Materials Included In Kit

Additional Materials Required

Prelab Preparation

The following instructions will make two gelatin refraction dishes.

1. Pour 200 mL of deionized water into a 400-mL beaker.
2. Place the beaker on a hot plate and heat until the water reaches a low boil.
3. Remove the beaker from the hot plate and add 10 drops of red food coloring
4. Use a glass stirring rod to slowly stir 8 g of gelatin into the colored water. Continue stirring until all the gelatin dissolves.
5. Pour the liquid gelatin solution into the semicircular refraction dishes and cover with plastic wrap.
6. Let stand for 3–4 hours or until the gelatin has solidified. This will occur more quickly if placed in a refrigerator.

Safety Precautions

Do not aim the laser pointer directly into anyone’s eyes. The low-power, coherent light can cause damage to the sensitive retina and may lead to permanent eye damage. Prevent stray laser light from projecting beyond the classroom to eliminate any unintentional exposure to the laser light. When refracting the laser light, it is best to do this on a low work surface to keep the refracted laser light below “normal” eye level. For people with sensitive eyes, it is recommended that dark, IR-protective, safety glasses be worn. 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. Do not leave burning candles unattended. Follow all laboratory safety guidelines. When preparing the gelatin, always wear chemical splash goggles and a lab apron.

Disposal

Please consult your current Flinn Scientific Catalog/Reference Manual for general guidelines and specific procedures, and review all federal, state and local regulations that may apply, before proceeding. Gelatin may be disposed of according to Flinn Suggested Disposal Method #26a. The dish may be washed, dried and stored for future use. All other materials should 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).
• Enough materials are provided in this kit for six student groups in the Introductory Activity and for a single demonstration setup of the Guided-Inquiry Activity. It is assumed the physics lab is already stocked with concave and convex lenses, as well as the materials required to conduct meter stick optics experiments. If such materials are not available, please consider purchasing Catalog No. AP8177, Meter Stick Optics Equipment Set, which includes materials for up to six student groups. Additional lenses are also available from Flinn Scientific.
• For best results, work in a darkened room. The room does not need to be completely dark.
• It is recommended that the lens support be placed at the 50-cm mark. Students should remember to adjust any measured image and object distances based on 50-cm being the zero-point.
• The top of the candle wick should align with the center of the lens. If the candle is too tall, remove it and cut off an appropriate amount from the bottom.
• Knowledge of ray diagrams is not necessary to complete this activity, nor is it addressed in the experiments. It is recommended that ray diagrams be covered in detail.
• In order to complete the Opportunities for Inquiry in the Further Extensions section, students will need working knowledge of ray diagrams. Specifically, they need to be familiar with how the image through one lens may be used as the object for a second lens.

Teacher Tips

• Photocopy at least two protractor papers per group.
• Students may have a difficult time understanding the difference between real and virtual images. A real image is one that is refracted through the lens and captured (focused) on a screen. The image is on the opposite side of the lens as the object. A virtual image is one that only appears “inside” the lens. If an image is visible in the lens, it is a virtual image.
• Students may hear references to slow and fast media when discussing the refraction of light. Explain to them that slow medium has a higher index of refraction compared to the other material; faster medium has a lower index of refraction. Students can prove this by calculating the speed of light in water (n = 1.33) and in benzene (n = 1.50) and comparing the values.
• When light travels from a slower medium to a faster medium, there is an angle at which the light will refract at 90° to the normal. This angle is called the critical angle. The critical angle can be calculated using Snell’s law by setting the angle of refraction to 90°. If the angle of incidence exceeds the critical angle for the specific media boundary, the light reflects off the boundary according to the law of reflection.
• Students will be most familiar with positive indices of refraction. While likely beyond the scope of the curriculum, materials with negative indices of refraction are possible. A class of metamaterials have been created that refract electromagnetic radiation on the same side of the normal. At the time of writing, materials with negative indices of refraction work on electromagnetic radiation of longer wavelengths. Materials do not yet exist that work on visible light.

Further Extensions

Opportunities for Inquiry
The focal length of a concave lens may be measured using another lens on the meter stick. Research ray diagrams involving two lens systems. Design an experiment to measure the focal length of the concave lens used in the Guided-Inquiry Design and Procedure. Include ray diagrams to support your experimental design.

Alignment to the Curriculum Framework for 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)
6E1: When light travels from one medium to another, some of the light is transmitted, some is reflected, and some is absorbed. (Qualitative understanding only.)
6E3: When light travels across a boundary from one transparent material to another, the speed of propagation changes. At a non-normal incident angle, the path of the light ray bends closer to the perpendicular in the optically slower substance. This is called refraction.
6E5: The refraction of light as it travels from one transparent medium to another can be used to form images.

