Pre-Lab: Introduction to Ray Optics

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1. What is the difference between reflection and refraction?

2. Can a light ray be both reflected and refracted at the same time?

3. Fiber optic cables are made out of many concentric layers of transparent material (usually glass or plastic), each with a slightly different index of refraction. How can these transparent cables keep light inside?

4. Briefly summarize the procedures you will follow in this lab. Write one or two sentences for each activity.

5. List any part (or parts) of the lab that you think may suffer from non-trivial experimental error, or may otherwise cause you trouble. How might this affect your results?

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Weather forecast for tonight: dark. Continued dark overnight, with widely scattered light by morning.

George Carlin

Objectives

• To investigate the behavior of light rays as they are reflected and refracted at plane and curved surfaces.

Overview

During the next two weeks you will be using Ray Optics equipment to investi- gate the effects of reflection and refraction. The experiment which will be done during each laboratory period actually will consist of a series of related “mini- experiments” which are coordinated with the material presented in lecture.

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126 Introduction to Ray Optics

Equipment Overview Optics Bench

The Optics Bench is shown above. The light Source, Component Holders, and Ray Table Base all attach magnetically to the bench as shown. For proper optical alignment, the edge of each of these components should be mounted flush to the alignment rail. Care should be taken not to scratch or abuse the surface of the magnetic pads.

Incandescent Light Source

To turn the light source on, connect the power cord to any grounded 105-125 VAC receptacle, and flip the switch on the rear panel to ON. If at any time the light fails to come on, check with your instructor.

The Filament Knob on the top of the unit moves the light bulb from side to side.

Introduction to Ray Optics 127

Component Holders

The Optics set comes with three regular Component Holders and one holder designed for use with the Ray Table (see Ray Optics Setup, below). The regular Component Holders attach magnetically to the optics bench. The notch at the top of each holder is for centering components on the holder. The notches in the base of the holders are for accurate distance measurements on the metric scale of the bench. These base notches—and also the rear edge of the component holder base—are positioned so that they align with the vertical axis of a mounted lens or mirror.

Components

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Basic Setup

The basic setup for Ray Optics is shown above. The Ray Table base should be flush against the alignment rail. The Ray Table fits over the pin on the top of the base.

Notice that the Ray Table Base is slightly slanted. When mounting the base on the Optics Bench, always be sure the Ray Table slants down toward the Light Source. This ensures sharp, bright rays. (In all the experiments described in this manual, the error introduced by this tilt is negligible).

Each side of the Ray table may be used. One side has a rotational scale, the other has both a rotational scale and a grid that may be used for linear measure- ments.

The Slit Plate is attached to a component holder between the Light Source and the Ray table. The positioning shown in the illustration will give clear, sharp rays in a slightly darkened room. However, the quality of the rays is easily varied by adjusting the distance between the Light Source and the Slit Plate. Narrower, less divergent rays may be obtained by sliding the Light Source farther away from the slits, but there is a corresponding loss of brightness.

The Ray Table Component Holder attaches magnetically to the Ray Table as shown. It may be used to mount the Viewing Screen, Polarizer, or other component.

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Single Ray Setup

Most quantitative ray optics experiments are most easily performed with a single ray. This can be obtained by using the Slit Mask, as shown above, to block all but the desired ray. For accurate measurements using the rotational scale, the incident ray must pass directly through the center of the Ray Table. To accomplish this, alternately adjust (1) the lateral position of the Slit plate on its Component Holder, (2) the position of the filament with respect to the optical axis, and (3) the rotation of the Ray Table. When one of the rays is aligned in this manner, place the Slit Mask on the other side of the Component Holder to block all but the desired ray.

Parallel Ray Setup

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Parallel rays are obtained by positioning the Ray Optics Lens between the Light Source and the slits, as shown above. Use the parallel lines of the Ray Table grid as a reference, and adjust the longitudinal position of the Ray Optics Lens until the rays are parallel.

Part I Ray Optics You will need:

• Optics bench

• Light source

• Ray table and base

• Component holder

• Slit plate

• Ray table component holder

• Viewing screen

Activity 1.1 Straight Line Propagation of Light

1. Set up the equipment as shown above, and turn on the Light source. Darken the room enough so the light rays on the Ray Table are easily visible.

Part I. Ray Optics 131

2. Observe the light rays on the Ray Table. Are the rays straight? How does the width and distinctness of each ray vary with the distance from the Slit Plate?

