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 n_{1}
and n_{2}, the angle of incidence θ_{i},
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,
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 p-polarization by
R_{p} = ((tan(θ_{i }- θ_{t})/tan(θ_{i} + θ_{t}))^{2},
and for s-polarization 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 s-polarization. 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. Vary n1 and n2 and observe the changes.
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.
If the magnification is negative, the image is inverted.
Things that always go together for spherical mirrors:
x_{o} and x_{i} 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 lab you will explore refraction at a plane
interface and image formation by reflection from spherical surfaces.
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.
Exploration 1
Use an on-line
simulation from the University of Colorado PhET group to explore the bending of
light.
Link to the simulation:
https://phet.colorado.edu/en/simulation/bending-light
(b) Design experiments to determine the index of refraction of mystery materials A and B.
(c) Design and describe a setup that has the refracted ray bend away from the normal?
(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.
(e) Now switch to white light and experiment with various prisms to answer the following questions.
Exploration 2:
Explore image formation with spherical mirrors. Use this interactive simulation.
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 x_{o}.
case | R | f | x_{o} | x_{i} | 1/x_{0} + 1/x_{i} | 1/f | M | image real? |
image upright? |
---|---|---|---|---|---|---|---|---|---|
concave mirror, real image: |hi| > |ho| |
|||||||||
concave mirror, real image: |hi| < |ho| |
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concave mirror, virtual image |
|||||||||
convex mirror |
In this experiment you will trace the path of a light ray through a block of glass and measure the index of refraction of the glass. For an air-glass boundary we can set the index of refraction of air equal to one. Snell's law therefore yields for the index of refraction of the glass
n_{glass }= sinθ_{air}/sinθ_{glass}.
It is easy to measure θ_{air}, but not θ_{glass} inside the glass. But when a light ray enters square block of glass from air making a nonzero angle θ_{air} with the normal to the interface, the ray is bent towards the normal as its enters and away from the normal as it leaves the glass block. The emergent ray moves in the same direction as the incident ray, but is displaced parallel to the incident ray. The parallel displacement d depends on index of refraction n_{glass} and the width w of the block. By measuring the displacement d, we can determine n_{glass}.
Procedure:
Click to open the "optics lab" simulation.
It contains a laser, an optical breadboard and several optical components. The components can be dragged to different positions on the breadboard and the components can snap to the holes on the breadboard which have a spacing of 1 unit = 2.5 cm. The screen is 4 units wide and 2 units high and the lines on the screen are spaced by ½ unit. Clicking anywhere on the breadboard you can rotate and zoom the view.
When the simulation opens the laser beam passes through a glass block. The dimensions of the glass block are 2.8 by 2.8 by 1.4 units.
Data Analysis:
Use your measurements to determine the index of refraction n_{glass} of the glass block.
The expected displacement of a ray passing through the glass block is d. From the figure on the right we see that
d/L = sin(θ_{air }- θ_{glass}),
w/L = cos(θ_{glass}).
d = wsin(θ_{air }- θ_{glass})/cos(θ_{glass}),
and applying Snell's law and trigonometric relations
d = w sinθ_{air}[1 - cosθ_{air}/(n_{glass}^{2} - sin^{2}θ_{air})^{½}].
This equation can be solved for n_{glass}.
n_{glass}^{2} = cos^{2}θ_{air}/(1 - d/(w sinθ_{air}))^{2 }+ sin^{2}θ_{air}.
Use your spreadsheet to calculate n_{glass} for each of your 4 measurements. Paste your spreadsheet table into your log.
Convert your log into a lab report.
Name:
E-mail address:
Laboratory 7 Report
Save your Word document (your name_lab7.docx), go to Canvas, Assignments, Lab 7, and submit your document.