Wednesday, April 4, 2012

Experiment 9: Concave and Convex Mirrors

Introduction
                The purpose of this experiment is to understand how images are formed differently in a plane, a concave, and a convex mirror. In this experiment, a concave, a convex, and a plane mirror are used, and the changes in image at different object distances are observed. A light ray diagram corresponding to each case is also constructed to confirm this observed behavior. The magnification of the concave and convex mirrors are also computed using the light ray sketches. 

Figure 1: Convex mirror
Figure 2: Concave mirror
Diagrams
Diagram 1: Light ray diagrams which show how the image in convex mirror changes depending on the object distance
Diagram 2: Light ray diagrams which show how the image in concave mirror changes depending on the object distance
  
Diagram 3: Light ray diagrams which were used to compute magnification of the mirrors

Data
Table 1: Comparison of magnification
Magnification ratio
Magnification of the mirror
Convex
Concave
hi/h0
0.318 ± 0.024
-0.339 ± 0.009
di/d0
-0.304 ± 0.023
0.297 ± 0.008

Sample Calculation

Conclusion
                According to the experimental observation, the image formed by the convex mirror appeared to be always smaller than the object, and it is always upright. As the object was moved further away from the mirror, the image also appeared smaller, and it became larger as the object was closer. The reason that the image appeared as it was, was illustrated by diagram 1. When a ray of light hit the convex mirror, the light was reflected, and these reflected rays were appeared as they were radiated from the image. Since the reflected rays of light did not pass through the image, the image was a virtual image. Based on this observation, it was concluded that a convex mirror always formed upright, virtual image which were smaller than the object.
                As for concave mirror, the image was observed to be inverted when the object was placed further away from the mirror. As the object got closer, at a certain distance, the image became erect. This was because the object distance determined how the image was formed. As shown in diagram 2, when the object distance was larger than the focal length, the image was always inverted. Once the object distance equaled the radius of curvature, the object distance and the image distance became the same, but the orientation was different. But the image disappeared if the object was at the focal length since the image was at infinity. On the other hand, when the object distance was smaller than the focal length, the image was always virtual and erect since the actual light rays did not pass through the image. Therefore, the observation was agreed with the light ray sketch illustrated in figure 2.
                In plane mirror, the image and the object always showed the same size and distance no matter where the object distance was. In addition, the images formed in plane mirror were virtual and erect images.
                In the last part of the experiment were the mirror magnification were to be computed based on the sketch, it was found that the magnification computed from the object and image distance ratio was agreed with that from the height ratio as shown in table 1. However, their signs were opposite. This was because, in convex mirror, the image was a virtual image, but both the object and image distances were erected. On the other hand, in concave mirror, the image is real and inverted. Therefore, the image height was negative.  These sign determinations were shown in diagram 3.  

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