Physics Multiple choice question?

Question

Hi everyone! I wanted to ask you a Multiple choice question appearing in my exam. The question is as follows:

3 students stand 2 m apart in front of a plane mirror which is 3 m long. Student Y is standing opposite the mid-point of the mirror while the other 2 students are standing 2 m from him in a staight line.


The question is how many students can see the images of the other two?

A) 0
B) 1
C) 2
D) 3


Only one answer is correct. Please explain your answer. I try to copy the figure provided in the question as below: X and Z are standing 2 m from Y who is at the middle of the mirror.

<- Mirror (3m) ->
X <- 2m -> Y <- 2m ->Z

Answer 1

Assuming that the straight line of the students is parallel to the mirror, the answer is D, all of them can see each other.

What you have to do is determine if the mirror exists at each of the half way points between the students. Staring with student Y looking for student X, the distance between them is 2m. Therefore the half point occurs at 1m to the left of student Y. Since the mirror is 3m long, and student Y is standing in the middle of the mirror, he/she has 1.5m of mirror to the left. This means that at the half way point (1m) the mirror exists and student Y can see student X and since it is a mirror, student X can see Y. The same thing happens when student Y looks for student Z. There is no difference in the spacing other than Z is on the right side.

So we established that X can see Y, Y can see X and Z, and Z can see Y.

Finally we have to determine if X can see Z. Does the mirror exist half way between X and Z? Yes. They are 4m apart so half is 2m which is the exact center of the mirror. And since X can see Z, Z can also see X. Therefore they can all see each other.

If the question had asked if they can see themselves, the same math would apply. The distance between X and X is zero so the half way point is exactly where X is standing. There is no mirror here (it ends at 1.5m to the left of student Y and student X is standing at 2m to the left of student Y) so student X cannot see himself. Using the same technique, student Z cannot see himself and student Y can see himself.

Answer 2

It is difficult finding actual questions from previous tests. Barron's and those third party study materials provide a very similar difficulty level as is on the AP test. But before going out and buying such stuff, talk to your Physics teacher. He/she is bound to have material for you to work on.

Answer 3

The correct choice is B. Draw the ray diagram and see for yourself. Y will be able to see himself as well as other two. X will be able to see Y but not Z and cannot see himself also and similar thing is true for Z.

Answer 4

Hi. I believe all three can see the other two. Only Y can see three.