Refraction and reflection
In this session you will explore the behavior of light at the boundary
between two transparent media with different indices of refraction. A
fraction of the incident intensity will be reflected, and the rest of the light
will be transmitted. The direction of propagation of the reflected and
transmitted light is given by the laws of reflection and refraction.
Law of reflection: θi = θr
- Snell's law or law of refraction:
nisinθi = ntsinθt.
How much of the light is reflected and how much is transmitted?
The reflectance R is the ratio of the reflected
flux to the incident flux, and the transmittance
T is the ratio of the transmitted flux to the incident flux.
Energy conservation requires that R + T = 1 (if there is no absorption).
R and T depend on the indices of refraction of the two media n1
and n2, the angle of incidence θi,
and the polarization of the incident light.
We distinguish between
p-polarization and s-polarization.
Consider, for example, an air-glass interface as shown. The plane of incidence contains the normal to the boundary and the
incident ray. The electric field vector E of the incident
wave is perpendicular to the direction of propagation and can have a component in the plane of incidence,
and a component perpendicular to the plane of incidence Es.
We have E = Ep+
The reflectance R depends of the polarization and is given for p-polarization by
Rp = (tan(θi - θt)/tan(θi+ θt))2,
and for s-polarization by
Rs = (sin(θi - θt)/sin(θi+ θt))2.
If θ1 + θ2 = π/2, then tan(θ1
+ θ2) = infinite and Rp = 0. If light is reflected, it
will have s-polarization. The incident angle at which this happens
is called the Brewster angle θB. We then have
n1sinθB = n2sin((π/2) -θB) = n2cosθB.
tanθB = n2/n1.
Reflection and refraction can result in
image formation. Spherical
mirrors form images by reflection. The mirror equation tells us
where the image is formed and if it is real or virtual.
- mirror equation: 1/xo
+ 1/xi = 1/f
- magnification: M = hi/ho=
If the magnification is negative, the
image is inverted.
Things that always go together for spherical mirrors:
- real image <--> inverted image <--> xi is positive
<--> M is negative
- virtual image <--> upright image <--> xi is negative
<--> M is positive
xo and xi are positive for locations in front
of the mirror and negative for locations behind the mirror. R and f are positive for concave and negative for convex mirrors,
and f = R/2.
In this session you will explore refraction at a plane
interface and image formation by reflection from spherical surfaces.
- Glass block (square)
- White paper
- Thick cardboard backing
- Millimeter ruler
Open a Microsoft Word document to keep a log of your procedures,
results and discussions. This log will become your lab report. Address the
points highlighted in blue. Answer all questions.
Use an on-line
simulation from the University of Colorado PhET group to explore the bending of
Explore the interface!
Link to the simulation:
Click the intro tab.
Tools and objects can be dragged out of the tool box and then
The objects in the Prism Break tab can be rotated by dragging the
In the Prism Break tab, the protractor rotates and the laser translates.
All the tools work in both Ray and Wave mode, but some are easier to use
in Wave mode because the region where the tool can read is larger.
(a) Let red light move from air into water.
For incident angles θi from to zero 80o in 10 degree
steps measure the angle of refraction θt and the reflectance R.
Download this spreadsheet and enter your measured
values on sheet 1.
- Plot R versus theta. Paste your graph into
your log. Compare to the graph above.
- Discuss your result.
- Is the laser light p-polarized, s-polarized,
- What do your results suggest?
- Calculate sinθi and sinθt.
- Remember that Excel functions require the angles to be in radians.
- Into cell D2 enter =sin(A2*pi()/180) and into cell E2 enter
- Copy these formulas into the other cells of columns D and E.
- Plot sinθi versus sinθt.
- What does the plot look like?
- Use the trendline to find the slope.
Paste the graph with trendline into your log.
- What value do you obtain for the slope?
- Given Snell's law, what value do you expect
for the slope? Discuss!
(b) Design experiments to determine the index of refraction of mystery
materials A and B.
- Describe your procedure and discuss why you
decided to proceed this way. What are your results for nA
(c) Design and describe a setup that has the
refracted ray bend away from the normal?
- Paste a screen shot of your setup into your log.
