Materials Included In Kit

Additional Materials Required

Prelab Preparation

1. Enough materials are provided in this kit for one meter stick optics bench setup for the Guided-Inquiry Activity. Assemble the meter stick optics bench as shown in Figure 4. Use this setup as a model for the students to use as they work through the Guided-Inquiry Design and Procedure.
2. It is assumed the physics lab is already stocked with concave and convex mirrors, as well the required equipment to conduct meter stick optics experiments. If such materials are not available, please consider purchasing AP8177, Meter Stick Optics Equipment Set, which includes the following materials:
   • Meter stick supports, 24
   • Lens/mirror supports, large (7–8 cm), 6
   • Lens/mirror supports, small (4–5 cm), 6
   • Candles, 6
   • Candle holders, 6
   • Optic targets (screens), 6
   • Screen supports, 6
3. Additional meter sticks, lenses and mirrors are also available separately.

Safety Precautions

This activity uses a burning candle; watch for hot wax drippings on hands and other objects. Use appropriate caution when working with a burning candle. Remove all flammable materials from the vicinity of the burning candle and keep the laboratory work area cleared of all nonessential items. Wear safety glasses. Do not leave a burning candle unattended. Follow all laboratory safety guidelines.

Disposal

All materials may be saved and stored for future use. Eventually candles will need to be replaced as they burn down.

Lab Hints

• This laboratory activity can be completed in two 50-minute class periods. It is important to allow time between the Introductory Activity and the Guided-Inquiry Activity for students to discuss and design the guided-inquiry procedures. Also, all student-designed procedures must be approved for safety before students are allowed to implement them in the lab. Prelab Questions may be completed before lab begins the first day, and analysis of the results may be completed the day after the lab or as homework. An additional lab period would be needed for students to complete an optional inquiry investigation (see Opportunities for Inquiry).
• It is recommended that ray diagrams be reviewed prior to this activity if needed.
• For best results, work in a darkened room for the Guided-Inquiry Activity. The room does not need to be completely dark.
• It is recommended that the mirror support be placed at the 10-cm mark on the meter stick to prevent the mirror from falling and breaking. Students should remember to adjust any measured image distances based on 10 cm being the zero point.
• Students will need to adjust the angle between the two meter sticks as the object distance changes in order to capture an image on the screen.
• The top of the candle wick should align with the center of the mirror. If the candle is too tall, remove it and cut off an appropriate amount from the bottom.

Teacher Tips

• Students may have a difficult time understanding the difference between real and virtual images. A real image is one that is reflected off the surface of a mirror and captured (focused) on a screen. The image is on the same side of the mirror as the object. A virtual image is one that only appears “inside” the mirror. If an image is visible in the mirror, it is a virtual image.
• Although a mirror reflects more light than it absorbs, an “infinite” hallway of mirrors takes on a green tinge. This is due to green light being better reflected than other colors over numerous reflections. Challenge students to create an “infinite” hallway of mirrors and explain any observations regarding the color of the images produced.
• The phenomenon of reflection occurs with more than just visible light. Satellite dishes use “reflective” surfaces to converge electromagnetic radiation to a receiver. The types of material used in dishes range from solid metals to frameworks covered in a metal mesh, depending on the frequency of the electromagnetic radiation. Some radio telescopes operate by reflecting radio waves from space to a receiver.
• Spherical mirrors experience aberration that causes reflected light on the very edges to converge to a different point.
• Another type of mirror used in consumer goods is called a parabolic reflector. As the name suggests, the inside surface of a paraboloid is covered with reflective material. Parabolic reflectors are better suited at converging parallel light rays to a single point. Parabolic reflectors also produce parallel light rays if the source is placed at the focus. Parabolic reflectors can be found in car headlights and in TV satellite dishes.

Further Extensions

Opportunities for Inquiry
When looking in a plane mirror, you may have noticed that your right hand appears to be the left hand of your reflected counterpart. A second plane mirror can be used to produce the correct handedness of your reflection. Using two plane mirrors, such as those in the Introductory Activity, investigate the reflections produced by the two mirrors and the effect of changing the angle between the mirrors. If possible, draw ray diagrams to support your observations and conclusions.