Learning Objectives
6E1.1: 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.
6E3.1: The student is able to describe models of light traveling across a boundary from one transparent material to another when the speed of propagation changes, causing a change in the path of the light ray at the boundary of the two media.
6E3.2: The student is able to plan data collection strategies as well as perform data analysis and evaluation of the evidence for finding the relationship between the angle of incidence and the angle of refraction for light crossing boundaries from one transparent material to another (Snell’s law).
6E3.3: The student is able to make claims and predictions about path changes for light traveling across a boundary from one transparent material to another at non-normal angles resulting from changes in the speed of propagation.
6E5.1: 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 refraction of light through thin lenses.
6E5.2: The student is able to plan data collection strategies, perform data analysis and evaluation of evidence, and refine scientific questions about the formation of images due to refraction for thin lenses.

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. What is the speed of light in a vacuum? In air?

   The speed of light in a vacuum is 3.0 x 10⁸ m/s. The speed of light in air is also 3.0 x 10⁸ m/s.

2. Using Equation 1 and the answers to Questions 1, calculate the index of refraction (n) for light in air.

   n = c/v
   n = 3.0 x 10⁸ m/s / 3.0 x 10⁸ m/s
   n = 1

3. Using Equation 2, the answer to Question 2, and the angles given in Figure 1, calculate the index of refraction for light in water (n₂).

   n₁ sinθ₁ = n₂ sinθ₂
   1 sin 45° = n₂ sin 32°
   n₂ = 1.33

4. Using Equation 1 and your answer above, calculate the speed of light in water (v).

   n = c/v
   1.33 = 3.0 x 10⁸ m/s/v
   v = 2.26 x 10⁸ m/s

5. Compare the speed of light in water to the speed of light in air. In which substance is the speed of light slower?

   The speed of light is slower in water than in air. This is because the density of water is greater than air.

Sample Data

Introductory Activity

Air into Gelatin

n_Gelatin = c/v_Gelatin
v_gelatin = c/n_Gelatin
v_gelatin = (3.0 x 10⁸ m/s)/1.29
v_gelatin = 2.33 x 10⁸ m/s

Gelatin into Air

n_Gelatin = c/v_Gelatin
v_gelatin = c/n_Gelatin
v_gelatin = (3.0 x 10⁸ m/s)/1.33
v_gelatin = 2.26 x 10⁸ m/s

Guided-Inquiry Activity

Double Convex Lens
Focal length: 9.99 cm Conclusion
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 close agreement with the predicted distance values. When the image size increased, it became more difficult to determine if the image was focused. As the object distance from the lens 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 lens 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 lens. 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.

Double Concave Lens

Conclusion
All images through the concave lens were virtual images regardless of the object distance. The images of the flame appeared smaller than the actual flame. The images were upright.

Answers to Questions

Guided-Inquiry Activity 

1. Why was it important to aim the laser at the intersection of 0° and 90°? Consider the path of the light as it travels through the semi-circular dish.

   By aiming the laser at the intersection of 0° and 90°, the path of the laser through the curved edge of the dish would be following a radial line from the center of the dish to the outside edge. The radial line corresponds to the normal line for that point on the circle. A tangent line drawn at that point on the circle would have a perpendicular line extending to the center of the circle. The laser would be 0° away from the normal, and sin(0°) is equal to 0. This indicates there would be no refraction at the curved edge of the dish, so long as the laser follows the radial line.

2. Based on the observations and data collected in the Introductory Activity, did the laser beam refract more when it traveled from air to gelatin or gelatin to air? Justify your answer and include a comparison of the speed of light in the two media.

   When the laser beam passed from the air into the gelatin, the beam bent towards the normal, that is, the angle of refraction was less than the angle of incidence. When the laser beam passed from the gelatin into the air, the beam bent away from the normal, that is, the angle of refraction was greater than the angle of incidence. The speed of light in the gelatin is slower than the speed of light in air, 2.30 x 10⁸ m/s versus 3.0 x 10⁸ m/s, respectively. Based on these observations, it can be generalized that when light travels from a faster medium (air) to a slower medium (gelatin), the light bends towards the normal, resulting in a smaller angle of refraction. When light travels from a slower medium (gelatin) to a faster medium (air), the light bends away from the normal, resulting in a larger angle of refraction.

