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. 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 in meters.
To solve this problem, we need to understand the concept of reflection and the properties of light.
When light reflects off a mirror, the angle of incidence (the angle at which the light hits the mirror) is equal to the angle of reflection (the angle at which the light bounces off the mirror).
In this scenario, we have a planar mirror, and we are given that the image of your friend is reflected in the mirror.
Let's assume that you are standing at point A, the mirror is at point B, and your friend is at point C. The distance between your friend's image in the mirror (point C') and the point of reflection of the light ray on the mirror (point D) is given as 4.0 m.
Now, we know that the distance between the point of reflection of the light ray (D) and your friend (C) is the same as the distance between you (A) and the point of reflection of the light ray (D). Let's call this distance x.
So, we have:
Distance from A to D = x
Distance from D to C = x
We are also given that the range of your squirt gun is 7.0 m. The range is the distance between you (A) and your friend (C).
Therefore,
Distance from A to C = Distance from A to D + Distance from D to C
= x + x
= 2x
Since the range is 7.0 m, we have:
Distance from A to C = 7.0 m
Substituting the value of 2x with 7.0 m, we can solve for x:
2x = 7.0 m
x = 7.0 m / 2
x = 3.5 m
So, the distance from the point of reflection of the light ray (D) to your friend (C) is 3.5 m.