Alignment to the Curriculum Framework AP^® Physics 2

Enduring Understandings and Essential Knowledge
The direction of propagation of a wave such as light may be changed when the wave encounters an interface between two media. (6E)
6.E.1: When light travels from one medium to another, some of the light is transmitted, some is reflected, and some is absorbed. (Qualitative understanding only.)
6.E.2: When light hits a smooth reflecting surface at an angle, it reflects at the same angle on the other side of the line perpendicular to the surface (specular reflection); this law of reflection accounts for the size and location of images seen in mirrors.6.E.4: The reflection of light from surfaces can be used to form images. 

Learning Objectives
6.E.1.1: The student is able to make claims using connections across concepts about the behavior of light as the wave travels from one medium into another, as some is transmitted, some is reflected, and some is absorbed. 
6.E.2.1: The student is able to make predictions about the locations of object and image relative to the location of a reflecting surface. The prediction should be based on the model of specular reflection with all angles measured relative to the normal to the surface. 
6.E.4.1: The student is able to plan data collection strategies and perform data analysis and evaluation of evidence about the formation of images due to reflection of light from curved spherical mirrors. 
6.E.4.2: The student is able to use quantitative and qualitative representations and models to analyze situations and solve problems about image formation occurring due to the reflection of light from surfaces. 

Science Practices
1.1 The student can create representations and models of natural or man-made phenomena and systems in the domain. 
1.4 The student can use representations and models to analyze situations or solve problems qualitatively and quantitatively. 
2.2 The student can apply mathematical routines to quantities that describe natural phenomena. 
3.2 The student can refine scientific questions. 
4.1 The student can justify the selection of the kind of data needed to answer a particular scientific question. 
5.1 The student can analyze data to identify patterns or relationships.
5.2 The student can refine observations and measurements based on data analysis. 
5.3 The student can evaluate the evidence provided by data sets in relation to a particular scientific question. 
6.4 The student can make claims and predictions about natural phenomena based on scientific theories and models. 
7.2 The student can connect concepts in and across domain(s) to generalize or extrapolate in and/or across enduring understandings and/or big ideas.

Answers to Prelab Questions

1. In order for a real image to form, explain what needs to occur in terms of the incident and reflected rays.

   In order for a real image to form, the reflected rays from a mirrored surface must converge on a single point in “real” space. The reflected rays must converge on the same side of the mirrored surface as the source of the incident rays. To capture the real image, a screen is needed.

2. From your experience, compare the size of the “person” in the mirror when looking at a plane mirror. Is the person smaller, larger, or the same size as you? Estimate the distance that your reflection appears to be away from you. Is there anything peculiar about the reflection compared to you?

   The person in the mirror appears to be the same size as me. The reflection appears to be the same distance “behind” the mirror as I am from the front of the mirror. My movements control the reflection’s opposite side (e.g. if I raise my right hand, the reflection raises its left hand).

3. Examine Figure 3. Which screen, if any, would person X and person Z see when looking at the mirror? Complete the ray diagrams to support your answer.
   {14017_PreLabAnswers_Figure_3}
   Person X would see screen B. Person Z would see screen C.
4. In order for person Z to see screen A, where would Z need to move? Assume person Z continues to stare at the same point on the mirror. Explain your steps for determining the new location. Draw in the correct location and the appropriate ray diagram on the figure above to support your answer.

   See Figure 3 for ray diagram. In order to determine the location of person Z to see screen A, a line was drawn from the initial point on the mirror to the right-most edge of screen A. This represents the reflected ray from the mirror to the screen. The angle between the reflected ray and the normal was drawn on the mirror. According to Snell’s law, the angle of incidence is equal to the angle of reflection. The incidence ray is drawn at the same angle on the opposite side of the normal. Person Z would be able to stand anywhere on this line and see screen A.

Sample Data

Introductory Activity

When the light rays were traced and extended into the mirror, all of the rays came to a single point. This shows that the angles of incidence and reflection were correctly measured and traced. The object and image distance are nearly equal. The small difference between the two values may have resulted from improper alignment of the reflection rays with the front of the cork. The image distance agrees with the point at which the ray tracings come together. In the mirror, it appears as though the image of the cork originates within the mirror.

