PHYS 2426 – Engineering Physics II
Refraction and the Focal Point of Lenses
Leader: ___________________
Skeptic: ___________________
Materials
Rotating protractor and light source
Pasco Ray Optics Kit
Laptop
Flashlights as needed
Recorder: __________________________
Encourager: ________________________
Ruler
Semicircular Cylindrical lens
Paper
Introduction
In this activity we will determine the relationship between the incident and refracted light at
the boundary between air and plexiglass. The relationship we will observe is called Snell's law
after a Dutch scientist who described it in the 17th century. This law has been known for much
longer, however. Ptolemy of Alexandria actually had tabulated data in his book The Almagest in
the 2nd century AD, and the law was described by Islamic scholars in the middle ages.
Part 1 Snell’s Law
Procedure
1. Set-up
Adjust the mask on the light source so that a single ray comes out which hits the center of the
protractor. Adjust the protractor so that 0° mark faces the light source. Place the semicircular
cylindrical lens with its flat side facing the light source and so it is aligned along the axis of the
protractor and so it is concentric with the protractor.
2. Data acquisition
Align the ray box so that the light hits the center of the protractor. Starting with an incident
angle of 0°, determine where the beam exits the lens. Record the incident and refracted angles in
the data table below. Be sure to measure both angles from the normal. Determine the sine of the
incident and refracted angles and record that value in the data table as well.
3. Repeat the Procedure
Rotate the table by 10° and repeat the procedure. Make sure that the incident ray hits the center
of the protractor each time. You may have to apply a push slightly on the light source to obtain
this. Record the incident and refracted angles and their sines in the data table. Repeat the
procedure increasing the incident angle by 10 each time until reaching 80. Record your data in
the table below. Make sure that the incident and refracted angles are measured from the normal.
Data Table
Incident Angle, i
Refracted angle, r
sin(i)
sin(r)
Data Analysis and Questions
Q1) For your first data point, the incident light was normal to the plexiglass. Did the light bend
in the plexiglass?
Q2) In general if light is normal to an interface what will be its refracted angle?
Q3) Why is it important in this procedure that the piece of plexiglass was semicircular? (Hint:
Does the light bend when it exits the plexiglass?)
Q4) Does all of the light pass through the plexiglass or does some of it reflect from the
plexiglass?
Use whatever software you like to make a correctly labeled graph of the incident angle vs. the
refracted angle. Add a regression line. Print and attach your graph.
Q5) Do your data appear to lie on a straight line? Hint: it probably will for the smaller angles,
but does anything happen at the larger angles?
Plot a properly labeled graph of the sine of the incident angle vs. the sine of the refracted angle.
Add a regression line. Print and attach your graph.
Q6) Do these data appear to lie on a straight line? In particular for the larger angles is it a better
fit than the previous graph?
The result you have observed is called Snell's law. It describes the relationship between incident
and refracted angle and is given by ni sini = nr sin r where n is the index of refraction of the
light in that medium. The index of refraction gives the speed of light in that medium as v = c/n,
where c is the speed of light in vacuum c = 3.0 x 108 m/s.
Q7) Given the definition of the index of refraction in the previous sentence, what are the units of
the index of refraction?
Q8) Is the angle larger in the air or in the plexiglass?
Q9) Assuming that the value of the index of refraction in air is 1.0, use the slope of your second
graph to determine the index of refraction of the plexiglass. Show your work and record your
result in the space below.
Q10) Determine the speed of light in the plexiglass that we used. Record your result.
5. Reverse the orientation of the lens
Keep the lens aligned along the axis of the protractor but rotate the table a half turn so that the
semicircular side faces the light source. Make sure that the incident ray hits the center of the
protractor each time. You may have to apply a push slightly on the light source to obtain this.
Record the incident and refracted angles in the data table. Repeat the procedure increasing the
incident angle by 10 each time until reaching 60. If you note anything that strikes you as odd,
you might refer to Q13) below. Record your data in the table on the next page. Make sure that
the incident and refracted angles are measured from the normal. Do not record data if you do not
observe a refracted ray.
