Video Transcript
The following diagram shows two light rays from the top of an object that reach the
top and bottom of the eye of an observer. The full distance from the object to the observer is not shown. The part of the distance that is not shown has a length 𝑑. Which of the following correctly describes how the value of 𝑑 compares to the part
of the distance that is shown in the diagram? (A) The value of 𝑑 is less than the part of the distance between the object and the
observer that is shown in the diagram. (B) The value of 𝑑 is about the same as the part of the distance between the object
and the observer that is shown in the diagram. (C) The value of 𝑑 is much greater than the part of the distance between the object
and the observer that is shown in the diagram.
This question is about parallel rays of light seen by an observer that do not start
out parallel when emitted by an object some distance away. This question is asking us about the relative size of a part of that distance labeled
𝑑. Option (A) says that 𝑑 is less than the distance shown in the diagram. This would make 𝑑 smaller than it appears in the diagram. Option (C) says that 𝑑 is much greater than the distance shown in the diagram. This would make 𝑑 much larger than it appears in the diagram. Option (B) says that 𝑑 is the same as the distance shown in the diagram.
We know that, in general, two rays of light traveling in the same direction are
parallel to each other if they neither converge, move closer together, or diverge,
move farther apart. This is the case for the two light rays entering the observer’s eye, which are
parallel. However, if we focus on the two light rays when they are emitted by the object, we
notice that they are not parallel. They are diverging, moving farther apart. We can approximate diverging light rays as parallel light rays if the distance they
travel is very large. Over shorter distances, this is not the case, as they still appear to diverge. But over very long distances, they appear parallel to each other.
Since we know that the distance between object and observer must be very large, the
correct answer must be option (C), as this makes 𝑑 much larger than it appears in
the diagram.
