# Refraction And Reflection Lab Conclusion Essay

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OBJECTIVE

The objective of this experiment is to study refraction and reflection and also to use Snell's law correctly to determine the optical properties and indices of refraction for a prism.

DATA

All data is included in an excel spreadsheet, attached to this write-up.

Some uncertainties that see probable in the case of general human error are the basic visualization of the location of the pin, the measuring of the angles with a protractor, the possibly imprecise way to draw the reflected and incident rays and a general error in calculation. It is also possible that some uncertainties were caused by equipment imperfections, such as the mirrors being warped or the pins being bent. Also, some protractors were more precise and easily read, while others were not.

RESULTS

µ=&#8721;(x) , where µ= mean in cm (also referred to as ), &#8721;= summation, x= the actual numbers obtained in the data set recorded in ohms, n= the number of data points.

Ex: (1.391+1.766+1.431+1.643+1.530+1.209+1.447+1.486)/8 = 1.488

n1sin&#952;1=n2sin&#952;2, where n1= the indices of refraction of air (denoted as 1), &#952;1= the angle from the parallel that corresponds to n1, n1= the indices of refraction of the prism, &#952;2= the angle from the parallel that corresponds to n2.

Ex: 1Sin34=n2Sin23

n2=1.431

There are no graphs associated with this experiment, however there are pictures where the angles measured and that rays determined are drawn in a labeled. These pictures are attached to this write-up.

DISCUSSION

We are first observing the reflection of a pin from a flat mirror. Reflection is defined as the rebounding of a particle or wave due to encountering a barrier or a change in the medium. An original pin was placed at a chosen distance in front of a flat mirror. While looking into the mirror from various chosen angles, additional pins were then placed in the path of the reflected ray and the angle from the perpendicular was measured. Since we know that the law of reflection applies we can then determine the position of the incident ray. If the original pin is in the path of the determined incident ray, then we can assume that the pin was places accurately in the path of the reflected ray.

When you place a real object in the position of the virtual image and they look like they are in the same position, regardless of the direction they are viewed from, you have just determined the location by parallax. This property stated that there is no obviously motion of the two objects, regardless of the direction they are viewed from, only if the two objects are at the same location. To determine if the locations of the two objects were equal, the distance from the original pin to the mirror surface and the real object to the mirror surface is measured. If the locations of the two objects are the same these measured distances would be equal.

We are secondly observing the general properties and characteristics of refraction. Refraction is defined as the change in speed of a wave due to being in a different medium. Pins were placed in a linear fashion along a chosen side of a square prism at a designated angle from the perpendicular. While viewing the virtual image through the opposite side of the square prism, more pins were placed in line with the virtual image, giving the illusion that there was only a single pin being viewed. To show the angle of refraction, the sites where both lines meet the sides of the prism were connected. All angles were measured from the perpendicular. Using Snell's Law and the measured angles, the desired index of refraction (n) can be determined. The index of refraction for air is set to 1 and is denoted as the variable n1.The index of refraction for the medium, n2, was found for both sides of the square prism. Since the square prism is a consistent medium, the indices of refraction for both sides should be equal. The process was repeated four times and the indices of refraction were compared. A total variation of .232 was found for the square prism, when considering all measured and calculated values. This number is larger then desired possibly due to a considerable amount of unknown sourced of error.

A triangle prism is then used instead of the square prism and the same procedure is taken. A total variation of .557 was found for the triangle prism, when considering all measured and calculated values. This number is much larger then desired; this number is also possibly due to a considerable amount of unknown sourced of error.

Some specific sources of error that seem to be apparent in our data observed and calculated are the imprecision of basic protractors that were used. Although this would not make a massive margin of error, it could change the margin of error by a few tenths, which is approximately what the values seem to be off by overall. Although it was not observed that the mirror that was bent or warped, the original mirror used was cracked and had to be replaced. If one was to overlook even a minuscule fracture in the

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When light crosses from one material to another, its straight line path will bend by an amount determined by the speed of light in both materials. This “bending” of light is called refraction. The interface between two materials also causes reflection of light. See Figure 1. The law of reflection states that the incident angle θi is equal to the reflected angle θr :

$$\theta_r = \theta_i$$ (1)

The law of refraction, referred to as Snell’s Law, states the following relationship between the incident angle θi and the refracted (transmitted) angle θt:

$$n_i sin\theta_i = n_t sin\theta_t$$ (2)

The parameter n represents the index of refraction, defined as the ratio of speed of light in a vacuum, c, to the speed of light in the material, v.

$$n = \frac{c}{v}$$ (3)

For example, the index of refraction for air is 1.00, for pure water 1.33 and for crown glass it is 1.52.