3. Rotate the Slit Plate slowly on the component holder until the slits are horizontal. Observe the slit images on the Viewing Screen.

4. How does the width and distinctness of the slit images depend on the angle of the Slit Plate?

5. For what angle of the Slit Plate are the images most distinct? For what angle are the images least distinct?

Activity 1.2 Locating the Light Bulb Filament

You can use the fact that light propagates in a straight line to measure the distance between the Light Source filament and the center of the Ray Table. The diagram below shows how. The rays on the Ray Table all originate from the filament of the Light Source. Since light travels in a straight line, you need only extend the rays backward to locate the filament.

132 Introduction to Ray Optics

1. Place a piece of blank white paper on top of the Ray Table, and make a reference mark on the paper at the position of the center of the Ray Table. Using a pencil and straight edge, trace the edges of several of the rays onto the paper.

2. Remove the paper. Use the pencil and straightedge to extend each of the rays. Trace them back to their common point of intersection. (You may need to tape on an additional sheet of paper). Label the filament and the center of the Ray Table on your diagram.

3. Measure the distance between your reference mark and the point of inter- section of the rays.

4. Use the metric scale on the Optics Bench to measure the distance between the filament and the center of the Ray Table directly. Compare.

Part II. The Law of Reflection 133

Part II The Law of Reflection In this experiment, you will observe the reflection of a single ray of light from a plane mirror. The principles you discover will be applied, in later experiments, to more complicated examples of reflection.

You will need:

• Optics bench

• Light source

• Ray table and base

• Component holder

• Slit plate

• Slit mask

• Ray optics mirror

Activity 2.1 The Law of Reflection

1. Setup the experiment as shown above. Adjust the components so a single ray of light is aligned with the bold arrow labeled “Normal” on the Ray Table Degree Scale. Carefully align the reflecting surface of the mirror with the bold line labeled “Component” on the Ray Table. With the mir- ror properly aligned, the bold arrow on the Ray Table is normal (at right angles) the plane of the reflecting surface.

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2. Rotate the Ray Table and observe the light ray. The angles of incidence and reflection are measured with respect to the normal to the reflecting surface, as shown below. The plane that contains the incident ray and the normal to the mirror is called the plane of incidence. In this experiment, the plane of incidence is the top surface of the Ray Table.

3. By rotating the Ray Table, set the angle of incidence to each of the settings shown in the table below. For each Angle of Incidence, record the Angle of Reflection.

Angle of Incidence [deg] Angle of Reflection [deg] 0 20 40 60 80

4. What is the relationship between the angle of incidence and the angle of reflection?

5. Do the reflected rays always lie in the plane of incidence?

Part III. Image Formation in a Plane Mirror 135

6. The Law of Reflection has two parts. The first relates the orientation of the reflected ray with respect to the plane of incidence. The second part relates the angle of reflection to the angle of incidence. State both parts of the Law of Reflection.

Part III Image Formation in a Plane Mirror

Looking into a mirror and seeing a nearly exact image of yourself hardly seems like the result of simple physical principles. But it is. The nature of the image you see in a mirror is understandable in terms of the principles you have already learned: The Law of Reflection and the straight-line propagation of light.

In this experiment you will investigate how the apparent location of an image reflected from a plane mirror relates to the location of the object, and how this relationship is a direct result of the basic principles you have already studied.

You will need:

• Optics bench

• Light source

• Ray table and base

• Component holder

• Slit plate

• Ray optics mirror

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Activity 3.1 Image Formation in a Plane Mirror

1. Set up the equipment as shown above. Adjust the Slit Plate and Light Source positions for sharp, easily visible rays.

2. As shown, place a blank white sheet of paper on top of the Ray Table, and place the Ray Optics Mirror on top of the paper. Position the mirror so that all of the light rays are reflected from its flat surface. Draw a line on the paper to mark the position of the flat surface of the mirror.

3. Look into the mirror along the line of the reflected rays so that you can see the image of the slit plate, and through the slits, the filament of the light source.

4. Do the rays seem to follow a straight line into the mirror?

5. With a pencil, mark two points along one edge of each of the incident and reflected rays. Label the points (r1, r2, etc.), so you know which points belong to which ray.

