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

Angle of incidence = angle of reflection. This also means that a ray will hit the mirror at the midpoint between origin and destination.

So,
for y to see z the ray must hit the mirror 1 meter from it's center. That puts it at 1/2 meter from the edge so you're OK. By symmetry y can also see x.

Also by symmetry, z can see y. But can z see x? The ray from x to z (and z to x) must strike the mirror at its midpoint.

So, it looks like all three can see the other two. I think the answer is D provided:

Y is standing in front of the center of the mirror, right?

Answer 2

One piece of info is missing:
Distance of center student from the mirror. This in turn will determine the angle of incidence for each student on the mirror surface.

Answer 3

C) 2

Based on the ratio formatting and obvious inexpliaration in physic relations.