3. Trace the path of light as it travels through air into glass into air. The index of refraction of the glass is 1.52. Does the light exit the glass object with the same angle as it entered? Justify your answer.
   {14018_Answers_Figure_7}
   Yes, the light exits the glass object with the same angle it entered. Calcuating the angles with Snell’s law gives θ₁ = θ₄.
4. Lenses can be approximated using simple geometric shapes. Using Snell’s law, finish drawing the ray diagrams for the convex and concave lenses. Identify the lenses 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).
   {14018_Data_Figure_8}
   This is a converging lens. The refracted rays come to a point on the opposite side of the lens as the very distant object.
   {14018_Data_Figure_9}
   This is a diverging lens. The refracted rays do not come to a point on the opposite side of the lens as the very distant object. Extensions of the refracted rays come to a point on the same side as the object.
5. Using the definitions of “real” and “virtual” provided in the Background, classify the focal points for the convex and concave lenses in Question 4.

   The light rays converge at a “real” focal point for the convex lens. The rays come to a point on the side opposite the object. The light rays diverge from the concave lens. When the rays are traced back, the “traced rays” come to the “virtual” focal point. It will appear as though the diverging rays originate from the same side as the object.

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

   Only the focal point of the convex lens could be experimentally determined or measured using a single lens. Because the refracted rays converge to a point in real space, a screen could be placed some distance away from the convex mirror until a clear image of the distant object appears. The distance from the lens to the screen is the focal length of the lens. The focal point of the concave lens cannot be measured because it is a virtual point, residing on the same side as the object.

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

         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

      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 opposite side of the lens and can be projected onto a screen.

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

         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 on the same side of the lens as the object.

8. Design an experiment to determine the focal lengths of the convex and concave lenses, where possible. Figure 2 shows a general setup for meter stick optics investigations.

   There are two methods by which the focal length of the convex lens may be determined. The focal length of the concave lens cannot be determined using the setup in Figure 2.
   
   Method A

   1. Set up the meter stick with the lens and screen as seen in Figure 2.
   2. The lens and screen should be oriented such that an image can be cast from the window on to 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 lens and the screen is the focal length.

   Method B

   1. Set up the meter stick with lens and screen as seen in Figure 2.
   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 until a clear image of the candle’s flame can be seen on the screen. Record the distance between the center of the lens and the screen.
   4. Use Equation 1 to solve for the focal length of the lens.
9. After finding the focal lengths of the lens(es), predict the image distance when an object is placed on the meter stick. Record the object distance, and predicted and actual image distances.

   Sample calculation:
   1/f = 1/d_O + 1/d_I
   1/9.99 cm^–1 = 1/25 cm^–1 + 1/d_I
   1/d_I = 0.0601 cm^–1
   d_I = 16.6 cm

Review Questions for AP Physics 2

1. Examine the diagram of a light ray as it passes between multiple media.
   1. Rank the indices of refraction, from smallest to largest.

      n₂ < n₃ < n₁

   2. Explain how you made your determinations.

      At the interface between substance 1 (n₁) and substance 2 (n₂), the light ray refracts at a larger angle. The ray bends away from the normal line. This indicates that n₂ is less than n₁. At the next interface between n₂ and n₃, the light ray bends towards the normal, creating a smaller refracted angle. This indicates that n₂ is less than n₃. At the final interface between n₃ and n₁, the light ray bends towards the normal, making a smaller refracted angle. This shows that n₃ is less than n₁. Combining all three comparisons together provides the answer of: n₂ < n₃ < n₁.

2. The following figure shows an object, arrow W, in front of a thin, symmetric lens that can be mounted within the dashed space, L. The lens 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.
   {14018_Answers_Figure_10}
   1. Which image(s) could not possibly be formed by either a concave or convex lens? Cite evidence from the experiment to support your answer.

      Images I₁ and I₃ could not possibly be formed by a concave or convex lens. In the experiment, a concave lens only produced virtual, upright images. A convex lens formed two possible images: a virtual, upright image or a real, inverted image, depending on the distance separating the lens and object. I₁ is a real, upright image and not an image observed in the experiment. I₃ is a virtual, inverted image and not an image observed in the experiment.

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

      A convex lens forms two possible images: a virtual, upright image or a real, inverted image, depending on the distance separating the lens and object. I₂ is on the opposite side of the lens as the object and is a real image. It is oriented in the opposite direction of the object arrow, W. Therefore, I₂ could be the real, inverted image formed by a convex lens. I₄ is on the same side of the lens as the object and is a virtual image. It is oriented in the same direction as the object arrow, W. Therefore, I₄ could be the virtual, upright image formed by a convex lens.

