Basic Optics lab for AP Physics

Physics                     Name________________________________

Stirring Up the Alphabet            Teacher______________________Pd______

 

 

1. Place a clear glass stirring rod directly over the phrase HIDE the COOKIE in the BOX

Write down your observations:

 

 

 

 

 

 

2. Raise the stirring rod slowly above the letters.

 

(a) How does the image of the letters change?

 

 

 

 

 

(b) Is there a single distance from the paper that the letters invert?

 

 

 

 

 

 

(c) Why are some letters inverted and some are not?

 

 

 

 

 

 

4. (a) Would a larger stirring rod invert the letters at the same distance as the smaller stirring rod? As far as the light is concerned, what would be different about a larger stirring rod?

 

 

 

 

 

 

(b) What would happen if you used two stirring rods? Try it.

Reflection of Light

Studying the Image Formed by a Plane Mirror

When a ray of light is incident on a mirror, the angle of incidence of the ray is equal to the angle at which it is reflected from the surface of the mirror. This phenomenon is called the law of reflection. Both angles are measured from a line drawn perpendicular from the surface of the mirror called the normal line.

 

Because of the law of reflection, if you can see your friend in a mirror, your friend can see you as well.

When you see your face in a plane mirror, the image is upright and left-right reversed, but no larger or smaller than your actual face. We say that the image is formed behind the mirror and is virtual. A virtual image is one that cannot be projected onto a screen, and can be located by drawing rays representing the light and extending them to a point where they intersect. In this activity, you will draw the ray diagram for a plane mirror, locating the image of a ball-tipped pin.

Purpose

The purpose of this activity is to produce an image formed by a plane mirror, and locate and describe that image.

Materials

ruler	sheet of 8.5"x11" paper
plane mirror	protractor
piece of cardboard	4 ball-tipped pins
block of wood	rubber band

 

 

 

Procedure

• Using your ruler, draw a line lengthwise across the center of the sheet of paper. You will eventually draw your ray diagram on this sheet of paper.
  
• Place the sheet of paper on the piece of cardboard, and the mirror upright on the line across the center of the paper. It may be helpful to secure the mirror to a block of wood with a rubber band so that the mirror will stand upright on its own.
  
• Place a pin approximately 5 cm in front of the left side of the mirror, and a second pin up against the mirror about halfway along its length.
  

 

• Using a third pin, designated Pin 3, line up pin 2, pin 3 and the image of pin 1 in the mirror. Draw a line segment connecting pin 1 and pin 2 (the incident ray). Draw another segment connecting pin 2 and pin 3 (the reflected ray).
  
• Move pin 2 about 3 cm to the right and repeat step 4. Your diagram should look similar to Figure 3 shown below.
  

 

 

 

 

 

 

Reflection of Light

Studying the Image Formed by a Plane Mirror

Analysis

1. Using the reflected rays on your ray diagram and a straight edge, determine the location of the image of the object pin (pin 1). Be sure and show the rays on your diagram that allowed you to locate the image.

2. What kind of image is formed by the plane mirror? What are some other characteristics of the image?

 

 

3. The object distance d_o is the perpendicular distance from the surface of the mirror to the location of the object (pin 1), and the image distance d_i is the perpendicular distanced from the surface of the mirror to the point at which the image is formed. How does the object distance compare with the the image distance? Make measurements, and justify your answer with your data. Label the object distance and image distance on your diagram.

 

 

 

4. Use your protractor to draw the normal line at each of the two points of reflection on the surface of the mirror. Measure the angle of incidence and angle of reflection for both reflections, and label the angles on your ray diagram.

 

 

5. Do the angles of incidence and reflection you measured and labeled verify the law of reflection? Justify your answer.

 

 

 

 

Conclusion Questions

1. Reflection from a rough surface (like this paper) is called diffuse reflection. Light rays which strike the rough surface parallel to each other are reflected from the surface at various angles, as shown in Figure 4 below.

 

Explain the reason why you cannot see your reflection in a piece of white notebook paper. Relate your answer to your ray diagram of the plane mirror.

 

 

 

 

2. A girl stands in front of a plane mirror mounted to a wall. The top of the mirror is mounted to the wall at the same height as the top of the girl's head. Compared to the girl's height, how long does the mirror have to be to show an image of her entire height? Sketch a ray diagram to justify your answer.

 

Finding the Index of Refraction and the Critical Angle

Light and matter appear quite different, however, there must be an underlying connection at some level because they interact with each other. Interaction implies some fundamental relationship between them. To observe and verify this interaction between light and matter, you will determine the index of refraction of water and the critical angle of water.

