Phys 1020 Lab 4: LENSES, Optics

NOTE: PRE-LAB ASSINGMENT is at the end of the lab description.

Lab Logistics:

You and your group will work together to complete the lab and write up the group lab report.  Remember, everyone will need to assume a new job.  For instance, if you were the manager for Lab 1, then you should either be the recorder or the skeptic for this lab.  Again, everyone should be helping with the hands-on stuff.

o The manager: This person is responsible for making sure that the group follows the lab procedure and completes everything that is asked for in the lab.

o The recorder: This person is responsible for keeping the lab notebook for the day, recording the observations observed by the group and the group’s answers to the questions asked in the lab. 

o The skeptic: This person is there to question the results of the lab.  Is everything making sense? Are we taking the data correctly?  Are the results and conclusions reasonable?  Did we skip a step?

Begin each lab report by titling the lab, listing your lab partners who are present, and listing the jobs that each lab partner has assumed for the lab. Remember, your lab report should give an explanation of all of your observations and measurements.   Also, you need to think of and try one additional experiment for either Part 1, 2, or 3 of this lab that will further test your explanation of the results that you found. 

INTRODUCTION

Lenses are the basis of many modern optical instruments, such as microscopes, telescopes, cameras, and eyeglasses. In this experiment, you will work with two lenses. You will measure their focal lengths in several ways and study the magnification (how much the image of the object is smaller or larger than the object itself). Finally, you will use both of them to measure the chromatic aberrations (differences between how the lens bends red light and how it bends blue light) of one of the lenses.

The main properties of any thin lens are summarized by the thin lens equation:

1 = 1 + 1 .

focal length distance to object distance to image

In this equation, f is the focal length of the lens and is positive for converging lenses (which you will be using in this experiment) but negative for diverging lenses. As shown in Fig. 1, d_o is the distance from the object to the lens, and is counted positive for real objects (which is all we shall ever consider). Similarly, d_i is the distance from the image to the lens and is counted positive for real images (as in Fig. 1) but negative for virtual images. (A virtual image is created when the rays of light from a point on the object are still diverging once they pass through the lens. These exit rays will appear as if they are coming from a point behind the lens.)

Fig.1. The distances d_o and d_i that appear in the lens equation, illustrated for the case of a real image produced by a converging lens. The two points labeled F are the focal points of the lens.

Part I: Focal lengths and Magnification factors

The first part of this lab is to find the focal lengths of lens A by measuring values of d_i and d_o and using eq. (1) to calculate the focal length.

1) Use the lighted object and lens A to create an image of the object (in focus) on the frosted glass screen. Is the image larger, smaller, or the same size as the object?

2) For lens A, make three sets of measurements of d₀, h₀, d_i, and h_i. h₀ is the height of the object and h_i is the height of the image. Between each set, adjust the distance between the object and the lens. Make sure you have at least one measurement where the image is smaller than the object and one where it is bigger than the object. Using the lens equation above, find f for each lens.

3) In figure 1, the image is larger than the object. Using Figure 1 as a model, draw a similar sketch which shows the object location and light rays that would form an image smaller than the object. You drawing should show the lens, the focal point of the lens, the object location, the light rays coming off one point on the object, and where the image will be formed by those rays. Note in Figure 1 the light rays shown are coming from the object passing through the lens and where they cross they will form the image in focus. The three rays drawn are special since we know how they will bend using the following guidelines:

a. When light rays come in parallel to the axis of the lens, they are bent by the lens such that they pass through the focal point

b. Rays that pass through the focal point of the lens before hitting the lens are bent by the lens such that they exit all parallel to the axis of the lens

c. Rays that pass through the very center of the lens exit the lens going in the same direction they were going originally.

4) As you bring the object closer and closer to the lens does the image get smaller or larger? At what distance will the lens no longer create an image in focus? Why? Make sure you make a prediction before you try it.

5) Use your measurements of the sizes of h_o and h_i of the object and image and compute the magnification of the object for one of the measurements you made:

Referring to Fig. 1 and using the fact that with similar triangles (all the angles the same) the ratio of the sides are also the same (e.g., di/hi=do/ho), you can see that M is also equal to

Using your measurements, check the agreement between these two expressions for M. (So, if you know the image and object distances, you know the magnification!)

Part II: Alternate Methods to Part I

The second part of this experiment is to measure the focal length for all three lenses.

6) How can you arrange a lens and a point source so that the rays that are coming out are parallel with respect to the source? Use lens A and the point source (remove the arrow cover) so that the rays are coming out of the lens all parallel as in Figure 2. Recreate figure 2, being careful to identify where the 2 focal points are.

Fig. 2. When a converging lens produces a parallel beam of light we say that the light is collimated. This happens when the source is at the lens's focal point (d_o = f). You can check that the light is collimated by seeing if the diameter, D, of the beam at points far from the lens is equal to the diameter of the lens itself.

7) Measure the distance from the point source to lens. Is it equal to f_A, the focal length of lens A, you measured in part I? Does it match your prediction for how you would need to arrange the point source and lens so that all the exiting light rays were parallel?

8) Now place lens B in the collimated beam produced by lens A as in Fig. 3. Since the light rays approaches B traveling parallel, the object distance for lens B is infinite and the image distance should now be the focal length of the lens in question. What is the focal length for lens B.

Part III: Chromatic Aberrations (Color matters)

Still using the point source of light, you can study the chromatic aberration of lens A. Chromatic aberration (slight differences in the lens focusing properties for different colors or frequencies of light) occurs in all but the most expensive lenses.

9) Set your lenses up as shown in Figure 3. Use a white piece of paper to closely examine the light beam as it focuses to a point. Locate the focus point and then move the piece of paper back and forth so that you can see the rays converging to the point and then diverging again once they pass through the point. What do you notice about the color/hue of the outer most ring of the light circle? Is it the same when the rays are converging and diverging? Record your observations.

Fig. 3. Using a collimated beam to measure f_B

10) What do your observations tell you about how much lens B is bending red light vs how much it is bending blue light? Use a drawing to back up your claim. Recall that the amount of bending depends on the difference in the speed of light between the air and the glass. Both red light and blue light will travel more slowly in the glass than in the air. But are they traveling the same speed in the glass? Given your observations which one travels more slowly in glass? (Check your reasoning with your TA!) Hint: (remember the concrete/sand interface to infer how the amount of bending depends on the difference in speed as the car (light) goes from the air to the glass and the glass back to the air.)

Basically what is happening is that the glass bends light of different wavelengths by slightly different amounts which is equivalent to saying the light of different frequencies travels at slightly different speeds through glass This phenomenon is put to good use in a prism when one wants to disperse the different colors of white light. It is also the cause for a rainbow.

11) For a given lens, therefore, the focal length for red light (f_red) is a little different from that for blue light (f_blue). Which is larger: f_blue or f_red? Is their difference large?

Additional Experiment

12) Think up an additional experiment using the equipment from this lab, and try it, recording the results in your lab book.

PRE-LAB:

1. You have a candle that is 60 cm away from a lens. You find that the lens creates a real image of the candle 20 cm away from the lens. Use the lens equation to determine the focal length of the lens.
2. You have a point source of light and a lens, and you are trying to create a collimated beam of light exiting the lens (as in Figure 2) (that is all rays parallel, not converging {getting closer together} or diverging {getting further apart}). You use a piece of paper to look at the light exiting the lens (so you move the piece of paper from just behind the lens to far from the lens and look at how the size of the light beam changes). If you find that the circle of light is continually growing bigger as it exits the lens, should you move the point source further away from or closer to the lens in order to get a collimated (rays are parallel) beam? Explain your reasoning.