Concave and Convex Mirrors Lab

We started this lab by first studying how objects were projected in front of a convex mirror. At first glance, the image looks smaller than it really is. The projection is still upright. When locating the image relative to the position mirror-object, the image looks further.

When we moved the object towards the mirror, it became gradually larger in size. On the other hand, if we moved the object away from the mirror, the object diminished its size considerably.

The magnification of a mirror can be calculated if height and distance measurements are available.

The heights of the object (h_o )and the image (h_i) were measured with a meter stick, which was also used as our optic axis. We also measured the distance between the object and the mirror (d_o). However, we had some issues trying to get the distance between the image and the mirror (d_i).

The following image is the ray diagram for the convex mirror:

 The formula for magnification is the following:

M = h'/h = -q/p

where h' is the height of the image. 

This relationship suggests that q and p are the distances of the object-mirror and image-mirror, and that they can be set aside so that we can just relate the two heights. The height of the image is h' and the height of the object is then h.

M =  (h_i)/(h_o) = (6.7±.05 cm) / (12±.10 cm) =  0.558±0.0062

The result is relevant since the image in the mirror looked smaller than the actual object by a factor of approximately .558 or 1/2 the original size.

The second part of this experiment was to study how the image of the object looked in a concave mirror. When putting the object in front of the concave mirror, the image appeared larger, although it was still upright. The image appeared to be closer than the object actually was.

  

 We noticed that by moving the object closer to the mirror, its image got smaller. When moving it away from the mirror, the image would get bigger until it started to invert upside down.

After doing some observations, we came up with this ray diagram for the concave mirror:

 Based on the previous calculations, the magnification for the concave mirror was:

M =  (h_i)/(h_o) = (21±.20 cm) / (12±.10 cm) =   1.75±0.022

The calculated magnification matches the image perception since the image in the mirror gets bigger when the object is somewhat far from the mirror. The concave mirror had a magnification 1.75x the size of the original object. 

Although it might not be significant, sources of error are present in the actual measuring of distances and heights. These, however, did not cause constraints to the results of the lab.