In any homogeneous material, light travels in straight lines. When light encounters a boundary (a change in optical medium) some of the light reflects back obeying the law of reflection and some of the light is transmitted into the new medium. The transmitted light does not travel in the same direction as the original light. Instead it is bent (refracted) at the boundary and travels in a different direction. This phenomenon is called refraction.

 

The refraction of light at the interface between two materials is described mathematically by Snell's Law. In Figure 1 above, the long dashed line represents the normal, a line perpendicular to the surface. The angle θ measures the angle of incidence relative to the normal. The angle measures the angle of refraction relative to the normal. Snell's Law avers:

 

The quantity n_i
is the index of refraction for the medium in which the light was incident. The quantity is the index of refraction for the medium in which the light was refracted. The index of refraction n of a material is a measure of the speed of light in that medium. It is defined as the ratio of the speed of light in vacuum to the speed of light v in the medium.

 

The index of refraction of vacuum is 1. The index of refraction of air, which depends somewhat on the temperature and density of the air, is very nearly 1 as well. We will use this approximation for the index of refraction of air.

The phenomenon of total internal reflection occurs when the light travels from a medium with a higher index of refraction to a medium with a lower index of refraction. When , the refracted ray bends away from the normal. If the angle of incidence is large enough, the angle of refraction will be 90˚ and the light travels parallel to the interface between the two media. The angle of incidence for which this occurs is called the critical angle. If the angle of incidence is increased further, then the calculated value of the angle of refraction is greater than one which is mathematically impossible! Nature does not want to flunk mathematics, so how can this dilemma be solved? At the critical incident angle, the light does not pass through the surface, it reflects off the surface, such that the surface becomes a mirror and obeys the law of reflection. Therefore, the critical angle for light passing from a more dense medium of to a less dense medium of , where , is

 

The phenomenon of total internal reflection is important in numerous fiber optic technologies, from communication to surgical procedures. Total internal reflection explains how light (and information) can be transmitted great distances with little loss of energy.

Purpose

In this activity you will investigate the refraction of light as it passes from water into air. Measurements of the angle of incidence and the angle of refraction, along with the critical angle will be utilized to determine the index of refraction of water.

Materials

laser pen	semicircular plastic dish
water	paper
protractor or polar graph paper	viewing screen or backing paper
metric ruler

 

Safety Alert

1. Caution—do NOT look into the laser and do NOT direct the laser at others.

 

 

• Place the Index of Refraction Worksheet on a flat surface or table. Fill a semicircular dish with water and center the semicircular dish on the outline of the dish.
  
• Sprinkle a small amount of non-dairy creamer on the water. Just as sprinkling chalk dust in the air will make the laser beam visible in the air, so a small amount of non-dairy creamer will make the laser beam visible in the water.
  
• The dish has an etch mark on its flat side at the center of the semicircle. Shine the laser into the dish through the curved wall of the dish. Aim the beam so that it hits the etch mark on the flat wall of the semicircle. Vary the angle beginning with an incidence angle of 5˚ and approaching 90˚, by moving the laser pen around the curve of the dish. Always shine the laser perpendicular to the curved wall so that the beam strikes the etch mark (midpoint) of the flat wall. Place a viewing screen or some backing paper opposite the flat wall of the dish and perpendicular to the flat surface or table. The purpose of the viewing screen or backing paper is to help you locate the exit point of the laser beam and measure the angle of refraction for a given angle of incidence.
  
• Draw a ray on the worksheet from the center of the semicircle (the etch mark on the flat surface) through each of the angles of refraction and extend it to the margin of the paper. Draw an arrowhead on each incident ray and all the refracted rays you used showing the path of the light. Measure the angle that the refracted rays make with the normal and record them in the data table. Fill in as much of the table as possible. Use the data and Snell's Law to determine the index of refraction.
  
• Move the laser pen around the curved surface of the semi-circular dish and observe the phenomenon of total internal reflection. At some position, the light ray exiting the flat side will reach an angle of 90˚ and then reflect back out the curved side of the dish. When the refracted angle reaches 90˚ draw a line along the flat side of the dish (parallel to the interface between the air and the water). Draw a line perpendicular to and through the center of the flat side of the dish. Measure the incident and reflected angles. The angle of incidence (which should also be the angle of reflection) is the critical angle. Determine the index of refraction for the water using the relationship:
  

 

 

 

 

 

Refraction of Light

Finding the Index of Refraction and the Critical Angle

 

Data and Observations

Index of Refraction Worksheet

 

 

θwater	θair	sin θwater	sin θair	nwater
5˚
10˚
15˚
20˚
25˚
30˚
35˚
40˚
45˚
50˚
55˚
60˚
65˚
70˚
75˚
80˚
85˚

 

 

Critical angle = _____________˚

 

 

Analysis

1. Calculate the index of refraction of water for each incident angle using Snell's Law. Record your values for n_water in the Data Table. Average all of your measurements. Calculate your % error. The accepted value for the index of refraction for water is 1.33.
   