Data Table
Incident Angle, i
Refracted angle, r
Q11) In this case the light came from the plexiglass and went into the air. Which was bigger,
the angle in the lens or in the air.
Q12) Compare your answer for Q11) to Q8). What do these answers suggest?
Q13) Did anything odd happen at an incident angle around 40° to 50°? Describe it.
You should have observed that once you reached an incident angle of around 45° that the light
only reflected and did not refract. This behavior is known as total internal reflection. There is
an angle called the critical angle where the behavior changes from having refracted light to
having no refracted light.
Q14) In general, what is the largest possible refracted angle?
Q15) Use Snell’s law to find the incident angle that gives the refracted angle you answered in
Q14. Use 1.0 for the index of refraction of air and the value that you determined previously for
the index of refraction of the plexiglass.
Q16) Experimentally determine the critical angle. Compare it to the value you predicted in Q15.
Part 2 Refraction by Lenses
Procedure and Questions
Adjust the mask in front of the light source so that you obtain four or five parallel rays. Remove
the semicircular cylindrical lens and place the white piece of paper on top of the optical table.
Place the biconvex lens in front of the rays on top of the white sheet of paper. Trace the incident
and refracted rays on the paper using a straight edge.
Q17) Sketch how the rays look.
Q18) Do the rays seem to come to a focus? If so determine the focal length.
Reverse the orientation of the lens.
Q19) Do the rays behave the same regardless of orientation of the lens?
Q20) Measure the focal length of the lens in this orientation. Is it the same as before?
Replace the biconvex lens with the biconcave lens.
Q21) How do the rays passing through the biconcave lens compare to those passing through the
biconvex lens?
Q22) Fill in the following blanks with either diverging or converging. A concave lens produced
_________________ rays, and thus a concave lens is also known as a ____________________
lens. A convex lens produced _________________ rays, and thus a convex lens is also known as
a ____________________ lens.
For the biconcave lens, use a straight edge totrace the incident and refracted rays on the white
piece of paper. Backtrack the rays passing through the biconcave lens.
Q23) Do the backtracked rays appear to come together at a point?
Q24) Determine the focal length of the biconcave lens.
Reverse the orientation of the lens.
Q25) Do the rays behave the same regardless of orientation of the lens?
Q26) Measure the focal length of the lens in this orientation. Is it the same as before?
You should have noticed that a lens has the same focusing properties if it is reversed. We
describe this property of lenses by saying that they have two focal points - one in front of the
lens and one behind.
Q27) Sketch a diagram of a converging lens and indicate its front and back focal points.
Q28) Sketch a diagram of a diverging lens and indicate its front and back focal points.
Q29) Notice that a concave lens, like a convex mirror, diverges parallel rays incident on it.
What is the sign of the focal length of a convex mirror?
Q30) By analogy what should be the sign of the focal length of a concave lens?
Part 3 Computer Exercises
Exercise 1
Open a browser and navigate to Problem 35.4 from the Physlet Physics 2e text.
(www.compadre.org/physlets)
The yellow box in the lower left gives the coordinates of the cursor in arbitrary units and the red
box for the point light source can be dragged around to various positions.
Q31) Determine a procedure for determining the focal length of the lens. Once your group has
decided on a procedure discuss it with your instructor. Record your final procedure in the space
below.
Q32) Record the value you have determined for the focal length of the lens.
Exercise 2
Proceed to Exercise 35.1 from Physlet Physics 2e.
Q33) Describe what each type of lens is behind the pink curtain. Explain your reasoning.
Object A.
Object B.
Object C.
Object D.
Q34) Rank the focal lengths of the lenses from the most negative to the most positive.
Most Negative1. ____ 2. ____ 3. ____ 4. ____ Most positive.
Q34) Carefully explain the reasoning behind your ranking.