Video Transcript
The reflected image of an object from a mirror is seen by an observer. The positions of the object and the eye of the observer are shown in the diagram. For each position shown, the same four possible orientations of the virtual objects seen in the mirror are shown. Which of the positions shown is the correct position of the virtual object? Which of the orientations shown is the correct orientation of the virtual object?
The three main elements of our diagram are this mirror, the observing eye, and the object. We’re told that the eye sees the reflection of the object in the mirror. This happens because rays of light come from the object and then reflect off of this surface to reach the observing eye. Interestingly, when the eye sees this light, it doesn’t understand, we could say, that it is reflected light. Rather, the eye traces the ray incident on it backward, even beyond the mirror. The eye perceives the object to exist on this other side of the mirror. Because that object does not exist in real space, we call it a virtual object.
The first part of our question asks, which of the positions shown is the correct position of the virtual object? On the left side of the mirror, we have four candidate positions: one, two, three, and four. As we’ve seen, the observing eye locates the virtual object by tracing back the ray incident on the eye. This ray traced backward passes through position one. This then is where the eye will perceive the virtual object to exist.
The next part of our question says, which of the orientations shown is the correct orientation of the virtual object? For all four of our candidate positions, we have four candidate orientations of the virtual object. One orientation is labeled as 𝑎, one as 𝑏, one as 𝑐, and one as 𝑑. Comparing these four orientations to our original object, we see that that object has yellow on top and green on bottom. It will be possible to see these color differences in the virtual object. Yellow light coming from the yellow top of the object will reflect off the mirror and reach the eye like this. If we trace that reflected ray backward, we see that it reaches the top of our virtual object. This means that the top of this virtual object will appear to the eye as yellow. On the other hand, green light coming from the bottom of the original object will be reflected in this way. Tracing that reflected ray of green light back, we see that it reaches the bottom of the virtual object.
To the observing eye then, the virtual object will appear yellow on top and green on bottom. We see that this agrees with one of the four orientations given. The orientation labeled 𝑎 is the correct orientation of the virtual object.
