare your result to step #4.
6. Is there a simple mathematical relationship between the focal length of the mirror and
the radius of curvature? If so, write the relationship in the bottom row of Data Table 2.
Data Table 2: Concave Mirror
Focal Length of the Mirror
(Equation)
f (focal length) =
Radius of Curvature of the Mirror
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CONVEX MIRROR
Caution: Objects In Mirror May Be Closer Than They Appear, due to the fact that
convex mirrors create virtual images. They are called virtual images because the focus is
located behind the mirror.
1. Trace the shape of a convex mirror on one side of a sheet of paper using the mirror
provided. Then line up the mirror on the curve you traced, just as you did with the
concave mirror.
2. Make sure the rays from the ray box are parallel, then aim the rays at the convex mirror
so that all the rays converge at the same focus.
3. Trace all of the incident and reflected rays, indicating whether they are incident or
reflected using arrowheads.
4. Use a ruler to measure the focal length of the mirror.
5. Use a compass to determine the radius of curvature and compare to your measurement
of the focal length in step #4.
6. Is there a simple mathematical relationship between the focal length of the mirror and
the radius of curvature? If so, write the relationship in the bottom row of Data Table 2.
Data Table 3: Convex Mirror
Focal Length of the Mirror
(Equation)
f (focal length) =
Radius of Curvature of the Mirror
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C. Spherical Lenses
CONVEX (Converging) LENS
We have all had an experience with a converging lens in the past, whether we realized it
or not. I’m sure everyone picked up a magnifying glass on a sunny day and felt the heat
from a bright point of light focused on their hand. Some of you may have tested this
phenomenon on some unsuspecting ants in your backyard. At the time did you
understand what was going on? You could tell that the intensity of the light was being
increased, but how? That is the concept we want to understand when we finish this
section.
1. Trace the shape of a convex lens on a sheet of paper using the lens provided. Leave the
lens inside the lines you traced.
2. Make sure the rays leaving the box are parallel to one another. Then aim the rays at the
convex lens. Do the rays come to a focus on the other side of the lens? Is it the same
focus for all the rays?
Figure 3: Convex Lens
Ray Box
Convex Lens
3. Trace all the incident and refracted rays, and indicate the direction of travel with
arrowheads.
4. Using a ruler to measure the focal length of the lens.
f (focal length of the lens) =
(units?)
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CONCAVE (Diverging) LENS
1. Trace the shape of a concave lens on a sheet of paper using the lens provided. Leave
the lens in the shape you traced.
2. Make sure that the rays leaving the box are parallel to one another. Then aim the rays
at the concave lens. Do the rays come to a focus on the other side of the lens?
3. Trace all the incident and refracted rays, and indicate the direction of travel with
arrowheads. Locate and draw the location of the virtual image.
4. Use a ruler to measure the focal length of the lens.
f (focal length of the lens) =
(units?)
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D. Index of Refraction (Snell’s Law)
1. Use a ruler to draw a straight line along one end of a piece of paper. Now draw a
perpendicular line through the center of the first line.
2. Line up the front of your plastic lens tray with the straight line and trace the outline of
the rest of the tray. Fill one-third of it up with water. Now you can find out what happens
to a ray of light when it passes from one medium to another.
3. Direct a ray of light at the intersection of the two lines you just drew (see Figure 4
below).
4. Draw the incident light ray and the refracted light ray. Remove the plastic tray and
draw a line connecting the incident and refracted rays.
Figure 4: Snell’s Law
Incident Ray
1 (angle of incidence)
n1
n2
2 (angle of refraction)
Refracted Ray
5. Now you can measure the angle of incidence and angle of refraction with a protractor.
Data Table 4: Snell’s Law
n1
1
sin 1
sin (
=
)
=
n2
sin 2
sin(
)
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6. Determine the index of refraction of water using Snell’s Law (solve for n2 in the data
table above). Calculate the percent error between the theoretical value and the
experimental value.
Index of Refraction of Water (Theoretical):
.
Index of Refraction of Water (Experimental):
.
Percent Error:
Show Work Below:
%
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E. Total Internal Reflection (Prism)
Fiber optics cables form the backbone of our modern communications network and they
rely on a simple physical property: Total Internal Reflection.
1. Aim a single light ray at the prism provided in your optics kit. Notice how the direction
of the light rays change as they enter and exit the prism. Rotate the prism and notice the
changes in the path of the light rays.
2. You should notice at least two exiting light rays. When the incident light ray that enters
the prism and hits the opposite side the ray will be split. Part of the ray will be
transmitted from the glass into the air, and the other part will reflect and pass out of the
prism at the bottom. Rotate the prism and pay close attention to changes in brightness of
each of the rays. This indicates the relative intensities of the reflected and refracted rays.
Figure 5: Total Internal Reflection
Ray Box
Incident Ray
Refracted Ray
Reflected Ray
Recall that the critical angle, c, for the prism is the angle for which the refracted ray will
run parallel to the surface (see Figure 5 below). For Total Internal Reflection to occur the
refracted must make an angle of at least 90 with the normal to the prism surface. In this
case we can simplify Snell’s Law:
n1 sin 1 = n2 sin 90
n1 sin 1 = n2 1.00
1 = c in this case
n1 sin c = n2
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Figure 6: Critical Angle
Incident Ray
1=c
2 = 90
Refracted Ray
Total Internal Reflection of Light Rays
3. Determine the critical angle of the prism. Then use the critical angle to calculate the
index of refraction of the prism.
Data Table 5: Critical Angle
sin c
n1
sin (
Index of refraction of the Prism:
Index of Refraction of Plexiglas: 1.51
)
.
=
n2
=
1
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Show Work Below: