Physics lab 6

- 1 -

Augusta Technical College

PHYS 1110L - Online Lab 6: Reflection and Refraction

Objectives:

The purpose of this experiment is to use simulation software to investigate and verify the law of

reflection and Snell’s law of refraction, including total internal reflection.

Equipment:

• Computer

• Scientific Calculator

• PhET Bending Light Simulation Software

Theory:

• The law of reflection states that the angle of incidence  i that the incident ray makes with the

normal to the surface is equal to the angle of reflection  r that the reflected ray makes with the

normal to the surface (Equation 1, Figure 1):

ri  = (1)

Figure 1: Law of Reflection – the angle of the incident ray (with respect to the surface normal)

is equal to the angle of the reflected ray.

- 2 -

Figure 2: The image of a real object formed by a plane mirror.

• The image of a real object formed by a plane mirror has the following properties:

1. It is upright

2. It is virtual and behind the mirror

3. Has the same size as the object: hi = ho

4. Is located as far behind the mirror as the object is in front of it: di = do

• The index of refraction n of a material is defined as the ratio of the speed of light in vacuum c

to the speed of light in the material v (Equation 2):

v

c n = (2)

• Snell’s law of refraction states that when light travels from material with refractive index n1

into material with refractive index n2, then the angle of incidence 1 that the incident ray makes

with the normal to the surface is related to the angle of refraction 2 that the refracted ray makes

with the normal to the surface by (Equation 3 and Figure 3):

2211 sinsin  nn = (3)

Figure 3: Snell’s Law sketch where the refractive index n1 < n2.

- 3 -

• Total Internal Reflection: When an incident ray of light passes from a material with a higher

refractive index (e.g., water) into a material with a lower index of refraction (e.g., air), the

refracted ray bends away from the normal to the interface (Figure 4). If the incident ray angle is

increased relative to the interface normal, the refracted ray bends more away from the normal,

until a “Critical Angle” is reached where the refracted ray bends to the point that is travels

horizontally along the interface between the two materials. At this point the refracted ray angle

is 90 degrees. Any further increase in the incident angle results in “Total Internal Reflection”

and the interface between the materials performs as if it was a mirror. Total internal reflection

is an important phenomenon as it is the principle by which fiber-optics functions!

Using Snell’s Law of refraction with the refracted angle θ =  degrees yields the “Critical

Angle” (θ c) for Total Internal Reflection (Equation 4 and Figure 4):

sin 𝜃𝑐 = 𝑛2/𝑛1

Figure 4: Total Internal Reflection – Schematic of an increasing incident ray angle (green, red,

blue) leading to refraction (green), “Critical Angle” (red with refracted angle = 90 degrees),

and Total Internal Reflection (blue).

Part A – The Law of Reflection:

• In this part of the experiment, we will verify the Law of Reflection by using simulation software

to create a virtual light ray and use a protractor to measure the incident and reflected ray.

• Open PhET Bending Light Simulation Software:

➢ https://phet.colorado.edu/en/simulation/bending-light

➢ Open the first tab “Intro”.

➢ Select option “Ray” (top left), and check “Normal” (bottom left).

➢ Arrange the window according to Figure 5, where the refractive index of the upper region

is set to 1.60, the refractive index of the lower region is set to 1.00, and the light ray is

activated by clicking on the “Red” button.

➢ Drag the protractor and position it at the point of reflection as shown in Figure 5.

- 4 -

Figure 5: Arrangement of the “Intro” page for the Law of Reflection experiment.

• Set the angle of the incident ray (θi) to 50.0 degrees from the vertical by rotating the laser, then

inspect the protractor and record the reflected ray angle (θr) with respect to the vertical in the

Data Table for Part A.

• Perform the same observation for incident ray angles (θi) 60.0, 70.0, and 80.0 degrees and record

the reflected ray angle (θr) in the Data Table for Part A.

• Save a screenshot (screen capture) of the simulation for one trial showing the incident and

reflected rays and their corresponding angles to include in the graphs section of your report.

Part B – Refraction: Low to High Refractive Index:

• In this part of the experiment, we will investigate Snell’s Law (Equation 3) for the case where a

ray of light travelling from a lower to a higher index of refraction material. Simulation software

will be used to create a virtual light ray, a protractor used to measure the incident and refracted

ray, and Snell’s Law used to calculate and compare to the simulation refracted-angle.

• Open PhET Bending Light Simulation Software:

➢ https://phet.colorado.edu/en/simulation/bending-light

➢ Open the first tab “Intro”.

➢ Select option “Ray” (top left), and check “Normal” (bottom left).

➢ Arrange the window according to Figure 6, where the refractive index of the upper region

is set to n1 = 1.00 (air), the refractive index of the lower region is set to n2 = 1.50 (glass),

the protractor is positioned at the point of reflection, and the light ray is activated by

clicking on the “Red” button.

Activate the light ray by clicking on the red button

Move the protractor to this position

Set the index of refraction to 1.60

Set the index of refraction to 1.00

- 5 -

Figure 6: Arrangement of the “Intro” page for the Refraction experiment where a ray of light

passes from lower refractive index material (air) into higher refractive index material (glass).