## Procedure:

### A. Law of Reflection

Pointing a laser purposely at anybody’s face is considered a serious offense and could result in a failing score on this lab!!!

1. Take a sheet of 8.5 × 11 inch paper and draw a set of perpendicular lines in the middle of it.

2. Support the mirror with at least one wooden slotted block (Figure 2) and place along the 8.5 long inch line, as illustrated in Figure 3. Be sure not to move the mirror during this part of the experiment or you will have to begin again.

3. Draw a single large dot approximately 5 inches in front of the mirror.

4. Shine the laser through the dot, towards the mirror.

5. Make a mark where the laser reflects off of the mirror and another somewhere along the exiting beam.

6. Connect the points to draw the path followed by the light in the reflection process. Draw both the incident and reflected beams. This will look like a large “V”.

7. Do this three more times, pointing the laser at different angles, but still passing through the single dot.

8. Select one of the light paths, measure the incident and reflected angle and find the difference.

9. Extend the reflected beams backwards, on the other side of the mirror. The point of intersection is the position of the image. (This is what your brain does when forming an image. It always asks “where did this light come from?” and when it sees all the beams that bounce off the mirror, it “back traces them”. This makes it appear the light came from a point behind the mirror.)

10. Find the percent difference between the distances of the object and image. Remember, object distance (p) is measure from the object to the incident surface and the image distance (q) is measured from the incident surface to the image.

Concept Checkpoint 1:

1. On your drawing, identify the angle of incidence and the angle of reflection, the object, and the image.

2. How should the angles compare?

3. Is the image real or virtual?

4. How can you tell?

5. Call over a TA or instructor and explain your conclusion to them.

### B. Snell's Law

1. Draw a set of perpendicular lines on an 8.5 × 11 inch sheet of paper.

2. Draw five lines on the paper, representing incident rays with angles 10°, 25°, 40°, 50° and 60° so that they all meet at the intersection of the perpendicular lines (Figure 6).

3. Fill the plastic semi-disk container with water and place it so that the flat side is centered along the 8.5 inch line.

4. Direct the laser beam toward the flat side of the semi-cylinder along the 10° line.

5. Mark the point where the light exits the semi-cylinder on the curved side.

1. (There are three rays that appear to be exiting the water. The ray that is directly opposite the incident ray without bending is the beam that is going over the water; you ignore that one. The shortest ray (you might not see it) is the beam going only through the plastic holder; you ignore this beam also. You want the middle length beam; it is the one that went through the water.)

6. Repeat this process for each incident angle. You will have five dots on the curved side of the semi-cylinder so make sure you mark the corresponding incident angle for each one.

7. Remove the container and draw lines through these points and the center of the paper (where the perpendicular lines intersect). These are the refracted light beams.

8. Measure the angles of refraction (θt) and complete a table of the data in your journal.

9. Using the Graphical Analysis software plot a graph of sin(θi) on the y-axis versus sin(θt) on the x-axis.

1. Enter your values for θt in the X column and double-click on the top of the column to change the name to theta t.

2. Enter your values for θi in the Y column and double-click on the top of the column to change the name to theta i.

10. Add a New Calculated Column name the column sin(theta t).

1. In Equation box enter:

sin( (“theta t”)*(pi/180) )

2. Where “theta t” is selected from your drop down variable box.

11. Add a New Calculated Column name the column sin(theta i).

1. In Equation box enter:

sin( (“theta i”)*(pi/180) )

2. Where “theta i” is selected from your drop down variable box.

12. Click on the y-axis and select sin(theta i) from the list.

13. Click on the x-axis and select sin(theta t) from the list.

14. Find the slope of the line.

15. Find the percent difference between the slope and the accepted value of the index of refraction of water nwater = 1.33.

Concept Checkpoint 2:

1. On your drawing, identify the angles of incidence and the angles of refraction.

2. Where do you measure them from? (What is the base of the angle?)

3. What would happen to the relative size of the angles of refraction if instead of being a dish of water in air, we had a dish of air underwater.

4. Call over a TA or instructor and explain your conclusion to them.

### C. Apparent Depth

1. Draw a set of perpendicular lines on an 8.5 × 11 inch sheet of paper.

2. Place the rectangular plastic plate so that the clear face is centered along the 8.5 inch line.

3. Draw a single dot where the edge of the glass and the center line meet.

4. Direct the laser beam at an angle toward the dot on the edge of the glass plate (see Figure 4). Be sure your laser is backed well away from the glass so the exiting beam will be long.

5. Mark the point at which the laser beam leaves the glass and mark a second point as far along the exiting beam as you can.

1. NOTE: make sure that it is the beam traveling through the glass, not over. To do this put your hand over the top of the glass, to block any stray light.

