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To develop an understanding of the Law of Reflection, to apply the Law of Reflection to finding images formed by plane and spherical mirrors, and to learn to draw ray diagrams to assist in predicting the locations of images formed by spherical concave mirrors.

Part 3

1. What statement can you make regarding the relative positioning of the normal, the incident ray and the reflected ray?

The angle between the incident ray and the normal is equal to the angle between the reflected ray and the normal.

2. Do your observations validate the Law of Reflection?

Yes, the observations validate the Law of Reflection as ?_i = ?_r or the values are extremely close in all trials.

3. Using your data above, create a graph in Graphical Analysis of pq vs. p + q. Your graph should appear linear. Perform a linear fit on the graph.

See graphs section.

4. There is an equation in geometrical optics called the mirror equation. It relates the object distance p and the image distance q to the focal length of the mirror f: 1/p + 1/q = 1/f. The mirror equation can be used to determine a mirror’s focal length. Solve the above equation algebraically for f.

In the instance of case 1, for trial 1 f = 4.0 cm, for trial 2 f = 4.1 cm, and for trial 3 f = 3.8 cm. In the instance of case 2, for trial 1 f = 4.1 cm. In the instance of case 3, for trial 1 f = 4.0 cm, for trial 2 f = 4.2 cm, and for trial 3 f = 4.3 cm. The average value for f is 4.1 cm.

5. How is your answer to Question 4 related to the slope of your graph from Question 3?

The slope of the graph from Question 3 is 4.0 cm, so these values are strikingly similar.

6. What is the percent difference between your slope and the focal length of the mirror that you measured?

The percent difference between the slope, 4.0 cm, and the focal length of the mirror that was measured, 5.5 cm, is 32%.

7. The magnification of the image of an object from a spherical mirror can also be expressed as the ratio –q/p. Calculate this ratio for each of your object and image distances and record in your data table.

See data table.

8. How does the ratio of –q/p compare to your calculated magnifications h_i /h_o for each entry? What is the percent difference?

In regards to case 1, the values for both h_i /h_o and –q/p are negative, but the values for h_i /h_o are more negative than that of –q/p. The percent difference for trial 1 is 126%, for trial 2 is 132%, and for trial 3 is 153%.

Case 2 shares the same characteristics of case 1. The percent difference is 112%.

In regards to case 3, the values are quite dissimilar because all h_i /h_o values are positive while all –q/p values are negative. The percent difference for trial 1 is 1200%, trial 2 is 700%, and trial 3 is 569%. It is thought that the images were recorded as upright when they were really inverted, which caused this error, but it cannot be validated by repeating the laboratory procedure at this time.

9. Do your data verify the prediction from your ray diagrams?

In regards to case 1, the values for –q/p verify the predictions made from the ray diagram, as when the object was moved further away from the mirror, the images became smaller. The values for h_i /h_o dot not support this claim however, as they say that the image way magnified, but in reality the projected image was smaller. The images were also inverted as told by the negative sign.

In regards to case 2, neither the value for –q/p nor h_i /h_o verifies the prediction made from the ray diagram. The magnification should have been 0.

In regards to case 3, the values for –q/p do verify the predictions made from the ray diagram, as when the object was moved closer to f, the images became more magnified. The images were recorded as being upright, but in reality were probably inverted as suggested by theory and the negative sign the –q/p value carries.

For part 1 of the experiment, the reflection of light from a plane mirror was measured. Equipment was set up on the optics bench so that light shone through a slit plate and slit mask onto a plane mirror. A ray table was used to measure the angle at which the line hit and reflected off the mirror. The ray table was rotated from 0 o to 90 o at 10 o intervals. The angle of incidence and angle of reflection were measured for each trial. The measured angles were identical or nearly identical in all trials, which seem to confirm the Law of Reflection. Any discrepancy in the measurements may be attributed to the ray optics mirror not being perfectly aligned on the ray table; without any way to secure it in place, it may have shifted slightly during some of the trials. This would have caused a difference in the angles of incidence and reflection.

For part 2 of the experiment, the focal points of a concave and convex mirror were measured. Equipment was set up on the optics bench so that light shone through a parallel ray lens and then through a slit plate and then onto the concave or convex mirror situated on a ray table. The parallel ray lens had to be adjusted to make the light rays project in a parallel fashion onto the mirror. Once parallel, the mirror was situated so that the centermost light ray would hit the center of the mirror perpendicularly. The light rays converged at a focal point which was measured and recorded. In the case of the convex mirror, a piece of paper was place underneath the mirror and the projected light rays were draw onto the piece of paper. The paper was then removed and the lines were extended to find the focal point which was located behind the mirror. In the case of the concave mirror, the focal point was in front of the mirror. The focal length of the concave mirror was 0.060 m and the focal point of the convex mirror was 0.058 m. This slight discrepancy could be attributed to difficulty tracing the lines projected by the convex mirror, but these values are rather close in value, which is expected.

For part 3 of the experiment, the cases of 3 ray diagrams were tested. Equipment was set up on the optics bench so that light shone through a crossed arrow target onto an angled spherical mirror which then reflected an image onto a viewing holder. The focal length of the mirror was first determined by placing the mirror as far away from the crossed arrow as target as possible. The viewing screen was moved to locate the point where the image of the target was focused, and that was designated as the focal point. In the case of this experiment, the focal length was 5.5 cm. The target was then placed at three positions beyond the curvature, directly on the curvature, and then at three positions between the curvature and the focal length. The viewing screen was situated in each trial to find the point where the projected image was focused. The distance from object to mirror, distance from image to mirror, height of the object, and height of the image were measured in each trial.

The results from this part of the experiment are not very consistent. In case 1, the values for both h_i /h_o and –q/p were both negative, but the values for h_i /h_o were more negative than that of –q/p. The percent difference for trial 1 was 126%, for trial 2 was 132%, and for trial 3 was 153%. The values for –q/p seems most reasonable as they predict that the image was shrunken and inverted, which was actually the case. The values for h_i /h_o suggest that the images were magnified and inverted, which was not what was observed. Case 2 shares the same characteristics of case 1, in that the value for both h_i /h_o and –q/p was negative, but the value for h_i /h_o was more negative than that of –q/p. The percent difference was 112%. During this case, it was predicted that the image would be inverted, but would be life size; not magnified or shrunken. In regards to case 3, the values were quite dissimilar because all h_i /h_o values were positive while all –q/p values were negative. The percent difference for trial 1 was 1200%, trial 2 was 700%, and trial 3 was 569%. It is thought that the images were recorded as upright when they were really inverted, which caused this discrepancy, but it cannot be validated by repeating the laboratory procedure at this time. The values for –q/p are most logical, as they suggest that the image was inverted and magnify, which is also what theory suggests.

The error from this part of the experiment came from the inability to distinguish when the image on the viewing screen was focused. Many times it was thought that the image was focused, but may not have truly been focused; there was not way to tell with certainty if it was focused or not. The viewing screen could be moved a few centimeters in either direction and the image would look about the same. All measurements for the height of the image are in question as well. The spherical mirror was placed at an angle in order to view the image, but this angle was never taken into consideration in any of the equations. The undoubtedly is what caused all the h_i /h_o values have such a stark difference from the –q/p values. It was not stated in the lab manual how to take that angle into consideration, and thus those values should most likely be thrown out. The –q/p values are most representative of the projected image, though the values for –q/p and h_i /h_o should have been equal.

C = 2f

1/p + 1/q = 1/f

Magnification = -q/p = h_i /h_o