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Understanding Reflection and Refraction: An Experiment with Optics, Study notes of Law

Law

An experiment designed to investigate the relationship between the angle of incidence and the angle of reflection for light rays hitting flat, concave, and convex mirrors, as well as the relationship between the angle of incidence and the angle of refraction for a light ray passing through a rhombus prism. The document also covers the concepts of reflection and refraction, including Snell's Law and the critical angle.

Typology: Study notes

2021/2022

Uploaded on 09/27/2022

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Reflection and Refraction
Equipment List
Qty Items Part Numbers
1 Light Source, Basic Optics OS-8517
1 Ray Optics Set OS-8516
2 White paper, sheet
1 Metric ruler
1 Protractor
Introduction
The purpose of the first part of this activity is to determine the relationship between the angle of
incidence and the angle of reflection for a light ray reflecting from flat, concave, and convex mirrors.
The purpose for the second part is to examine the relationshop of the angle of incidence and the angle of
refraction for a light ray passing through a rhombus prism. Use a light source, three-way mirror,
rhombus prism, and protractor to measure angles of a light ray.
Background:
Reflection
When a ray of light strikes a plane mirror, the light ray reflects
off the mirror. Reflection involves a change in direction of the
light ray. The convention used to express the direction of a light
ray is to indicate the angle which the light ray makes with a
normal drawn to the surface of the mirror (a line that is
perpendicular to the surface). The angle of incidence is the
angle between this normal and the incident ray; the angle of
reflection is the angle between this normal and the reflected ray.
According to the law of reflection, the angle of incidence equals
the angle of reflection.
To view an image of an object in a mirror, you must sight along
a line at the image location. As you sight at the image, light
travels to your eye along the path shown in the diagram. The
diagram shows that the light reflects off the mirror in such a
manner that the angle of incidence is equal to the angle of
reflection.
Refraction
The most common example of refraction is the bending of light
on passing from air to a liquid, which causes submerged objects
to appear displaced from their actual positions. Refraction is
also the reason that prisms separate white light into its
constituent colors. Refraction is commonly explained in terms
of the wave theory of light and is based on the fact that light
travels with greater velocity in some media than it does in
others. When, for example, a ray of light traveling through air
strikes the surface of a piece of glass at an angle, one side of the wave front enters the glass before the
rev 08/2019
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1

Reflection and Refraction

Equipment List

Qty Items Part Numbers 1 Light Source, Basic Optics OS- 1 Ray Optics Set OS- 2 White paper, sheet 1 Metric ruler 1 Protractor

Introduction

The purpose of the first part of this activity is to determine the relationship between the angle of incidence and the angle of reflection for a light ray reflecting from flat, concave, and convex mirrors. The purpose for the second part is to examine the relationshop of the angle of incidence and the angle of refraction for a light ray passing through a rhombus prism. Use a light source, three-way mirror, rhombus prism, and protractor to measure angles of a light ray.

Background:

Reflection

When a ray of light strikes a plane mirror, the light ray reflects off the mirror. Reflection involves a change in direction of the light ray. The convention used to express the direction of a light ray is to indicate the angle which the light ray makes with a normal drawn to the surface of the mirror (a line that is perpendicular to the surface). The angle of incidence is the angle between this normal and the incident ray; the angle of reflection is the angle between this normal and the reflected ray. According to the law of reflection, the angle of incidence equals the angle of reflection. To view an image of an object in a mirror, you must sight along a line at the image location. As you sight at the image, light travels to your eye along the path shown in the diagram. The diagram shows that the light reflects off the mirror in such a manner that the angle of incidence is equal to the angle of reflection.

Refraction

The most common example of refraction is the bending of light on passing from air to a liquid, which causes submerged objects to appear displaced from their actual positions. Refraction is also the reason that prisms separate white light into its constituent colors. Refraction is commonly explained in terms of the wave theory of light and is based on the fact that light travels with greater velocity in some media than it does in others. When, for example, a ray of light traveling through air strikes the surface of a piece of glass at an angle, one side of the wave front enters the glass before the

rev 08 /201 9

2

other and is retarded (since light travels more slowly in glass than in air), while the other side continues to move at its original speed until it too reaches the glass. As a result, the ray bends inside the glass, i.e., the refracted ray lies in a direction closer to the normal (the perpendicular to the boundary of the media) than does the incident ray. A light ray entering a different medium is called the incident ray. After bending, the ray is called the refracted ray. The speed at which a given transparent medium transmits light waves is related to its optical density (not to be confused with mass or weight density ). In general, a ray is refracted toward the normal when it passes into a denser medium, and away from the normal when it passes into a less dense medium. The law of refraction relates the angle of incidence (angle between the incident ray and the normal) to the angle of refraction (angle between the refracted ray and the normal). This law, credited to Willebrord Snell, states that the ratio of the sine of the angle of