Guided-Inquiry Activity

Concave Mirror
Focal Length: 20.5 cm When the object was placed outside of the focal length, the images produced were all real and inverted. The images were projected onto a screen indicating the light rays were converging to a point in real-space. The image distances were in approximate agreement, except when the object was placed less than 30 cm from the mirror. When the image size increased, it became more difficult to determine if the image was focused. As the object distance from the mirror increased, the size of the image decreased.

When the object was placed inside the focal length, no image was projected. The object was visible “inside” the mirror indicating the image was virtual. The virtual images are in agreement with the predicted image distances because those were negative values. The negative values indicate the images would be “inside” the mirror. The images all appeared larger than the object and were upright.

When the object was placed at the focal length, there was no image projected nor was the object visible in the mirror. This agrees with the predicted image distance because the value is equal to a number divided by zero and would be at an infinite distance.

Convex Mirror
All reflections were virtual images regardless of the object distance. The images of the flame appeared smaller than the actual flame and were upright.

Answers to Questions

Guided-Inquiry Activity

1. Do the reflected rays converge or diverge from the surface of the plane mirror? Cite evidence from the Introductory Activity.

   The reflected rays diverge from the surface of the plane mirror. The reflected rays leave the mirror traveling at angles that will not intersect on the object side of the mirror.

2. What type of image was formed by the plane mirror? Explain how you determined this.

   The image in the plane mirror is a virtual image. The reflected rays diverge from the mirror. This means a real image can’t be formed by a plane mirror. The reflected rays must converge on the object side of the mirror to form a real image.

3. Recall that a curved surface can be considered as an infinite number of infinitely small planar surfaces. Explain, in your own words, how this statement is helpful when drawing ray diagrams for curved mirrors.

   When light rays strike a curved mirror surface, the rays will reflect off at the same angle relative to the normal. Thinking of the curved mirror as tangential plane mirrors makes the ray diagram of a curved mirror like that of a plane mirror.

4. Finish drawing the ray diagrams for the analogous concave and convex mirror configurations below. Identify the mirror configurations as converging or diverging. Note: The light rays are coming from a light source infinitely far away (compared to the focal points of the lenses).
   {14017_Answers_Figure_10}
5. Using the definitions of “real” and “virtual” provided in the Background, classify the focal points for the concave and convex mirrors in Question 4.

   The focal point of the concave mirror is a real focal point. The reflected rays converge to a point on the object-side of the mirror. The convex mirror has a virtual focal point because the ray lines had to be extended to “inside” the mirror. The reflected rays diverged from the convex mirror surface.

6. If possible, explain how the focal points for the curved mirrors could be experimentally determined or measured.

   Only the focal point of the concave mirror could be experimentally determined or measured. Because the reflected rays converge to a point in real space, a screen could be placed some distance away from the concave mirror until a clear image of the distant object appears. The distance from the mirror to the screen is the focal length of the mirror. The focal point of the convex mirror can’t be measured because it is a virtual point, residing “inside” the mirror.

7. Using information from the Background, answer the following questions.
   1. Concave mirror – focal length = 15 cm
      1. What is the image distance of an object 25 cm away from the mirror?

         1/f = 1/d_O + 1/d_I
         1/15 cm^–1 = 1/25 cm^–1 + 1/d_I
         1/d_I = 2/75 cm^–1
         d_I = 37.5 cm^–1

      2. Is the image real or virtual?

         The image will be real. The sign of the image distance is positive, indicating the image is on the object side of the mirror and can be projected onto a screen.

   2. Convex mirror – focal length = 15 cm
      1. What is the image distance of an object 25 cm away from the mirror?

         1/f = 1/d_O + 1/d_I
         –1/15 cm^–1 = 1/25 cm^–1 + 1/d_I
         1/d_I = –8/75 cm^–1
         d_I = –9.38 cm

      2. Is the image real or virtual?

         The image is virtual. The sign of the image distance is negative, indicating the image is “inside” the mirror.

8. Design a series of experiments to determine the focal lengths of the concave and convex mirrors, where possible. See Figure 4 for a general setup for meter stick optics investigations.

   There are two methods by which the focal length of the concave mirror may be determined. The focal length of the convex mirror cannot be determined using the setup in Figure 4.
   Method A

   1. Set up the two meter sticks with the mirror and screen as seen in Figure 4.
   2. The mirror and screen should be oriented so a reflection can be cast from the window onto the screen.
   3. Adjust the position of the screen until a clear, sharp image of the view through the window can be seen on the screen.
   4. The distance between the center of the mirror and the screen is the focal length.
   Method B
   1. Set up the two meter sticks with the mirror and screen as seen in Figure 4.
   2. Place the candle at the far end of the meter stick. Record this distance.
   3. Light the candle. Adjust the position of the screen and the angle between the two meter sticks until a clear image of the candle’s flame can be seen on the screen. Record the distance between the center of the mirror and the screen.
   4. Use Equation 1 to solve for the focal length of the mirror.
9. After finding the focal lengths of the mirror(s), predict the image distance when an object (candle) is placed on the second meter stick. Record the object distance, and the predicted and actual image distances.

   Sample Calculation:
   1/f = 1/d_O + 1/d_I
   1/20.5 cm^–1 = 1/90 cm^–1 + 1/d_I
   1/d_I = 0.0377 cm^–1
   d_I = 26.5 cm

Review Questions for AP^® Physics 2

1. A student wishes to take a picture of himself in a mirror. He is standing four feet in front of the mirror. However, each picture has a blurry image of him. The camera has an automatic focus that detects the closest surface to serve as the focus plane of the picture. Explain to the student what is occurring, why his images are blurry, and a needed change to the camera to obtain clear images.

   When the camera performs its auto-focus, it detects the mirror surface at four feet away. The camera then sets the mirror surface as the focus plane of the picture. However, the reflection of the student is four feet behind the mirror (inside the mirror surface). The image distance for an object placed in front of a plane mirror is the same distance as the distance between the object and the mirror. In order to capture the reflection, the student needs to manually focus the camera at a plane eight feet from his position (four feet from the student to the mirror plus four feet from the mirror to the image), if possible.

2. Telescopes can use mirrors or lenses to collect light from distant stellar objects. Which type of mirror would be used in a reflecting telescope: concave or convex? Explain how you made your determination.

   Light that originates from very distant objects can be considered as parallel rays upon arrival at Earth and the space around Earth. To collect those rays for analysis, they need to be focused/converged to a single point. A concave mirror is capable of converging parallel light rays to a single point. A convex mirror diverges light rays and would not be capable of focusing the distant light rays to a single point for analysis.

3. On the side mirror of an automobile, there is a warning that reads: “Objects in mirror are closer than they appear.” A student notices that she looks smaller in the mirror when investigating the claim. She asserts, “The side mirror is concave.” Do you agree or disagree with the student’s claim? Use evidence from the experiment to support your position in a paragraph- length response.

   The student’s claim is incorrect. The side mirror on an automobile is a convex mirror. Concave mirrors create both real and virtual images. A real image is formed when the object is outside the focal point of the mirror; a virtual image is formed when the object is inside the focal point. The real image is inverted and varies in size relative to the size of the object (sometimes larger, sometimes smaller). A virtual image formed by a concave mirror creates an image that is larger than the object and upright. The size of the virtual image gives the illusion that the object is closer than it actually is.
   A convex mirror only forms virtual images. The images in a convex mirror appear smaller than the object. The size of the image gives the illusion that the object is farther away than it actually is. Therefore, the side-view mirror must be a convex mirror.

4. Figure 6 shows an object, arrow W, standing in front of a spherical mirror that can be mounted within the dashed space, M. The mirror extends above and below the central axis. The four arrows, I₁ – I₄, represent possible images formed by the mirror. The image distance and size are not drawn to scale.
   {14017_Answers_Figure_6}
   1. Which image(s) could not possibly be formed by either a concave or convex mirror? Cite evidence from the experiment to support your answer.

      Images I₄ and I₂ could not be formed by either a concave or convex mirror. A convex mirror only forms virtual, upright images. A concave mirror forms virtual, upright images and real, inverted images. I₄ is a real, upright image. I₂ is virtual, inverted image. These two images cannot be made with concave or convex mirrors.

   2. Which image(s) would be caused by a convex mirror? Identify the image(s) as real or virtual. Justify your answer.

      A convex mirror forms virtual, upright images. I₁ is a virtual image because it is on the opposite side of the mirror as the object, arrow W. I₁ is also upright and in the same orientation as the object.

