Concave and Convex Mirrors

Purpose:

            The primary purpose of this laboratory experiment is to explore the property of images that are formed in mirrors. More specifically, we will be exploring the properties of both concave and convex mirror and the properties of the images generated by these mirrors. We will be holding a notable oriented object in front of the mirrors and describing the way each object’s has changed by the mirror.

Procedure:

1.      Two different mirrors were retrieved. One of the mirrors was convex (first picture) while the other mirror was concave.

2.      An expo dry erase marker was used as the object. The colored cap made it clear to tell if the object was inverted or not in the image.

3.      A meter stick was placed in front of the mirror with the marker placed atop it. This enabled us to move the marker further or closer to the mirrors while also being able to measure the object distance.

4.      The images were viewed inside the mirror and the changed properties from the original object were recorded.

Data Analysis: 

            Convex Mirror

            This part of the experiment will be dealing with the convex mirror. As previously described, the mirror was set up and the marker was placed in front of the mirror on the meter stick. 

The picture maybe a little hard to see, but inside the mirror the image of the object, the marker, was erect and seemed smaller than the original objects height. This virtual image was located inside of the mirror.

Next, we moved the object closer to the mirror. When this was done, the image of the object got bigger until it reached a size that was equal to the original size of the object. The distance of the image inside the mirror also appeared to decrease. We then moved the object further away from the mirror. This caused the image size to decrease and the object distance behaved opposite, increasing and appearing further away.

While doing these experiments, we measured the height of the object as well as the height of the objects image in the mirror and the distance of the object from the mirror. Using both of these heights, we can determine the magnification of the mirror on the object and the image distance. The calculations are as fallowed:

h_object = 12 ± .5 cm   h_image = 4 ± .5 cm    d_object = 50 ± .5 cm

d_i/h_i = d_o/h_o

d_i = d_oh_i/h_o = 50*4/12 = 16.7 ± 2.2 cm

M = h_image / h_object

M = 4/12 = .333 ± .044

From this calculation, it shows that the magnification is less than one; therefore, the image must seem smaller in the mirror than the actual object. A ray sketch for this type of mirror was made and the results from the sketch match our observations. 

As you can see from the ray sketch, the image is located inside the mirror and is demagnified. It is also notable that the object is not inverted but rather it is erect.

            Concave Mirror

            For this part, the convex mirror was switched with a concave mirror. The same process was followed and the object was placed on top of the meter stick and the image was viewed. For this mirror, however, the object was very different. As oppose to the convex mirror, this concave mirror showed an image that was magnified and inverted. Also, the image itself appeared to be located in front of the mirror as oppose to inside of it.

We then started by moving the object further away from the mirror. This resulted in the image becoming very small and still inverted. After that was done, we then moved the object closer to the mirror. As this was done, the properties of the image changed once again. When the image got closer to the mirror, the image became larger while still inverted. Then at some point, the object became as big as to cover the entire mirror. As we moved the object even closer, the image of the object flipped and became erect and still magnified. Once this point was reached however, the object began to get smaller. 

As the picture shows, the image is now erect and smaller as the marker is moved closer to the mirror. The image itself is still located outside of the mirror in between the object and the surface of the mirror. The object’s height was measured once again as well as the height of the image of the object and the object distance. These were used to find the magnification of the object and the image distance.

h_object  = 12 ± .5 cm    h_image = 16.5 ± .5 cm   d_o = 100 ± .5 cm

d_i = d_oh_i/h_o = 100*16.5/12 = 137.5 ± 12.2 cm

M = h_i / h_o = 16.5 / 12 = 1.4 ± .071

This magnification provided a value that is greater than 1. This means that the mirror does magnify the object and makes the image appear larger than the original object height. To check this, a ray diagram for this mirror was also constructed. 

Upon first glance, it appears that the sketch does not agree with my observations. But, this sketch is being taken with the assumption that the object is a large distance away from the mirror. As stated earlier, as the object moved further from the mirror, the magnification effect became less and the image became smaller. So yes, this sketch does in face agree with my observations.

Summary:

            From this experiment, many conclusions can be made about these two specific types of mirrors. For the convex mirror, the image will always be erect and the image height will never be greater than the actual height of the object. For the concave mirror, the image is always outside of the mirror and the orientation of the image depends on the distance away from the mirror the object is.