• Set the angle of the incident ray (θ1) to 20.0 degrees from the vertical by rotating the laser, then

inspect the protractor and record the refracted ray angle (θ2) with respect to the vertical in the

Data Table for Part B.

• Perform the same observation for incident ray angles (θ1) 40.0, 60.0, and 80.0 degrees and record

the reflected ray angle (θ2) in the Data Table for Part B.

• Using Snell’s Law, calculate the refracted angles (θ2) for the incident angles (θ1) 20.0, 40.0,

60.0, and 80.0 degrees and record the refracted angle values in the Data Table for Part B:

𝒏𝟏 𝒔𝒊𝒏 𝜽𝟏 = 𝒏𝟐 𝒔𝒊𝒏 𝜽𝟐 → 𝜽𝟐 = 𝒔𝒊𝒏−𝟏(𝒏𝟏 𝒔𝒊𝒏 𝜽𝟏 /𝒏𝟐)

• Show your detailed Snell’s Law calculations in the calculations section of your lab report.

• Save a screenshot (screen capture) of the simulation for one trial showing the incident and

refracted rays and their corresponding angles to include in the graphs section of your report.

Part C – Refraction: High to Low Refractive Index:

• In this part of the experiment, we will investigate Snell’s Law for the case where a ray of light

travelling from a higher to a lower index of refraction material. Simulation software will be

used to create a virtual light ray, a protractor used to measure the incident and refracted ray, and

Snell’s Law used to calculate and compare to the simulation refracted-angle.

• Open PhET Bending Light Simulation Software:

➢ https://phet.colorado.edu/en/simulation/bending-light

- 6 -

➢ Open the first tab “Intro”.

➢ Select option “Ray” (top left), and check “Normal” (bottom left).

➢ Arrange the window according to Figure 7, where the refractive index of the upper region

is set to n1 = 1.33 (water), the refractive index of the lower region is set to n2 = 1.00 (air),

the protractor is positioned at the point of reflection, and the light ray is activated by

clicking on the “Red” button.

Figure 7: Arrangement of the “Intro” page for the Refraction experiment where a ray of light

passes from higher refractive index material (water) into lower refractive index material (air).

• Set the angle of the incident ray (θ1) to 10.0 degrees from the vertical by rotating the laser, then

inspect the protractor and record the refracted ray angle (θ2) with respect to the vertical in the

Data Table for Part C.

• Perform the same observation for incident ray angles (θ1) 20.0, 30.0, and 40.0 degrees and record

the reflected ray angle (θ2) in the Data Table for Part C.

• Using Snell’s Law, calculate the refracted angles (θ2) for the incident angles (θ1) 10.0, 20.0,

30.0, and 40.0 degrees and record the refracted angle values in the Data Table for Part C:

𝒏𝟏 𝒔𝒊𝒏 𝜽𝟏 = 𝒏𝟐 𝒔𝒊𝒏 𝜽𝟐 → 𝜽𝟐 = 𝒔𝒊𝒏−𝟏(𝒏𝟏 𝒔𝒊𝒏 𝜽𝟏 /𝒏𝟐)

• Show your detailed Snell’s Law calculations in the calculations section of your lab report.

• Save a screenshot (screen capture) of the simulation for one trial showing the incident and

refracted rays and their corresponding angles to include in the graphs section of your report.

- 7 -

Part D – Refraction: Total Internal Reflection:

• In this part of the experiment, we will investigate Snell’s Law for the case where a ray of light

travelling from a higher to a lower index of refraction material exceeds the “Critical Angle”

resulting in “Total Internal Reflection”. Simulation software will be used to create a virtual light

ray, a protractor used to measure the incident and refracted ray, and Snell’s Law used to calculate

and compare to the simulation refracted-angle.

• Open PhET Bending Light Simulation Software:

➢ https://phet.colorado.edu/en/simulation/bending-light

➢ Open the first tab “Intro”.

➢ Select option “Ray” (top left), and check “Normal” (bottom left).

➢ Arrange the window again in the same configuration according to Figure 7, where the

refractive index of the upper region is set to n1 = 1.33 (water), the refractive index of the

lower region is set to n2 = 1.00 (air), the protractor is positioned at the point of reflection,

and the light ray is activated by clicking on the “Red” button.

Figure 8: Arrangement where the incident ray is nearly at the “Critical Angle” (θc) for Total

Internal Reflection and the refracted ray is nearly at the horizontal (at the water/air interface).

• Set the angle of the incident ray to 40.0 degrees from the vertical by rotating the laser, then

slowly increase the incident angle until the refracted ray is just at the horizontal (at the interface

between the air and water). See above Figure 8. Any increase in the incident angle leads to Total

Internal Reflection. Record this “Critical” incident angle (θc) in the Data Table for Part D.

• Using “Critical Angle for Total Internal Reflection” equation, calculate Critical Angle (θc) for

the air-water combination. Record the calculated “Critical Angle” values in the Data Table for

Part D:

𝒔𝒊𝒏 𝜽𝑪 = 𝒏𝟐/𝒏𝟏 → 𝜽𝑪 = 𝒔𝒊𝒏−𝟏(𝒏𝟐/𝒏𝟏)

• Show your detailed Critical Angle calculations in the calculations section of your lab report.