   3. Which image(s) would be caused by a concave mirror? Identify the image(s) as real or virtual. Justify your answer.

      A concave mirror can form both virtual, upright images and real, inverted images. I₁ is a virtual image because it is on the opposite side of the mirror as the object, arrow W. I₁ is also upright and in the same orientation as the object. I₃ is a real image because it is on the same side of the mirror as the object, arrow W. I₃ is in the opposite orientation as the object.

   4. One image is shared between the concave and convex mirrors. Based on your answers to parts b and c, is additional information needed to determine if that image is formed by a concave or convex mirror? Use evidence from the experiment to support your answer.

      The concave and convex mirrors share I₁ as a potential common image. The height of the object, arrow W, and the height of image I₁, can be used to make a distinction between the two mirrors. A convex mirror will produce a virtual, upright image that is smaller than the object regardless of where the object is placed in front of the mirror. A concave mirror will produce a virtual, upright image that is larger than the object as long as the object is placed inside the focal point of the mirror.

References

AP^® Physics 1: Algebra-Based and Physics 2: Algebra-Based Curriculum Framework; The College Board: New York, NY, 2014.

Introduction

You most likely use mirrors to see your reflection every day, but do you know why the image forms? The mirrors on the sides of cars read “Objects in mirror are closer than they appear.” What makes the image of an approaching car seem farther away than the real car? Both of these questions can be answered with the law of reflection.

Concepts

• Reflection
• Concave versus convex mirror
• Law of reflection
• Real versus virtual image

Background

Light is partially absorbed and partially reflected off every surface. The manner and amount of light that is absorbed or reflected depends on the type of material and smoothness of the surface. Mirrors reflect almost all incoming light, unlike an opaque object, which absorbs more of the incoming light and reflects less.

Reflected light is governed by one simple principle: the angle of the incident light is equal to the angle of the reflected light, with respect to the normal line at the surface. This is known as the law of reflection (see Figure 1).

The law of reflection is easily observed when light reflects off a smooth surface, such as a mirror, a shiny table or even water. This type of reflection is known as a specular reflection (see Figure 2a). When light encounters a rough, textured surface, however, it will reflect in many different directions, resulting in a diffuse reflection. The reflected light still follows the law of reflection, but the various reflected angles are the result of the many angles and ridges at the surface the incident light strikes (see Figure 2b). When multiple light rays reflect off a mirror surface, the rays either converge or diverge from the central axis. When reflected rays converge, the rays come to a point somewhere in real space. That is to say, a screen could be placed at that point and the reflected image could be seen. The reflected image is called a real image because it forms on the object side of the mirror and can be projected. When reflected rays diverge from the mirror, the rays appear to originate from a point “inside” the mirror. The image formed by diverging rays cannot be projected onto a screen and is therefore called a virtual image.

Three important values when working with mirrors are the focal length (f), object distance (d_O), and image distance (d_I). Equation 1 allows for the third value to be solved as long as the other two values are known. By convention, the sign of the object distance is positive. If the focal point is on the object side of the mirror, the focal length is positive. If the focal point is behind the mirror, the focal length is negative. If the image is real, the image distance is positive. A virtual image has a negative image distance.

Experiment Overview

In this advanced inquiry experiment, the law of reflection for a plane mirror will be confirmed by tracing a ray diagram of an object and analyzing the ray angles and object–image distances. In the guided-inquiry section, the properties of concave and convex mirrors will be determined. A series of leading questions provide a model for determining the properties of images formed by concave and convex mirrors and provide a guide for assessing those predictions.

Materials

Prelab Questions

1. In order for a real image to form, explain what needs to occur in terms of the incident and reflected rays.
2. From your experience, compare the size of the “person” in the mirror when looking at a plane mirror. Is the person smaller, larger, or the same size as you? Estimate the distance that your reflection appears to be away from you. Is there anything peculiar about the reflection compared to you?
3. Examine Figure 3. Which screen, if any, would person X and person Z see when looking at the mirror? Complete the ray diagrams to support your answer.
   {14017_PreLab_Figure_3}
4. In order for person Z to see screen A, where would Z need to move? Assume person Z continues to stare at the same point on the mirror. Explain your steps for determining the new location. Draw in the correct location and the appropriate ray diagram on the figure above to support your answer.