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

      A concave lens only produces virtual, upright images. I₄ is on the same side of the lens as the object and is a virtual image. It is oriented in the same direction as the object arrow, W. Therefore, I₄ could be the virtual, upright image formed by the convex lens.

   4. There is one image that is shared between the concave and convex lenses. Based on your answers to parts b and c, is additional information needed in order to determine if that image was formed by a concave or convex lens? Use evidence from the experiment to support your answer.

      Image I₄ could be produced by both concave and convex lenses. The height of the object arrow, W, and the height I₄ could be used to distinguish between the lenses. A concave lens produces virtual, upright images that are smaller than the actual object, regardless of the object distance. A convex lens produces virtual, upright images that are larger than the actual image when the object is placed inside the focal length of the lens.

3. A human eye has a lens that can be reshaped by the contraction and relaxation of muscles surrounding it. The effect of doing this allows objects at varying distances to be brought into focus on the retina (light-sensing organ in the rear of the eye). The distance between the center of the lens and the retina is 2.4 cm on average.
   1. A student predicts that the human eye contains a convex lens. Do you agree or disagree with this prediction? Justify your answer.

      The student’s prediction is correct. A convex lens will converge the light entering the eye to fall upon the retina, allowing an image to be seen. A concave lens would diverge the light entering the eye and not form a coherent image on the retina.

   2. The eye described above is staring off at a very distant object. What is the focal length of the lens? Explain.

      The light coming off of a very distant object can be thought of as parallel light rays. When parallel light rays enter a convex lens, the rays converge to form an image at the focal point. In this case, the image must form at the retina in order for the object to be seen. The image distance is 2.4 cm. The object distance can be considered infinity (∞). Plugging these values into Equation 1 results in: 1/ f = 1/∞ + 1/2.4 cm^–1. The inverse object distance turn is considered to be zero (0). Therefore, 1/ f = 1/2.4 cm^–1; f = 2.4 cm.

   The object is repositioned to be 30.0 cm away from the eye. The muscles surrounding the lens respond and change its shape.
   3. Using Equation 3, qualitatively predict whether the focal length of the lens increases or decreases when the object is brought closer. Confirm your prediction with a calculation of the new focal length.

      When the object was placed at an infinite distance, equation 1 reduced to: 1/f = 1/d_I, because 1/d_O was considered to be zero (0). The image distance remains constant at 2.4 cm, so the 1/d_I term remains constant. When a non-infinite value is used for the object distance (d_O), the right side of Equation 1 increases in value. In order for the left side of the equation to remain equal, the value of the focal length must change. Because the right side increased in value, the focal length must decrease because the inverse of a smaller number is larger.
      1/f = 1/30 cm^–1 + 1/2.4 cm^–1
      f = 2.2 cm
      The calculated focal length agrees with the predicted change.

   4. A student states, “The lens doesn’t change shape and therefore the focal length remains the same. The length of the eye increases or decreases based on where the object is located.” Do you agree or disagree with this statement? Justify your answer by explaining an analogous setup from the experiment.

      The student’s statement is incorrect. In the experiment, the focal length of the lens was constant. When an object was placed some distance away, the screen position was adjusted until a clear image was captured. In the experiment, the screen was able to be moved until the image appeared. In a human eye, the retina at the rear of the eye is the screen. However, the retina cannot be moved around to capture the image. The distance between the lens and the retina is constant (2.4 cm). Therefore, in order to capture an image on the retina, the focal length of the lens must change. This would be similar to keeping the screen and lens the same distance apart, and changing the lens until an image appeared.

4. Chromatic aberration can sometimes be seen in photographs around the edges of the picture. Objects in the photograph will often have a colored silhouette surrounding them. The following figure demonstrates what occurs when white light refracts through the outer edge of a lens in a camera.
   {14018_Answers_Figure_11}
   1. Propose a hypothesis of what causes chromatic aberration when light passes through a thin lens.

      White light is composed of all of the colors of the visible light spectrum. The figure is showing parallel rays of white light entering the convex lens and refracting through to the other side. However, the white light is split into three separate colors: red, green, and blue. The three colors do not converge at one point. Instead, the red rays converge farther down the axis than the green rays which are farther down the axis from the blue rays. Because the refracted rays are leaving the lens at different angles, it can only be assumed that the indices of refraction for the colors (red, green, and blue) are different when passing through the glass lens.