The refracted ray is nearly horizontal (along the water/air interface.)

The incident ray is nearly at the “Critical Angle” for Total Internal Reflection.

- 8 -

• Perform the same observations and calculations to find the “Critical Angle” (θc) for total internal

reflection for the following value of Index of Refraction (n):

o Upper n1 = 1.05 & Lower n2 = 1.00

o Upper n1 = 1.10 & Lower n2 = 1.00

o Upper n1 = 1.20 & Lower n2 = 1.00

o Upper n1 = 1.33 & Lower n2 = 1.00

o Upper n1 = 1.40 & Lower n2 = 1.00

o Upper n1 = 1.60 & Lower n2 = 1.00

• Record the observed and calculated values of the “Critical Angle” (θc) in the Data Table for

Part D. Remember to show all your detailed Critical Angle calculations in your lab report.

• Save a screenshot (screen capture) of the simulation for one trial showing the incident, reflected,

and refracted rays and the critical angle to include in the graphs section of your report.

Analysis:

• Part A – The Law of Reflection:

1. Compare the incident angles (accepted) and the observed (experimental) reflected angles

by calculating the % error. Record values in the below table.

Percentage error is used to compare experimental (observed) to accepted (true) values:

% Error = %100 || 

−

A

EA ; Where: A = accepted value and E = experimental value.

2. Is there a difference between the incident and reflected angles? Discuss in your lab report.

3. Consider that instead of the light ray reflecting from a smooth and flat surface, that a broken

mirror – consisting of many small fragments of mirror glass at different angles – is used

for the reflecting surface. Does the Law of Reflection still work?

• Part B – Refraction: Low to High Refractive Index:

1. Compare the observed and calculated refracted ray angles by calculating the % error.

Record values in the below table.

2. Is there a difference between the observed and calculated refracted ray angles? Discuss in

your lab report.

3. What would happen if the incident ray angle remained constant and the refractive index of

the lower “higher refractive index” material was decreased to 1.20 – does the Refracted ray

angle increase or decrease? What happens if the refractive index was reduced to 1.00?

Discuss in your lab report.

- 9 -

• Part C – Refraction: High to Low Refractive Index:

1. Compare the observed and calculated refracted ray angles by calculating the % error.

Record values in the below table.

2. Is there a difference between the observed and calculated refracted ray angles? Discuss in

your lab report.

3. What happens if the incident ray angle remained constant at 45.0 degrees and the refractive

index of the upper “higher refractive index” material is slowly increased from 1.33 to 1.60?

Discuss in your lab report.

• Part D – Refraction: Total Internal Reflection:

1. Compare the observed and calculated “Critical” incident angles for Total Internal

Reflection by calculating the % error. Record values in the below table.

2. Is there a difference between the observed and calculated “Critical” incident angles?

Discuss in your lab report.

3. Imagine a flat piece of glass with parallel sides and surrounded by air. Sketch what you

think would happen when a light ray is travelling in the glass and the angle of the ray is

above the “Critical Angle”? (NOTE: This is analogous to how a fiber optic works!).

Lab Report:

• When writing the lab report, you must review and follow very carefully the Physics Lab Report

instructions and outline document.

• In your lab report, include the Title Page, Objectives, Theory, Equipment, Data, Graphs and

Screenshots, Calculations, Conclusions, Sources of Error, and References.

• Remember to show all equations and calculations in detail and to round the results to the correct

number significant digits and precision.

• In the conclusions section, be sure to summarize the final results, comment on the agreement

or disagreement of the results with the theory or expectations, answer analysis questions, and

discuss what you personally learned from this experiment and your observations/comments.

• Remember to also answer and discuss all analysis questions in your conclusions section.

• Submit your complete lab report electronically by the due date!

- 10 -

Physics - Online Lab: Reflection and Refraction

Tables of Data and Results

• Part A – The Law of Reflection:

Incident Angle θ i

(Degrees)

Reflected Angle θ r

(Degrees) % Error

50.0

60.0

70.0

80.0

• Part B – Refraction: Low to High Refractive Index:

Incident Angle θ1

(Degrees)

Observed

Refracted Angle θ2

(Degrees)

Calculated

Refracted Angle θ2

(Degrees)

% Error

20.0

40.0

60.0

80.0

- 11 -

• Part C – Refraction: High to Low Refractive Index:

Incident Angle θ1

(Degrees)

Observed

Refracted Angle θ2

(Degrees)

Calculated

Refracted Angle θ2

(Degrees)

% Error

10.0

20.0

30.0

40.0

• Part D – Refraction: Total Internal Reflection:

Refractive Index of

Upper Material n1

(Figure 8)

Refractive Index of

Lower Material n2

(Figure 8)

Observed

Critical Angle θC

(Degrees)

Calculated

Critical Angle θC

(Degrees)

% Error

1.05 1.00

1.10 1.00

1.20 1.00

1.33 1.00

1.40 1.00

1.60 1.00