incidence,  i , to the sine of the angle of refraction,  r , is equal to the ratio of the speed of light in the

original medium, v (^) i , to the speed of light in the refracting medium, v (^) r. Snell's law is often stated in terms of the indexes of refraction of the two media rather than the speeds of light in the media. The index of refraction, n , of a transparent medium is the ratio of the speed of light in a vacuum, c , to the speed of light in the medium: n = c/v.

Using indexes of refraction, Snell’s Law (also known as the Law of Refraction) takes the form sin  i /sin

 r = nr /ni , or ni sin  i = nr sin  r.

Snell’s law has two special cases: critical angle and total internal reflection. When the angle of incidence makes a 90° angle of refraction, total internal reflection occurs. When there is total internal reflection, then you can obtain the critical angle. The critical angle is measured with respect to the normal at the refractive boundary and is equivalent to

𝜃௥ ൌ 90° → 𝜃௜ ൌ 𝜃௖ ൌ arcsin ൬

The critical angle only takes place when the light is traveling from a medium with a higher index of refraction to a medium with lower index of refraction. This is to say, we find the critical angle when the value of the incident theta is equal to 90° and thus sin(θi) is equal to 1. The resulting value of the refracted theta will then be equal to the critical angle. For total internal reflection to occur, nr must be greater than ni.

N 1

N 2

4

Setup: Refraction

  1. Place the Light Source, label side up, on a new sheet of paper on a table. Adjust the mask on the end of the light source so one white ray is showing.
  2. Place the rhombus on the paper so that the long side faces the light source and the textured side of the rhombus faces down. Also, position the rhombus so the ray passes through the parallel sides.

Procedure: Refraction

  1. Trace the shape of the rhombus and then position the light ray entering the rhombus at 30 degrees such that the light enters and exits the rhombus through parallel sides. Then trace the incoming and outgoing rays with arrows in the appropriate directions.
  2. Reposition the light source so the light strikes the rhombus at a 45 degree angle of incidence and trace the incoming and outgoing light rays.
  3. Repeat step 2 but with a 60 degree angle of incidence.

Analysis: Refraction

  1. Remove the paper from under the light and rhombus.
  2. Using your protractor and ruler, draw a line perpendicular to and through the surface of the rhombus at the point where the ray of incidence strikes the rhombus. This line is the normal.
  3. Trace the path of the light ray as it moves through the rhombus. This is the line that connects the point where the light ray enters the rhombus to the point the light ray exits the rhombus.
  4. Measure the angle of incidence (angle of the incoming ray relative to the normal) and the angle of refraction (angle of the ray transmitted through the rhombus relative to the normal) and record the value in the chart.
  5. Repeat steps 2-4 for each trial. Record the values in the Lab Report.

Rhombus prism

Setup: Critical Angle

  1. Place the Light Source, label side up, on a new sheet of paper on a table. Adjust the mask on the end of the light source so one white ray is showing.
  2. Place the rhombus on the paper so that the long side faces the light source and the textured side of the rhombus faces down. Also, position the rhombus so the ray passes through the parallel sides.

Procedure: Critical Angle

1. Trace the shape of the rhombus.

  1. Shine a single slit light source into the rhombus, increasing the angle of incidence until total internal reflection occurs.
  2. Trace the incoming light ray and mark the position on the opposite side of the rhombus where the internal light beam strikes the side of the rhombus.

Analysis: Critical Angle

  1. Remove the rhombus, connect the incoming ray to the position just marked.
  2. Trace a line in the internal normal direction where the internal light ray struck the rhombus.
  3. The angle formed from this normal and the internal light ray formed is the critical angle for the rhombus.
  1. Describe what happens as the ray of light enters the rhombus. (10 points)
  2. Describe the relationship between the angle of incidence and angle of refraction. (10 points)
  3. Using the measured index of refraction, calculate the critical angle for the rhombus surrounded by air. Show work. (5 points)
  4. What is the percent error between the measured and calculated values of the critical angle? Use the calculated as the theoretical value. Show work. (5 points)
  5. Using Snell’s Law, explain why the index of refraction is a dimensionless quantity. (5 points)

8

  1. What are some reasons for our percent error in this experiment? (5 points)
  2. Did our experiment confirm the Laws of Reflection and Refraction? Why or why not? (5 points)