   2. Using the figure, rank the indices of refraction for the blue, green and red light in increasing order.

      The blue ray refracted the most and bent the farthest from the normal. The red ray refracted the least and bent the least from the normal. The green ray is somewhere in between the blue and red ray.
      n_red < n_green < n_blue

Teacher Handouts

14018_Teacher1.pdf

References

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

Introduction

When looking at a fish in water, the location of the fish is not the same as where you see it. Light rays reflect from the fish and bend as they pass from water into air. This same phenomenon is utilized to make corrective lenses in eyeglasses. Investigate how light rays refract using Snell’s law.

Concepts

• Refraction
• Concave versus convex lenses
• Snell’s law
• Real versus virtual images

Background

When light hits a boundary between two different substances, three phenomena can occur—reflection, absorption and/or transmission. Reflection is when a wave bounces off a surface, such as when light strikes a mirror. Absorption is when light is retained in a substance and changed into another type of energy such as heat. A classic example of this is a black surface becoming extremely hot on a summer day. The black surface absorbs light energy that is then converted into heat energy. Transmission is when light strikes a new substance and then continues to travel through that substance, such as light that travels in air then passes into water. Most of the time when light strikes a surface, all three phenomena will occur simultaneously. This is why, when looking out a window, you will often see a faint reflection of yourself while still being able to see through the window. In this case, reflection and transmission are both occurring.

This lab activity focuses on the transmission of light. As light is transmitted, refraction often occurs. Refraction is the bending of a wave that occurs when it enters a new substance. This bending occurs because the speed of light changes when it passes from one substance to another due to a difference in the densities of the two substances. The accepted speed of light in a vacuum and in air is about 3 x 10⁸ m/s. When light travels from air into a substance with a higher density, the speed of light will decrease, and vice versa. The speed of light in a substance other than air can be calculated using Equation 1. In order to use this formula, the index of refraction (n) for the substance must be known.

n = index of refraction
c = speed of light in a vacuum
v = speed of light in a substance

In 1621, Dutch astronomer and mathematician Willebrord Snellius (1580–1626) came up with a quantitative law of refraction, which is known today as Snell’s law. Equation 2 represents Snell’s law where n₁ and n₂ are the indices of refraction for the substances on either side of a boundary, θ₁ is the angle of incidence, and θ₂ is the angle of refraction.

n₁ = index of refraction for substance 1
n₂ = index of refraction for substance 2
θ₁ = angle of incidence
θ₂ = angle of refraction

Figure 1 represents a ray of light traveling from air into water. If three of the values in this formula are known, the fourth can then be calculated. This formula can therefore be used to find the index of refraction for an unknown substance, but only if the index of refraction (n) for the other substance is known. Once the index of refraction (n) for the unknown is found, the speed of light in this substance can be calculated using Equation 1. When multiple light rays refract through a thin lens, the rays either converge or diverge from the central axis. When refracted rays converge, the rays come to a point somewhere on the opposite side of the lens than the object. That is to say, a screen could be placed at that point and the refracted image could be seen. The refracted image is called a real image because it forms on the side of the lens opposite the object and can be projected. When a lens causes light rays to diverge, the rays appear to originate from the same side of the lens as the object. The image formed by a diverging lens cannot be projected onto a screen and is therefore called a virtual image.

Three important values when working with lenses are the focal length (f), object distance (d_O) and image distance (d_I). Equation 3 allows for the third value to be solved so long as the other two values are known. By convention, the sign of the object distance is positive. For calculations, the focal length is considered positive if the refracted rays come to a point on the side of the lens opposite the object and is called a real focal point. The focal length is considered negative if the refracted rays come to a point on the same side of the lens as the object and is called a virtual focal point. A thin lens that is curved on both sides will have two focal lengths. If the image is real, the image distance is positive. A virtual image has a negative image distance.

Experiment Overview

The purpose of this advanced inquiry lab is to design a procedure to identify the properties of lenses, both concave and convex. The lab begins with an introductory activity to investigate Snell’s law using a gelatin-filled dish and laser pointer. You will draw the rays of incidence and refraction and compare the angles. Then a series of guided-inquiry questions lead to predictions of the focal lengths of concave and convex lenses, and the location and type of images formed. An experiment will be designed to test these predictions.

Materials

Prelab Questions

1. What is the speed of light in a vacuum? In air?
2. Using Equation 1 and the answers to Question 1, calculate the index of refraction (n) for light in air.
3. Using Equation 2, the answer to Question 2, and the angles given in Figure 1, calculate the index of refraction for light in water (n₂).
4. Using Equation 1 and your answer, calculate the speed of light in water (v).
5. Compare the speed of light in water to the speed of light in air. In which substance is the speed of light slower?

