# Snells Law Experiment Evaluation Essay

In 1

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

## Certification: /2

• Include a statement that the work done in this lab and submitted in this report is yours and your partners.

Hanne Martine G. Ræstad 1.j Physics 25.03.2014 1

Snell’s Law

Verification of Snell

’s Law of Refraction

Apparatus

glass slab pins graph sheet compass ruler cork board pencil eyesight

Theory

When a light ray passes from one medium to another, its velocity changes with respect to the difference in refractive indices of the two media.

Snell’s law states that the ratio of the sine of the angle of

incidence (



to the sine of angle of refraction (



will be equal to the ratio of refractive indices of the second media to the first. (

 

)

 

The refractive index of a substance (

) is defined as the ratio of velocity of light in vacuum (

) to the velocity of light in the medium (

).

 

Procedure

The goal of the experiment itself was to find and note the refractive angles corresponding to various angles of incidence, so

that we can use these to later verify Snell’s law of refraction.

We first began with a sheet of graph paper which was to be used to record our findings. We drew a coordinate system approximately in the middle of the paper and proceeded to draw a circle of radius 10 centimetres with its centre in the point of origin using the compass. The graph paper was then placed on the cork board. The glass slab was placed so that one of the edges was in line with the x-axis of the coordinate system. Then a pin was pinned in the point of origin (shown by a small circle in the diagram). Another pin was placed on a random point of the circle which was on the positive side of the y-axis. Then we used our own eyesight to place the third and final pin, located next to the glass slab so that when seen through the glass, the pins appear to be perfectly aligned. However, what we see through the glass has already been refracted, so the pins will then indicate the refracted light ray. When the angle had been indicated on the graph sheet using a pencil and a ruler. This was repeated for seven different angles of incidence.