6. Repeat this for a different angle on the same side of the 11 inch line and twice more on the other side of the line. Be sure each time you shine the laser through the dot.

7. Trace the outline of the glass plate and measure the width, p, of the plate.

8. Connect the points from the exiting beam and extend them back into the area where the glass was.

9. Mark the point where the lines converge and measure the distance q.

10. Calculate the index of refraction of the glass from the equation:

$$\frac{n_1}{p} = \frac{n_2}{q}$$

where n2 is the index of refraction for air.

11. Record this index of refraction and compare to crown glass which has n=1.52. Is this more or less optically dense?

Concept Checkpoint 3:

1. On your drawing, identify an angle of incidence and an angle of refraction (you will have several to chose from), the object, and the image. Keep in mind, there are two places where the ray changes from one media to the other. Which one do we actually care about for forming the image?

2. How should the angles compare?

3. Is the image real or virtual?

4. How can you tell?

5. Call over a TA or instructor and explain your conclusion to them.

### D. Total Internal Reflection

1. Using the same setup from part B, turn the plastic semi-disk so that the curved side is facing the laser.

1. Note: You may use a similarly shaped piece of glass instead of the water, this might be easier. Just ask your lab instructor if this is an option.

2. Place the container so that the 11 inch line is passing through the center and the flat side is along the 8.5 inch line.

3. Aim the laser beam at the center of the container so that it exits on the 8.5 inch line. Point the laser at different angles until the beam reaches the critical angle and is completely reflected inside the container.

4. Mark the points where the beam is entering and exiting the container and connect each point with the center point of the disk, this shows the path of the beam.

5. Measure the critical angle, θc, and calculate the index of refraction for water.

6. Compare the value calculated with the accepted value of nwater = 1.33 by finding the percent difference.

Concept Checkpoint 4:

1. On your drawing, back your laser up a bit until you can again see some light refracting through.

2. Identify the angle of incidence, the angle of refraction, and the angle of reflection.

3. What do you notice about the strength of the various beams as you change the angle of incidence?

4. Call over a TA or instructor and explain your conclusion to them.

## Layout: /2

• Title:

• Names: (Indicate who the scribe was. Alternate duties for each lab.)

• Date

• Time In & Out:

## Preliminaries: /4

• Personalized Statement of Objectives:

• Methods Used: (Insert a labeled webcam image of apparatus. Describe what and how measurements are made.)

• Predictions:

## Data: /8 and Results: /6

### A. Law of Reflection

1. Describe your data collection techniques for verifying the law of reflection.

2. Insert a labeled webcam image of your experiment below including the lines you have drawn.

3. For one beam, record the angles of incidence and reflection:

1. θinc =

2. θrefl =

3. % Diff =

4. Record the object and image distances below:

1. dobject =

2. dimage =

3. %Diff =

### B. Snell’s Law

1. Describe your procedure for verifying Snell’s Law and measuring the index of refraction of water.

2. Insert a labeled image of your experiment including any ray traces.

3. Record incident and refracted angles below in Table 1.

Table 1: (Title this Table).

Angle of Incidence (θi) Angle of Refraction (θt)
10°
25°
40°
50°
60°
1. Insert a graph of sin(θinc) vs. sin(θrefl) below including a linear fit.

2. Record the slope of your fit:

1. m =

3. Discuss the relationship between the slope of this graph and the index of refraction of water.

4. Compare the slope of your graph with the standard value of 1.33:

1. % Diff =

### C. Apparent Depth

1. Describe your procedure for measuring the index of refraction of glass.

2. Insert a labeled webcam image of your experiment below including any ray traces.

3. Record the actual depth of the glass plate:

1. p =

4. Record the apparent depth of the image:

1. q =

5. Use the actual and apparent depths to calculate the index of refraction:

1. nglass = |p/q| =

6. Compare with the standard value for crown glass of 1.52:

Is this more or less optically dense?

### D. Total Internal Reflection:

1. Describe your procedure for measuring the critical angle below.

2. Insert an image of your experiment including ray traces of the beam.

3. Record the critical angle:

1. θcritical =

4. Use the critical angle and snell's law to compute the index of refraction of water,

1. nwater = $\frac {1}{\sin \theta_c}$ =

5. Compute the percent error with the standard value of 1.33:

1. % Diff =

## Conclusion: /4

In this section you can include general statements saying:

• Whether your measurements confirm the stated objectives.

• What fundamental physical laws were illustrated by the experiment

• How the experimental error could have been reduced in the experiment.

Also include a constructive critique of the lab, stating what went well, what didn’t, and how the laboratory could be improved.

## Abstract: /4

This is a formal statement of what this laboratory experiment was all about.

Included in this paragraph should be something about:

• The Objectives