6. Remove the paper and reconstruct the rays as shown on the next page, using a pencil and straightedge. If you need to, tape on additional pieces of paper. Draw dotted lines to extend the incident and reflected rays.

Part III. Image Formation in a Plane Mirror 137

7. On your drawing, label the position of the filament and the apparent posi- tion of its reflected image.

8. What is the perpendicular distance from the filament to the plane of the mirror (d1 as shown in the illustration below)?

9. What is the perpendicular distance from the image of the filament to the plane of the mirror (d2)?

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Part IV The Law of Refraction

As you have seen, the direction of light propagation changes abruptly when light encounters a reflective surface. The direction can also change when light passes from one medium of propagation into another. In this case, the change of direc- tion is called Refraction.

As for reflection, a simple law characterizes the behavior of a refracted ray of light. According to the Law of Refraction, also known as Snell’s Law:

nair sin(θincident) = nmaterial sin(θrefracted) ,

where n, called the index of refraction, is a constant for a given material. In this experiment you will test the validity of this law, and also measure the index refraction for acrylic. Note: Here the light is going from air (nair = 1) into the acrylic (nmaterial). What do you think is the smallest index of refraction for any material?

For this part, you will need:

• Optics bench

• Light source

• Ray table and base

• Component holder

• Slit plate

• Slit mask

• Cylindrical lens

• Computer

Part IV. The Law of Refraction 139

Activity 4.1 The Law of Refraction

1. Set up the equipment as shown above. Adjust the components so a single ray of light passes directly through the center of the Ray Table Degree Scale. Align the flat surface of the Cylindrical Lens with the line labeled “Component.” With the lens properly aligned, the radial lines extending from the center of the Degree Scale will all be perpendicular to the circular surface of the lens.

2. Without disturbing the alignment of the lens, rotate the Ray Table and observe the refracted ray for various angles of incidence.

3. Is the ray bent when its passes into the lens perpendicular to the flat surface of the lens? (What is the angle of incidence?)

4. Is the ray bent when it passes out of the lens perpendicular to the curved surface of the lens?

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5. By rotating the Ray Table, set the angle of incidence to each of the settings shown in the table below. For each angle of incidence, record the angle of refraction.

θincident [deg] sin(θincident) θrefracted [deg] sin(θrefracted) 0 20 40 60 80

6. Use Excel to construct a graph with sin(θrefracted) on the x-axis and sin(θincident) on the y-axis. Add a best-fit trend line.

7. Is your graph consistent with the Law of Refraction? Explain.

8. Measure the slope of your best-fit line. What does the slope represent?

9. Determine the index of refraction for acrylic.

Part V Dispersion and Total Internal Reflection In this experiment you will look at two phenomena related to refraction: Disper- sion and Total Internal Reflection. Dispersion introduces a complication to the

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Law of Refraction, which is that most materials have different indexes of refrac- tion for different colors of light. In Total Internal Reflection, it is found that in certain circumstances, light striking an interface between two transparent media cannot pass through the interface.

You will need:

• Optics bench

• Light source

• Ray table and base

• Component holder

• Slit plate

• Slit mask

• Cylindrical lens

• Ray table component holder

• Viewing screen

Set up the equipment as shown above, so a single light ray is incident on the curved surface of the Cylindrical Lens.

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Activity 5.1 Dispersion 1. Set the Ray Table so the angle of incidence of the ray striking the flat surface of the lens (from inside the lens) is zero-degrees. Adjust the Ray Table Component Holder so the refracted ray is visible on the Viewing Screen.

2. At what angle of refraction do you begin to notice color separation in the refracted ray?

3. At what angle of refraction is the color separation at maximum?

4. What colors are present in the refracted ray? (Write them in the of minimum to maximum angle of refraction).

5. Measure the index of refraction of acrylic for red and blue light. Note: in this case, the ray is going from acrylic to air.

n= sin(θrefracted) sin(θincident)

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Activity 5.2 Total Internal Reflection 1. Without moving the Ray Table or the Cylindrical Lens, notice that not all of the light in the incident ray is refracted. Part of the light is also reflected.

2. From which surface of the lens does reflection primarily occur?

3. Is there a reflected ray for all angles of incidence? (Use the Viewing Screen to detect faint rays).

4. Are the angles for the reflected ray consistent with the Law of Reflection?

5. Is there a refracted ray for all angles of incidence?

6. At what angle of incidence is all the light reflected (no refracted ray)?