Law of reflection: θ_{i} = θ_{r}  
Snell's law or law of refraction: n_{i}sinθ_{i }= n_{t}sinθ_{t}. 
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 n_{1} and n_{2}, the angle of incidence θ_{i}, and the polarization of the incident light. We distinguish between ppolarization and spolarization.
Consider, for example, an airglass 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, E_{p},
and a component perpendicular to the plane of incidence E_{s}.
We have E = E_{p}+ E_{s}.
The reflectance R depends of the polarization and is given for ppolarization by R_{p} = (tan(θ_{i } θ_{t})/tan(θ_{i }+ θ_{t}))^{2}, and for spolarization by R_{s} = (sin(θ_{i } θ_{t})/sin(θ_{i }+ θ_{t}))^{2}.

If
θ_{1 }+ θ_{2}
= π/2, then tan(θ_{1
}+ θ_{2}) = infinite and_{ }R_{p} = 0. If light is reflected, it
will have spolarization. The incident angle at which this happens
is called the Brewster angle θ_{B}.
We then have
n_{1}sinθ_{B }= n_{2}sin((π/2)  θ_{B}) = n_{2}cosθ_{B}. tanθ_{B} = n_{2}/n_{1}. Explore using this spreadsheet! 
Open a Microsoft Word document to keep a log of your procedures and results. This log will become your lab report. Address the points highlighted in blue. Answer all questions.
Exploration:
Use an online
simulation from the University of Colorado PhET group to explore the bending of
light.
Link to the simulation:
http://phet.colorado.edu/en/simulation/bendinglight
Click "Run Now!" or "Download".
Tools and objects can be dragged out of the tool box and then returned.  
The objects in the Prism Break tab can be rotated by dragging the handle.  
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. 
Plot R versus theta. Paste your graph into your log. Compare to the graph above.  
Discuss your result.
 
Calculate sinθ_{i} and sinθ_{t}.
 
Plot sinθ_{i} versus sinθ_{t}.

(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 n_{A} and n_{B}? 
(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 colordependent? How can you tell?  
Which shapes split the white light into different colors the best? Did you find a setup that demonstrates this well?  
Try to arrange a situation so that the light light forms a rainbow. What shape did you choose? 
Experiment:
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 airglass boundaries and use these angles to determine the index of refraction of crown glass.
For an airglass boundary we can set the index of refraction of air equal to one. Measuring the angles a light ray make with the normal to the interface both in the air and in the glass, we can solve Snell's law for the index of refraction of the glass.
n_{glass }= sinθ_{air}/sinθ_{glass}
Millimeter ruler  
Protractor 
Procedure:
The images below show a laser beam passing through a square block of glass. The angle of incidence is different in each of the images. Click on each thumbnails to obtain a larger image and print out that larger image. 
For each larger image carefully complete the diagram as shown in the figure below. 
Measure the angles θ_{air} and θ_{glass}
with an uncertainty of less than 1^{o}. Use a protractor, or
count squares and use trigonometric relations. Measure the width w of
the block and the displacement d of the ray with an uncertainty of less than
1 mm. The sides of each small square on the paper in the images are 2
mm long, the sides of each bigger square are 1 cm long. Scale your
measured w and d appropriately (or count squares) and enter your
measurements into the table on sheet 2 of your spreadsheet. Table 
image#  θ_{air}  θ_{glass}  n_{measured}  w  d_{measured}  d_{calc}  difference in d's (%) 
Data Analysis:
Use the results you obtained from each of the images 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(θ_{air } θ_{glass})/cos(θ_{glass}).
 
Use your measured values of the width of the block w and of the angles θ_{air} and θ_{glass} to calculate d. Compare this calculated value with your measured value of d and find the percent difference.  
Paste your table into your log.  
Report your average value of the index of refraction of crown glass and the percent difference between this average value and the accepted value.  
Comment on your three diagrams. How does the deviation d vary with θ_{air}? 
Add your name and email address to your log that contains your graphs, comments and
answers.
Save your Word document (your name_lab10.docx), go to Blackboard, Assignments,
Lab 10, and attach your document.