You and a friend are playing a game of squirt-gun tag in a maze. Suddenly you see your friend's image in a small planar mirror (see illustration). You take a shot over the barrier in front of you and find that your friend is just at the end of the 7.0 m range of your squirt gun. If you are 4.0 m from the point of reflection of the light ray, how far from the point of reflection of the light ray is your friend?

Question

You and a friend are playing a game of squirt-gun tag in a maze. Suddenly you see your friend's image in a small planar mirror (see illustration). You take a shot over the barrier in front of you and find that your friend is just at the end of the 7.0 m range of your squirt gun. If you are 4.0 m from the point of reflection of the light ray, how far from the point of reflection of the light ray is your friend?

Answer 1

To solve this problem, we can use the principle of reflection and the geometry of triangles. Let's break down the given information:

1. You see your friend's image in a small planar mirror.
2. You are 4.0 m away from the point of reflection of the light ray.
3. Your squirt gun has a range of 7.0 m, and your friend is at the end of this range.

Now let's determine the distance from the point of reflection to your friend:

1. Draw a diagram to visualize the situation. Label the point of reflection as "R," your position as "You," and your friend's position as "Friend." Draw a line segment from the point of reflection to your position and another line segment representing the range of your squirt gun towards your friend's position.

2. Since the light ray reflects off the mirror, the angle of incidence (the angle between the incoming light ray and the mirror) is equal to the angle of reflection (the angle between the reflected light ray and the mirror). These two angles can be labeled as ∠i and ∠r.

3. The line segment from the point of reflection to your position (You) forms a right triangle with the line segment representing the range of your squirt gun. Let's label the distance from the point of reflection to your friend as "x".

4. Apply the law of reflection: Since the angle of incidence (∠i) is equal to the angle of reflection (∠r), the triangle formed in step 3 is an isosceles triangle.

5. Therefore, the distance from the point of reflection to your friend (x) is equal to the sum of your distance from the point of reflection (4.0 m) and the distance your squirt gun can reach (7.0 m).

x = 4.0 m + 7.0 m
x = 11.0 m

So, your friend is approximately 11.0 meters away from the point of reflection of the light ray.