 

 

 

 

 

Average of all your measurements: n_{wate r}= _____________        %Error = _____________

 

1. On the axes below, plot a graph of sin θ_air (y-axis) vs. sin θ_water (x-axis). Be sure to sure to use proper graphing techniques, including a title, scaling, and labeling the axes, and drawing the best-fit curve that represents the average of the data.
   

 

1. Calculate the index of refraction from the slope of the graph.
   

 

 

 

 

 

 

Graphical Estimate of n_water = _____________    %Error = ___________

1. In the space provided calculate the index of refraction for water and your % error.
   

 

 

 

 

Critical angle= _______˚     n_water(from the critical angle) = ____________    %Error =____%

1. Using n_water = 1.33, determine the velocity of light in water.
   

 

 

 

1. If a medium has a large index of refraction, what does that say about the speed of light in that medium? What can you say about the way the light ray bends in relation to the perpendicular (or the normal) to the surface to the media?
   

 

 

1. What happens when light travels to a medium of lower refractive index?
   

 

 

1. Will light be refracted more while passing from air into water or while passing from water into glass? Explain.
   

 

 

 

1. Will light traveling from air into water undergo total internal reflection? Explain.
   

Conclusion Questions

• A diligent physics student is given the following equipment: a transparent acrylic cube, a visible-spectrum laser, a metric ruler, a protractor, and a viewing screen. Her instructor asks her to devise a method to measure the index of refraction of the transparent solid. After much reflection, the lights come on and she readily measures the index of refraction of the transparent solid. Describe in detail how she determined the index of refraction. The results of her illumination are shown in the two diagrams below. P₂ is the path of the light from the laser through the air and P₁ represents the path of the light through the transparent cube.
  

 

 

 

 

 

 

 

 

 

 

 

• Use Snell's Law to determine the path of the light through this rectangular sheet of glass (=1.50). Draw a normal, perform the appropriate measurements and calculations for the entry point and draw the refracted ray for the light entering the glass. Continue the ray to the opposite side, draw a normal, perform the appropriate measurements and calculations for the exit point and draw the refracted ray for the light exiting the glass. Please show all your calculations in the space below.
  

 

 

 

 

• Use Snell's Law to determine the path of the light through the triangular glass (). Draw a normal, perform the appropriate measurements and calculations for the entry point and draw the refracted ray for the light entering the glass. Continue the ray to the opposite side, draw a normal, perform the appropriate measurements and calculations for the exit point and draw the refracted ray for the light exiting the glass. Please show all you calculations in the space below.
  

 

 

 

 

 

 

• In our experiment, the beam of light actually passed through three different media (air, plastic, and water). We assumed that the interaction of the light with the plastic could be ignored. Is that assumption reasonable or is it an additional source of error? We will examine this question by imagining three media in layers as shown in the diagram below. The beam passes from air into medium X and then from medium X into the water. There are four angles to measure. Use your knowledge of geometry and Snell's Law to find the relationship between angles 1 and 4. Given that relationship, how important is it to find the index of refraction of X, assuming we are interested in knowing the index of refraction of the water?
  

 

 

Convex Lens and Concave Mirror

Studying the Images Formed by Converging Optical Devices

Concave mirrors and convex lenses cause light rays to converge. A convex lens converges parallel rays that pass through it such that they intersect at the focal point. Likewise, a concave mirror causes incident light rays parallel to its principal axis to converge at the focal point. Hence converging lenses and mirrors may produce real images, virtual images, or no images. Light rays actually pass through real images, which can be projected onto a viewing screen. Virtual images cannot be projected onto a screen and in the case of a mirror appear behind the plane of the mirror. In the case of a lens, a virtual image appears on the same side of the lens as does the object.

In similar fashion, both converging lenses and mirrors create images that can be upright or inverted, larger or smaller in size, or the same size as the object. The position and characteristics of the image depend upon the location of the object relative to the focal length of the lens.

The relationship between the object distance d_o, the image distance d_i, and the focal length f of a lens or mirror is given by the fundamental lens/mirror equation.

 

Purpose

In this activity you will describe the position and characteristics of images produced by converging lenses and mirrors. In addition, you will measure the focal length of the convex lens and the concave mirror.