Safety Precautions

This activity uses a burning candle; watch for hot wax drippings on hands and other objects. Use appropriate caution when working with a burning candle. Remove all flammable materials from the vicinity of the burning candle and keep the laboratory work area cleared of all nonessential items. Wear safety glasses. Do not leave burning candle unattended. Follow all laboratory safety guidelines.

Procedure

Introductory Activity

1. Draw a vertical line on the side of the cork (see Figure 4).
   {14017_Procedure_Figure_4}
2. Place the mirror in the mirror support (see Figure 5). Note: Make sure the bottom of the mirror support is flat against the work surface so the mirror stands upright without leaning forward or back.
   {14017_Procedure_Figure_5}
3. Draw a horizontal line across a plain piece of paper, perpendicular to the long edge.
4. Place the mirror on the line with the reflected side facing the observer.
5. Make a mark on the paper 4 cm from the center of the reflective side of the mirror.
6. Place the cork on the paper so the vertical line is on the mark and facing the mirror.
7. Get down to eye level with the paper.
8. Close one eye and look at the reflection of the cork in the mirror from a position at least 5 cm to the left of the actual cork.
9. Take a ruler, set it on its long edge, and align it from your line of sight to the vertical line in the mirror. Note: Be careful not to bump the mirror or the cork with the ruler.
10. Holding the ruler steady, draw a line on the paper along the ruler (see Figure 6).
    {14017_Procedure_Figure_6}
11. Repeat steps 7–10, looking at the image from a different location to the left of the cork.
12. Repeat steps 7–11, looking at the image from the right side of the cork.
13. Remove the mirror and cork from the paper.
14. If needed, extend each ray line to the horizontal line on the paper representing the mirror.
15. Extend each ray line behind the mirror with a dashed line.
16. Draw the incident ray line from the mark on the paper representing the vertical line on the cork to meet each reflected ray line, respectively.
17. Draw a dashed line to represent the normal line for each pair of incident and reflected ray lines (see Figure 7 for one example).
    {14017_Procedure_Figure_7}

Analyze the Results 
Determine the angles of incidence and reflection for the four rays drawn on the paper. For a plane mirror, how do the object distance and image distance compare? How far from the real cork would the image of the cork appear?

Guided-Inquiry Design and Procedure

1. Do the reflected rays converge or diverge from the surface of the plane mirror? Cite evidence from the Introductory Activity.
2. What type of image was formed by the plane mirror? Explain how you determined this.
3. Recall that a curved surface can be considered as an infinite number of infinitely small planar surfaces. Explain, in your own words, how this statement is helpful when drawing ray diagrams for curved mirrors.
4. Finish drawing the ray diagrams for the analogous concave and convex mirror configurations below. Identify the mirror configurations as converging or diverging. Note: The light rays are coming from a light source infinitely far away (compared to the focal points of the mirrors).
   {14017_Procedure_Figure_8}
5. Using the definitions of “real” and “virtual” provided in the Background, classify the focal points for the concave and convex mirrors in Question 4.
6. If possible, explain how the focal points for the curved mirrors could be experimentally determined or measured.
7. Using information from the Background, answer the following questions.
   1. Concave mirror – focal length = 15 cm
      1. What is the image distance of an object 25 cm away from the mirror?
      2. Is the image real or virtual?
   2. Convex mirror – focal length = 15 cm
      1. What is the image distance of an object 25 cm away from the mirror?
      2. Is the image real or virtual?
8. Design a series of experiments to determine the focal lengths of the concave and convex mirrors, where possible. See Figure 9 for a general setup for meter stick optics investigations.
   {14017_Procedure_Figure_9}
9. After finding the focal lengths of the mirror(s), predict the image distance when an object (candle) is placed on the second meter stick. Record the object distance, and the predicted and actual image distances.
10. Pay close attention to the following properties of the image and object: size (height), orientation (inverted/upright) and type (real/virtual).

Analyze the Results
Summarize your data and observations in a coherent data table(s). Compare the properties of concave and convex mirrors. Do the object distance, image distance and focal length values agree with Equation 1 in the Background? Explain any discrepancies. Were there any object distances that resulted in no image formation? For which mirror did this occur? What does this distance represent for the mirror? Explain, in your own words, why this occurred.

Student Worksheet PDF

14017_Student1.pdf