Safety Precautions

Do not aim the laser pointer directly into anyone’s eyes. The low-power, coherent light can cause damage to the sensitive retina and may lead to permanent eye damage. Prevent stray laser light from projecting beyond the classroom to eliminate any unintentional exposure to the laser light. When refracting the laser light, it is best to do this on a low work surface to keep the refracted laser light below “normal” eye level. For people with sensitive eyes, it is recommended that dark, IR-protective safety glasses be worn. 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 non-essential items. Do not leave burning candles unattended. Follow all laboratory safety guidelines.

Procedure

Introductory Activity

1. Place a semicircular dish containing gelatin on the protractor paper so the dish is on the opposite side of lines A–G. Make sure the center of the dish is at the intersection of 0° and 90°.
2. Open a manila folder and stand it vertically at the round side of the semicircular dish. The manila folder should act as a backstop for the laser light.
3. Place the laser pointer on the line labeled A 10°. Squeeze the button on the pointer and aim the laser beam at the intersection of 0° and 90°.
4. Observe the laser beam travel from the air into the gelatin. Using a pencil, place a mark on the sheet where the laser light exits the gelatin on the curved side of the dish. Write A1 next to this mark.
5. Repeat steps 3 and 4 for the incident angles B–G marked on the diagram. Label where the laser light exits as B1–G1.
6. Remove the semicircular tray, and draw a line from the intersection of 0° and 90°, to the mark labeled A1, where the laser light exits the water.
7. Repeat step 6 for the pencil marks labeled B1–G1.
8. Record each refracted angle (A1–G1) in the proper section of the data table.
9. Place a semicircular dish containing gelatin on the protractor paper so the dish covers lines A–G. Make sure the center of the dish is at the intersection of 0° and 90°.
10. Repeat steps 2–7. For this experiment, light travels from the gelatin into the air. Remember to set up the manila folder. This folder should act as a backstop for the laser light. It will also help to see where the light exits the gelatin. Adjust the manila folder as you proceed from points A to G in order to make sure that laser light does not travel beyond your work area toward others.

Analyze the Results 

• Organize the collected data into a data table.
• For each ray/line, determine the index of refraction for gelatin, as well as an average index of refraction for gelatin. Hint: See the Prelab Questions for the index of refraction for light in air.
• Calculate the average speed of light in gelatin. How does this speed compare to the speed of light in air?

Guided-Inquiry Design and Procedure

1. Why was it important to aim the laser at the intersection of 0° and 90°? Consider the path of the light as it travels through the semi-circular dish.
2. Based on the observations and data collected in the Introductory Activity, did the laser beam refract more when it traveled from air to gelatin or gelatin to air? Justify your answer and include a comparison of the speed of light in the two media.
3. Trace the path of light as it travels through air into glass into air. The index of refraction of the glass is 1.52. Does the light exit the glass object with the same angle as it entered? Justify your answer.
   {14018_Procedure_Figure_5}
4. Lenses can be approximated using simple geometric shapes. Using Snell’s law, finish drawing the ray diagrams for the convex and concave lenses below. Identify the lenses 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).
   {14018_Procedure_Figure_6}
5. Using the definitions of “real” and “virtual” provided in the Background, classify the focal points for the convex and concave lenses in Question 4.
6. If possible, explain how the focal points for the lenses could be experimentally determined or measured.
7. Using the information from the Background, answer the questions about the following lenses.
   1. Convex lens – focal length = 15 cm
      1. What is the image distance of an object 25 cm away from the lens?
      2. Is the image real or virtual?
   2. Concave lens – focal length = 15 cm
      1. What is the image distance of an object 25 cm away from the lens?
      2. Is the image real or virtual?
8. Design an experiment to determine the focal lengths of the convex and concave lenses, where possible. Figure 4, shows a general setup for meter stick optics investigations.
   {14018_Procedure_Figure_4}
9. After finding the focal lengths of the lens(es), predict the image distance when an object is placed on the meter stick. Record the object distance, and 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 data and observations in a coherent data table(s).
• Compare the properties of concave and convex lenses.
• Do the object distance, image distance, and focal length values agree with Equation 3 in the Background? Explain any discrepancies.
• Were there any object distances that resulted in no image formation? For which lens did this occur? What does this distance represent for the lens? Explain why this occurred.

Student Worksheet PDF

14018_Student1.pdf