The mirror in FIGURE EX34.5 deflects a horizontal laser beam by 60°. What is the angle ϕ?

Verified step by step guidance

1. Identify the type of mirror used and the geometry of the situation. In this case, assume a flat mirror is used which follows the law of reflection, stating that the angle of incidence equals the angle of reflection.
2. Understand that the deflection of the beam by 60° implies the change in direction of the beam after reflecting off the mirror. This is not the angle of incidence or reflection directly, but rather the total change in the angle of the beam's path.
3. Set up the relationship based on the law of reflection. If the beam is initially horizontal, the angle of incidence (\( \theta_i \)) is the angle the incoming beam makes with a line perpendicular (normal) to the mirror surface at the point of incidence.
4. Since the beam is deflected by 60°, the outgoing beam makes an angle of 60° with the direction of the incoming beam. Using the geometry of the situation, calculate the angle of incidence (\( \theta_i \)) and the angle of reflection (\( \theta_r \)) which should be equal.
5. Determine the angle \( \phi \) which is typically the angle between the normal to the mirror and the reflected ray. This can be calculated using the angles of incidence or reflection as found from the previous steps.