In a church choir loft, two parallel walls are 5.70 m apart. The singers stand against the north wall. The organist faces the south wall, sitting 0.900 m away from it. So that she can see the choir, a flat mirror 0.600 m wide is mounted on the south wall, straight in front of the organist. What width of the north wall can she see? (Hint: Draw a top-view diagram to justify your answer.)
4.56
To find the width of the north wall that the organist can see, we need to consider the geometry of the situation. Let's break it down step by step:
1. Draw a top-view diagram of the situation. Draw two parallel walls representing the church choir loft, with the north wall on the left and the south wall on the right. Mark the distance between the walls as 5.70 m.
2. Place an arrow or a dot to represent the position of the organist on the south wall, 0.900 m away from it.
3. Draw a vertical line from the position of the organist to the north wall. This line will represent the line of sight of the organist.
4. Place a mirror on the south wall, facing the organist. The mirror should be perpendicular to the wall and directly in front of the organist.
5. Mark the width of the mirror as 0.600 m.
Now, we need to use the principle of reflection to determine what the organist can see in the mirror.
6. Draw a dashed line from the organist's position, perpendicular to the south wall, and extending to the mirror. This line represents the incident ray, or the light that hits the mirror.
7. Draw another dashed line from the mirror to the north wall, making sure it makes the same angle with the mirror as the incident ray does. This line represents the reflected ray, or the light that bounces off the mirror.
8. The point where the reflected ray hits the north wall represents what the organist sees in the mirror. Mark this point on the north wall.
9. Measure the distance between the organist's position and the point on the north wall. This will be the width of the north wall that the organist can see.
By drawing a top-view diagram and applying the principle of reflection, you can determine the width of the north wall that the organist can see.