OBJECTIVES
1. Explore the difference between converging and diverging lenses and determine their focal lengths.
2. Determine the focal length of a diverging lens by direct measurement and by using the Lensmaker’s equation.
3. Experimentally measure the image distance and confirm the thin lens equation.
4. Explore how the human eye creates images and the difference between nearsightedness and farsightedness.
5. Analyze and measure the behavior of images formed by a two-lens system and a lens-mirror system.
EQUIPMENT
Basic Optics Kit, Ray Box, converging and diverging lenses, concave mirror, optical bench, metric ruler, human eye model, and telescope.
THEORY
Parallel rays of light passing through a thin converging lens cross at the focal point of the lens. For a diverging lens, parallel rays of light appear to have originated from a focal point on the same side of the lens as the incoming light. The focal length is measured from the center of the lens to the focal point. The Lensmaker’s equation is used to calculate the focal length of a lens based on the radii of curvature of its surfaces and the index of refraction of the lens material:
1 f lens






1

1 r r
1 2

 where f lens
is the focal length, n is the relative index of refraction of the lens material, and r
1
and r
2 are the radii of curvature of the lens surfaces. Another way to calculate the focal length is used the image-object equation for a thin lens:
1

1

1 f p i
For a two-lens system or a lens-mirror system, the image from the first lens becomes the object for the second lens (or mirror). The magnification is equal to the multiplication of the magnifications of the individual lenses (or the lens and mirror): m
 m m
1 2



 i
1 p
1


 i
2 p
2


PROCEDURE
Part 1: Measuring the Focal Length of a Lens a. Place the ray box on a white piece of paper. Using five white rays from the ray box shine the rays straight into the converging lens. Trace around the surface of the lens and trace the incident and transmitted rays. b. The place where the five refracted rays cross is the focal point of the lens. Measure the focal length from the center of the converging lens to the focal point. c. Block out the center 3 rays and mark the focal point for the outer two rays. Next, block out the outer two rays and mark the focal point for the inner 3 rays. Are the two focal points the same? d. Repeat steps (a) – (c) for the diverging lens. e. Nest the converging and diverging lenses together and place them in the path of the parallel rays. What does this tell you about the relationship between the focal lengths of these two lenses? Slide the converging and diverging lenses apart to observe the effect of a combination of two lenses. Then reverse the order of the lenses.
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Part 2: Lensmaker’s Equation applied to a Diverging Lens a. Call the results of part 1(d) the experimentally measured focal length f expt
. b. To determine the radius of curvature of each surface, put the diverging lens back in the path of the rays and observe the faint reflected rays off the first surface of the lens. The front of the lens can be treated as a concave mirror having a focal length f mirror
( ≠ f lens
) and a radius of curvature. Measure the distance from the center of the front curved surface to the point when the faint reflected rays cross. From this distance, calculate the radius of curvature r
1
. c. Flip the diverging lens and repeat the above process to calculate the radius of curvature r
2
. d. Predict the focal length f thy of the lens using the Lensmaker’s equation (n acrylic
= 1.49). e. Compare f thy
with f expt
using a percent difference. How do they compare? f. Is the focal length of a diverging lens positive or negative? How might the thickness of the lens affect the results of this experiment?
Part 3: Converging Lens a. Measure the focal length f of a 20 cm lens using a distance object ( i.e. don’t trust the value indicated on the lens). Then mount a light source near one end of the optical bench and place a converging lens with the focal length measured above near the other end. b. Using the thin-lens and magnification equations, predict the object distance p thy
and images distance i thy
necessary to produce a real image with a magnification |m| = 2. c. Use a screen to locate the image where |m| = 2. Measure (p expt
& i expt
) and predict
(p thy
& i thy
) the object & image locations. Compare them using a percent difference.
How do they compare? d. Use ray tracing to draw an accurate scaled ray diagram of this optical system.
Part 4A: The Human Eye - Focusing an image on the retina a. Make sure the small plastic lens marked +400 is inside the eye. Put your hand about
50 cm from the eye and illuminate it with a desk lamp. Find the image on the retina.
Move your hand until the image is sharp.
Describe the image characteristics (orientation and magnification)? If the image is inverted, why does the world not look upside down to us? b. Replace the plastic lens with the adjustable water filled lens. Use the optics light box as an object and place it about 20 cm from the eye. c. With the plunger, GENTLY adjust the shape of the lens until the image is relatively focused (it won’t get perfect). d. Now move the light source farther from the eye until the image gets fuzzy. Before trying it, make a prediction:
How you will need to adjust the lens to focus the image now – more converging or less converging? Why?
Try it, see if you were right, and report on your results. e. Insert the black plastic ‘pupil’ into slot A. This simulates squinting or a closed-up pupil in bright light. How does this affect the image?
Part 4B: The Human Eye – Nearsightedness and Farsightedness
For this station, we’ll use a fixed lens marked 62 inside the eye to represent the eye’s lens. Keep this lens in place the whole time. a. With the retina (white plastic screen) in the “normal” position, find the near point of this eye (that is, the closest distance it can see clearly). What is this distance? b. Farsighted Eye: A farsighted person has a shorter than normal eyeball, making the screen too close to the lens. Simulate this by moving the white retina screen closer to the lens, to the position l abeled “FAR.”
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c. Describe what happens to the image. This is what a far sighted person sees when trying to look at a near object. Now have the eye model ‘look’ at the far away light source. Is it clearer? Why? d. Make the eye look back at the near object. If you were designing glasses to help this eye see the near object, would you use converging or diverging lenses? Why? Find a lens in the set that makes a clearer image (remember, + focal lengths are converging and – ones are diverging). Which one did you use? e. Near sighted eye. A nearsighted person has a longer than normal eyeball, making the screen (retina) too far from the lens. Simulate this by moving the white retina screen farther from the lens, to the position labeled “NEAR.” f. What kind of glasses would help this eye see the far object - converging or diverging lenses? Why? Find a lens in the set that makes a clear image. Which one did you use? Describe the images produced by both near and far objects. Which one is clearer? g. What kind of glasses would help this eye see the far object - converging or diverging lenses? Why? Find a lens in the set that makes a clear image. Which one did you use?
Part 5: Two-Lens System a. Mount a light source near one end of the optical bench and place a converging lens with focal length f = 10 cm (100 mm) at a distance of 30 cm from the light source. b. Place a diverging lens of focal length f =− 15 cm ( − 150 mm) at a distance of 10 cm from the first lens.
c. Using the thin-lens and magnification equations, predict the images distance i thy
and the magnification of the image m thy
for this two-lens system. d. Use a screen to locate and measure the image location i expt
and the magnification m expt
. Compare i thy
& i expt
and m thy
& m expt
using a percent difference. How do they compare?
Part 6A: Lens-Mirror System a. Mount a light source near one end of the optical bench and place a converging lens with focal length f = 10 cm (100 mm) at a distance of 20 cm from the light source. b. Place a concave mirror of focal length f = 5 cm at a distance of 35 cm from the first lens.
c. Using the thin-lens and mirror equations, predict the image distance i thy
for this lensmirror system. d. Use a half-screen to find the image location i expt
. Compare i thy
& i expt
using a percent difference. How do they compare?
Part 6B: Telescope
Look at the model telescope that is set up.

What kind of lens (converging or diverging) and mirror (concave or convex) does it use?

Describe how the telescope works using short concise sentences.

What is the function of the mirror? What is the function of the lens?
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