(d) Click on the prism break tab. Use red light with a wavelength
of 650 nm. Try to arrange various prisms in such a way, so that the laser
beam after total internal reflections moves parallel to the incident beam but in
the opposite direction. Try to use as few pieces as possible.
- Paste a screen shot of your design into your log.
(e) Now switch to white light and experiment with various prisms to
answer the following questions.
- Are the reflection and refraction of light
color-dependent? How can you tell?
- Which shapes split the white light into different
colors the best? Did you find a set-up that demonstrates this well?
- Try to arrange a situation so that the light light
forms a rainbow. What shape did you choose?
In this experiment you will trace the path of a light ray through a block of
glass. You will determine the angle of incidence and the angle of refraction at
two air-glass boundaries and use these angles to determine the index of
refraction of crown glass.
- Place a sheet of paper onto the cardboard backing. Place the glass block
onto the paper and outline its position accurately with a sharp hard pencil. Use the protractor to draw a normal to the block close to one corner. Draw
another line through the intersection making an angle of about θair = 20o with the normal.
- Make sure the block is at its original position on the paper. Place a
pin P1 on the θair = 20o
line close to the intersection with the normal on side 1. Place a second pin
P2 at least 5 cm away on the θair = 20o
line. Both pins should be as vertical as possible. The line P1P2
defines an incident ray.
- Place your head, so that you can look into the glass block from side 2. View the image of pins P1 and P2 and line up both
images. Place a pin P3 close to the block on side 2, where your
line of sight, which lines up P1 and P2, enters the
block. P3 must be lined up with the images of both P1
and P2. (A common error is to line up P3 with the
image of only one of the pins, P1 or P2.) Now place
fourth pin P4 at least 5 cm from P3 along your line of
sight on side 2, so that all four pins appear to be placed along a straight
Remove the glass block and carefully complete the diagram on the sheet
of paper as shown in the figure below.
- Measure the angles θair and
θglass with an uncertainty of less
than 0.5o. Measure the width w of the block and the displacement
d of the ray with an uncertainty of less than 0.5 mm. Enter your
measurements into the table on sheet 2 of your spreadsheet.
- Repeat this process two more times for angles θair
of approximately 45o and 60o. Use fresh sheets of
paper. It becomes more difficult to align the pins when θair gets larger, but the precision of the measurements
- Use the results of each of your trials to determine the index of
refraction n of crown glass.
- Find the average value.
- Find the percent
difference between this average measured value and the nominal index of
refraction for crown glass, n = 1.52.
- The expected displacement of a ray passing through the glass block is
d = wsin(θair - θglass)/cos(θglass).
From the figure on the right we see that
d/L = sin(θair - θglass),
w/L = cos(θglass),
d = wsin(θair - θglass)/cos(θglass).
- Use your measured values of the width of the block w and of the angles θair and θglass
to calculate d. Compare this calculated value with your measured value of d and find the percent difference.
- Insert your table into your log.
- Report the average value of the index of
refraction of crown glass from your measurements and the percent
difference between this average value and the accepted value.
- Comment on
your three diagrams. How does the deviation d vary with θair?
- Hand in your diagrams to your instructor.
Explore image formation with spherical mirrors.
Open the simulation at
Note: If Java is blocked, add http://www.shermanlab.com to the Exception Site List in the Java Control Panel.
- You can choose the radius of curvature of the mirror R (positive or
negative), the object position xo = o, and the height of the object ho = h.
- The simulation calculates the image position xi = -i and the
height of the image hi = h'.
Note. the simulation displays the image position i with the wrong sign.
Use xi = -i.
- The simulation also draws a ray diagram.
Investigate 4 different situations and fill out the
table on sheet 3 of your spreadsheet. You choose the radius of curvature R
and the object position xo.
- Use a concave mirror to produce a real image which is bigger that
- Use a concave mirror to produce a real image which is smaller that
- Use a concave mirror to produce a virtual.
- Use a convex mirror to produce an image.
||1/x0 + 1/xi
|concave mirror, real image:
|hi| > |ho|
|concave mirror, real image:
|hi| < |ho|
|concave mirror, virtual image
- Paste the table into your log.
- Discuss your results.
- Can you think of situations where spherical
mirrors are used to produce the images explored in case 1 - 4.
Convert your log into a session report, certify with you signature that
you have actively participated, and hand it to your instructor.