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

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Identify the relationship between the angles of incidence and reflection. According to the law of reflection, the angle of incidence is equal to the angle of reflection.

Recognize that the total deflection angle of the laser beam is given as 60°. This deflection angle is the sum of the angle of incidence and the angle of reflection.

Let the angle of incidence be denoted as θ. Since the angle of incidence equals the angle of reflection, the total deflection angle can be expressed as 2θ = 60°.

Solve for θ by dividing both sides of the equation by 2: θ = 60° / 2.

The angle ϕ is the angle between the mirror's surface and the incident beam. Since the angle of incidence θ is measured relative to the normal to the mirror, ϕ can be calculated as ϕ = 90° - θ.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Reflection of Light

Reflection of light occurs when a light beam strikes a surface and bounces off. The angle of incidence, which is the angle between the incoming beam and the normal (a perpendicular line to the surface), is equal to the angle of reflection. This principle is crucial for understanding how mirrors work and how they redirect light beams.

Angle of Deflection

The angle of deflection refers to the angle by which a beam of light is redirected after striking a surface, such as a mirror. In this context, if a laser beam is deflected by a certain angle, it is essential to understand how this angle relates to the angles of incidence and reflection to determine the resulting angles in the system.

Geometry of Angles

Understanding the geometry of angles is vital for solving problems involving reflections. In this scenario, the total angle change can be calculated by considering the initial angle of the beam, the angle of incidence, and the angle of reflection. This geometric approach allows for the determination of unknown angles, such as ϕ, based on the known deflection.