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Reflection from Plane Mi
or and Curved Mi
or, and Snell's Law
Part I: Snell’s Law: When a light ray passes through an interface between two materials with different indices of refraction, the light ray direction changes according to Snell's Law. The incoming light ray is termed the incident ray and the bent ray which is transmitted through the interface is called the refracted ray. The law states:
?? sin(??) = ?? sin(??)    (1)
FIGURE 1. Snell's law
LAB
9
Here, the subscript i indicates incident and r indicates refracted. We can solve for the following relation:
XXXXXXXXXXSin θi = (n
ni) Sin θr XXXXXXXXXX2)
So if we plot sin(qi) on the vertical axis and sin(qr) on the horizontal, we should get a straight line with slope equal to n
ni, the ratio of the refractive indices.
This lab is designed to have students investigate the relationship between the angle of incidence and refraction between two medium and test Snell’s law. You will measure the angle of incidence and refraction for four different cases. For each case you will follow the same procedure to record data. You will also see the phenomenon of total internal reflection.
OBJECTIVES
·    Determine the relationship between incident and refracted angles.
·    Compare simulated refraction with theoretical formula.
·    Observe phenomenon of total internal reflection.
·    Determine angle of internal reflection for glass/water interface.
·    Make images with plane mi
or and curved mi
ors.
INITIAL SETUP
Follow this link and open simulation lab:
https:
phet.colorado.edu/en/simulation
ending-light
You should see the screen shown in Figure 2.
FIGURE 2: the simulation
FIGURE 3: How to measure the angles.
PROCEDURE:
This protocol will generate data that you will be able to analyze. Do this protocol for each type of interface (the types of interface are listed in Table 1).
·    First choose the upper and lower material using the controls on the right.
·    Now, place the protractor to measure the angles as shown in Figure 1.
·    Now adjust the position of the laser to an angle of incidence.
·    Record the values of the angle of incidence and the angle of refraction in a table.
·    Repeat for angle of incidence from 0 to 90 in steps of 10 degrees.
Repeat this protocol for four interfaces:
TABLE 1: the types of interfaces
Interface
Upper material
Lower material
1
ai
wate
2
ai
glass
3
wate
glass
4
glass
wate
ANALYSIS
So there will be 4 data sets. For each data set follow the analysis steps:
·    enter all data into excel
·    create a graph of angle of incidence on horizontal axis and angle of refraction on vertical. Label all axes. Include in report.
·    Now transform the data to create two new columns containing the sine of the angles.
·    create a new plot of sin(qi) on the vertical axis and sin(qr) on the horizontal. (Note this is flipping the horizontal and vertical axis from step 2.)
·    Add a linear trend line. Include graph of transformed data with linear fit with equation in your report.
·    Record the slope of the line from step 5 to the data table and consider it as experimental value of n
ni.
·    Determine the theoretical slope or theoretical value of n
ni from the simulation page. Record it on the table.
·    Find percent e
or between theoretical and experimental value of n
ni.
Answered 1 days After Apr 24, 2024

Solution

Baljit answered on Apr 26 2024
5 Votes
Objectives
· Determine the relationship between incident and refracted angles.
· Compare simulated refraction with theoretical formula.
· Observe phenomenon of total internal reflection.
· Determine angle of internal reflection for glass/water interface.
· Make images with plane mi
or and curved mi
ors.
Materials
· Computer w/ internet access
· Simulation link (https:
phet.colorado.edu/en/simulation
ending-light)
· Excel
Theory
1. Snell’s Law:- The law states that "The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, for the light of a given color and for the given pair of media." Mathematically, Snell’s law is expressed as:
Figure 1 Snell's Law
Here
· refractive index of incident medium
· refractive index of refractive medium
· incident angle
· refractive angle
Initial Setup
Figure 2 Initial setup
Data Tables and Plots
1. When upper material is air and lower material is wate
Here =1 and ...
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