Saturday, March 31, 2012

Experiment 9 --- Concave and Convex Mirror

 Introduction:
               The purpose of this experiment is to observe how the image will change with the changing distance between the object and the mirror (concave or convex), as to see how the image will change with different surface of the mirror being applied.
               In order to do this experiment, there are three different kinds of mirror would be used for completing this experiment, the plane mirror, the concave mirror, and the convex mirror. For this experiment, the plane mirror would be used to be the control mirror, as well as the comparison for the other two mirrors. It is because the image refracted by the plate mirror would be the same size as the object. Besides, the image would be virtual and erect, with the same distance as the distance between the mirror and the object. To be short, the object distance would equal to the image distance. Therefore, with all properties provided, the image produced by the plane mirror could be the control image.
               After knowing the size of image produced by the plat mirror, now the object would be put in front of the convex mirror.As the object was put in front of the convex mirror, the image appeared was smaller than the object. However, no matter what the object distance was, the image was always erect and smaller. By comparing the image appeared in the convex mirror and the image appeared in the plane mirror, the image appeared in the convex mirror seemed to be further than the plane mirror. When the object was moved away from the mirror, the image distance also increased proportionally with the object distance, but the image was always smaller and erect.
               As the object was put in front of the concave mirror, the image appeared was larger than the object when the object distance was very small. However, as the object was gradually moved away, the image suddenly turned inversely and smaller. After passing this point, the image started to become smaller proportionally with the increasing object distance. Now it showed us that the point, where the image was turned upside down, was known as the focal point. Therefore, when the image appeared in the concave mirror (inside the focal point) was compared to the image appeared on the plane mirror, the mirror appeared on the formal one was closer in the mirror than the later one. The image appeared on the concave mirror when the object was inside the focal point was always larger and erect. However, the image appeared on the concave mirror became further than the image appeared on the plane mirror when the object was moved outside and away from the focal point. Besides, the image appeared on the concave mirror when the object was outside of the focal point was always smaller and inverted.


Plane mirror, the image has the same size as the object 
concave mirror, the image was inverted when the object was away from the mirror
concave mirror
convex mirror, the appeared image was erect

Diagrams, data, and the calculations

Convex Mirror:
Ray diagram---

h0
hi
d0
di
2.2 cm ± 0.05cm
0.7 cm ± 0.05cm
5.6 cm ± 0.05cm
-2.0 cm ± 0.05cm


Calculate magnification:
M = y’/y = -s’/s
M=0.7/0.22=0.318
  =-(-2.0/5.6)=0.357
Average M= (0.318+0.357)/2=0.3375



Concave Mirror:
Ray diagram---


h0
hi
d0
di
2.3 cm ± 0.15cm
-0.7 cm ± 0.05cm
11.9 cm ± 0.45cm
3.4 cm ± 0.2cm

Calculate magnification:


M = y’/y = -s’/s
M=-0.7/0.23=-0.304
  =-(3.4/11.9)=-0.286
Average M= (-0.304-0.286)/2=-0.295

Uncertainty:



Conclusion:
               For the convex mirror,since the M obtained from the –s’/s is positive number, the appeared image would be erect, and since the image was formed behind the mirror, which was the opposite direction of the outgoing light, the image was virtual.
               For the concave mirror,since the M obtained from the –s’/s is negative number, the appeared image would be inverted, and since the image was formed in front of the mirror, which was the same direction of the outgoing light, the image was real. However, this diagram only showed the image appeared when the object was outside of the focal point, if the object was put on the center point, the image would not be formed, and this was the instantaneous moment when the image changed from erect to inverted. If the object was put inside the focal point, the m would be positive number, but the image is going to appear behind the mirror, which is the opposite side of the outgoing ray. Therefore, the image would be virtual and the image would be erect.
               The magnification constant calculate from y’/y  should  equal to -s’/s, however, from the above calculations, the magnification constants calculated from each one did not equal to each other. With the uncertainty, the value could not be matched to each other, so the average of the magnification constant would be taken in this case.The inaccuracy for both the convex and the concave diagram could be due to the inaccuracy of the its diagram. 
               As a result, it showed us that when the object was put in the different distance from the mirror, the image appeared would also be different. The changing factor would produce the different distance of the image, erect or the inverted image was formed, the virtual or the real image was formed, and also the position the image was formed.

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