Materials

2 meter sticks	masking tape
convex lens	concave mirror
small cardboard screen	light source or candle
holders for screen, light source, lenses, & mirrors	sunlight or flashlight or image projected on screen from overhead

 

Safety Alert

1. Do not look directly at the sun with either optical device since this can cause severe damage to your eyes.
2. If using the candle as a light source, tie hair back and keep it away from the flame.
3. If using the light source, care should be taken when using electrical equipment.

 

 

Procedure

Part I

• Find the focal length of your lens by arranging the lens, meter stick, and screen as shown in Figure 1 below. Point the lens at a distant object and move the screen back and forth until you obtain a clear, sharp image of the object on the viewing screen. The distance between the lens and the screen is the approximate focal length of the lens. Record your measurement of the focal length on the student answer page.
  
• Place the light source at each of the distances listed on your student data table. Move the screen back and forth until a clear, sharp image is formed on the screen. See Figure 2 below.
  
• Record the object distance, the image distance, and whether the image is real or virtual, upright or inverted, and smaller, larger, or the same size as the object.
  
• If you are unable to focus a clear image on the screen, the image is either virtual or there is no image. If the image is virtual you may look back through the lens and see an enlarged image of the object.
  
• Using a ruler, draw the ray diagrams to scale for each of the five scenarios. Label the object, image, and all distances.
  

  
   

  
   

Part II

 

1. Find the focal length of your concave mirror by arranging the mirror, meter stick, and screen as shown in Figure 3. Point the mirror at a distant object and move the screen until you obtain a sharp image of the object on the screen. The distance between the mirror and the screen is the approximate focal length of the mirror. Record your measurement of the focal length on your student answer page.
   

 

1. Place the light source at each of the distances listed on your student data table. Move the screen back and forth until a clear, sharp image is formed on the screen as shown in Figure 4 below. Use a piece of masking tape to hold the meter sticks in place.
   

 

1. Record the object distance, the image distance, and whether the image is real or virtual, upright or inverted, and smaller, larger, or the same size as the object.
   
2. If you are unable to focus a clear image on the screen, the image is either virtual or there is no image. If the image is virtual you will see the enlarged image behind the plane of the mirror.
   
3. Using a ruler, sketch the ray diagrams for each of the five scenarios. Label the object, the image, and all distances.
   

 

 

 

 

 

Convex Lens and Concave Mirror

Studying the Images Formed by Converging Optical Devices

 

Data and Observations

 

 

Convex Lens focal length _______ (cm)

Object placed at:	Object distance do(cm)	Image distance di (cm)	Real or virtual	Upright or inverted	Enlarged, reduced, or same size

 

 

 

 

 

 

 

Concave Mirror focal length ______ (cm)

Object placed at:	Object distance do(cm)	Image distance di (cm)	Real or virtual	Upright or inverted	Enlarged, reduced, or same size

 

Analysis

1. Ray Diagrams for Convex Lens
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. Ray Diagrams for Concave Mirror
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. Use your data to summarize the characteristics of images formed by converging lenses and mirrors in each of the following situations.
   

• The object is located beyond the center of curvature.
  

  
   

  
   

  
   

  
   

• The object is located at the center of curvature.
  

  
   

  
   

  
   

  
   

• The object is located between the center of curvature and the focal point.
  

  
   

  
   

  
   

  
   

• The object is located at the focal point.
  

  
   

  
   

  
   

  
   

  
   

• The object is located inside the focal point.
  

  
   

  
   

  
   

  
   

  
   

1. For each of the real images you observed, use the lens equation to calculate f . Do your calculated values agree with each other?
   

   
    

   
    

   
    

   
    

   
    

   
    

   
    

   
    

2. Average the values of f that you previously calculated. How does your average focal length compare with the measured value for f recorded in the convex lens data table?
   

   
    

   
    

   
    

   
    

   
    

   
    

   
    

   
    

3. For each of the real images you observed, use the mirror equation to calculate f. Do your calculated values agree with each other?
   

   
    

   
    

   
    

   
    

   
    

   
    

   
    

   
    

4. Average the values of f that you previously calculated for the concave mirror. How does your average focal length compare with the measured value for f recorded in the concave mirror data table.
   

    

Conclusion Questions

1. An object, initially at a distance of 3f from a concave mirror is moved toward the mirror. Sketch the image distance as the object distance moves from 3f to 0.
   

 

 

 

 

 

 

 

 

 

 

 

 

 

1. Discuss how the graph would change if a convex lens were used rather than a concave mirror.
   

 

 

1. What would happen to the image if no light was allowed to enter the top half of the lens?
   

 

 

Would the focal length of the lens increase, decrease, or remain the same if the lens were submerged in water? Explain your reasoning.