Experiment 17
Experiment 17: Ray Tracing with Lenses and
Mirrors
Purpose
To observe and study the behavior or rays of light passing through lenses and reflected by a concave mirror.
Theory Lenses
Formation of images by lenses is governed by equation 1 :
1 1 + 1 = 1
s s' f
where f is the focal length of the lens, s is the distance from the lens to the source object and s' is the distance from the lens to the image. All distances are measured from the center of the lens.
Distances are positive if images are real (i.e. you can put a piece of paper there and see the image) and negative if they are virtual (light seems to be coming from somewhere but there isn’t a real image there). For example; f and s' are real and positive for the converging lens in Figure 1 since a real image is formed. However; f, and s' are virtual and negative for the diverging lens in Figure 2 while s is real and positive since there is a real source of light.
From equation 1 we can understand the behavior of lenses when the source object is parallel light. When the source object is parallel rays, this is similar to the situation when the source is very far away and s is very large. Then 1/s is very small and the equation becomes:
1 = 1
s' f
This means that the image is at the focus and all parallel rays incident on a lens go through the focal point.
Concave Mirrors
Formation of images by concave mirrors is governed by a similar equation:
2 1 + 1 = 1 = 2
s s' f R
where f, s, and s' are defined as for Equation 1 and R is the mirror’s radius of curvature. The sign convention for Equation 2 is the same as for Equation 1.. Concave mirrors behave similarly to lenses in that parallel light incident on a mirror goes through the focal point (Figure 5).
Apparatus
A ray box; a set of three lenses (a plano-convex collimator, concave and convex lenses), a concave mirror, a metric ruler, triangles, a sharp pencil, unruled paper, masking tape, and a desk lamp.
Procedure – Alignment
(1) Check that your ray box is using only three rays (the central ray and the two outer rays). Any other openings should be blocked by tape.
(2) Set up the apparatus as shown in the top view in Figure A. Tape a sheet of unruled paper to the table in front of the ray box. Place the ray box about 3 cm from the edge of the paper. Adjust the collimator lens (the plano-convex lens) so that the three rays emerging from it are parallel.
Suggestion: To make sure the rays are parallel, measure the perpendicular distance between the two outer rays as they enter and leave the paper. These distances should be the same within
1 mm.
CHECK WITH YOUR INSTRUCTOR BEFORE PROCEEDING.
IMPORTANT NOTE: Once your alignment is checked and approved, PERFORM ALL EXERCISES WITHOUT DISTURBING THE RAY BOX AND COLLIMATOR LENS.
Procedure – Part I. Lenses
Note: Your drawings are your data sheets in this lab. If you are working with a partner, you may make photo copies of the drawings after the lab since each partner needs their own set.
Exercise 1. Focal Length of a Converging Lens
Place the converging lens about 5 cm from the edge of the paper, as in Figure 1. Notice that the collimator lens has not been moved since the rays were aligned. Make sure the convex lens is perpendicular to the central ray and intercepts all three rays. The central ray should stay straight and the outer rays intersect it at the same point. Remember that parallel rays meet at the focal point of a converging lens in a real image. This point is the focus of the lens Fc and the distance between the center of the lens and the focus is the focal length fC.
Outline the surface of the lens with pencil. Trace the rays outside the lens by making a few dots along their length and then connect the dots with a ruler.
Mark, measure and record the focal length fcon your drawing. Your accuracy in measuring fc is the KEY TO ACCURACY to the exercises in this lab. Make sure you measure it to the best accuracy and precision you can.
Exercise 2. Focal Length of a Diverging Lens
In order to save paper, use the back of your paper from Exercise 1. Place the diverging lens about 10 cm from the edge of the paper, as in Figure 2. Follow the same instructions as in Exercise 1. After you are done, remove the lens and complete your drawing by extending the rays backwards with dotted lines to locate the virtual focal point FD and focal length fD.
CAUTION: You may see some faint rays intersecting at a point in front of the diverging lens. These are rays reflected from the front surface of the lens. Do not mark them. They are irrelevant to this exercise.
Exercise 3. Focal Length of a Combination of Lenses
Place the converging lens 2-3 cm from the edge of the paper. Make sure it is perpendicular to the central ray. Mark the focal point FC. Place the diverging lens (also perpendicular to the central ray) a distance d from the converging lens as shown in Figure 3. Adjust the diverging lens until the rays emerge parallel to each other. Trace all lenses and rays.
Can you explain what is happening? Where is the source image for the diverging lens? Remember that rays coming from the focal point of a lens emerge parallel to each other.
Exercise 4. Real Image from a Combination of Lenses
(Use the back side of Exercise 3.) Start as in Exercise 3 but place the diverging lens further from the converging lens than in Exercise 3. You should see the rays intersecting at a point further from the converging lens than in Figure 1. What is the virtual object distance s and the real image distance s' for the diverging lens? Complete the drawing as usual.
Procedure – Part II. Concave Mirror and Lenses
Exercises 5, 6, and 7 can fit on one side of a sheet of paper, but draw each one in a different area.
Exercise 5. Focal Length of Concave Mirror
Intercept the original parallel rays by the concave mirror as in Figure 5. Mark the focus FM and complete the drawing.
Exercise 6. Image from Converging Lens and Concave Mirror
Make the parallel rays from Exercise 5 converge by inserting the converging lens. Then intercept them with the mirror by placing the mirror as close to the lens as practicable as in Figure 6. Record at least two relevant distances, marking them clearly. What are s and s' in this exercise?
Exercise 7. Image from Diverging Lens and Concave Mirror
This exercise is similar to Exercise 6 except that you use a diverging lens. Record the two relevant distances.
BEFORE YOU LEAVE THE LAB
Sign all your drawings and make sure they are initialed by your instructor.
Lab Report
The key part of your report is your drawings. All of them must be properly completed as follows:
(a) Trace all relevant rays. Virtual rays should be traced with dashed lines as shown
in Figures 2 and 3.
(b) Mark, measure, and quote all important distances such as s, s', d, to one
millimeter accuracy.
(c) Measure all relevant distances from the centers of lenses and from the vertex for
mirrors.
Part I:
Exercise 1. What is your measured fC?
Exercise 2. What is your measured fD?
Exercise 3. Use fC from Exercise 1 and your measured value of d. Find fD = (fC – d). Find the percent discrepancy between (fC – d) and your measured fD from Exercise 3.
Question 1. Why do we expect (fC – d) to be equal to the value of fD from Exercise 2?
Question 2. What are the major reasons (apart from “human error”) for the discrepancy between (fC – d) and fD.
Exercise 4. Measure s’ = the distance between the final intersection of rays and the diverging lens. Using fC from Exercise 1 and fD (the average of Exercises 2 and 3) and equation 1 to calculate s’. Display the percent discrepancy between the calculated and measured values.
Part II:
Exercise 5. What is your measured fM?
Exercise 6. Use the measured distance between the lens and the mirror and your value of fC to calculate s, the object distance for the mirror. Is s positive or negative? Use your calculated value of s and the measured value of s' to calculate fM.
Exercise 7. Find fM for Exercise 7 as you did for Exercise 6. Use your average value of
fD in your calculation of s.
Question 3. Where is the source image for the mirror in Exercise 7? Is s positive or negative?
Question 4. Tabulate your three values of fM and find the average. Using (fM)average, find the radius of curvature of the mirror.
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