A beam of light bounces on a mirror at 26 degrees. A second mirror adjacent to the first mirror is raised 70 degrees. Find the following.
Answer (1)
To understand the situation, we need to apply the principles of light reflection and geometry. Here's the breakdown of the problem and the steps to get an answer:1. Reflection Angle and Law of Reflection:The law of reflection states that the angle of incidence (the angle between the incoming ray and the normal to the surface) is equal to the angle of reflection (the angle between the reflected ray and the normal).In the first part of the question, the light bounces off the first mirror at an angle of 26 degrees. We’ll assume that this angle refers to the angle of incidence, which would also be the angle of reflection because of the law of reflection.So, the angle of incidence and reflection on the first mirror are both 26° with respect to the normal (perpendicular line to the mirror).2. Interaction with the Second Mirror:The second mirror is placed at a 70° angle. This is crucial because the light will now hit the second mirror at some angle, and it will reflect again.The angle between the first mirror's reflected light and the second mirror needs to be calculated. The angle of reflection on the first mirror (26°) plus the angle of the second mirror (70°) gives the total angle between the reflected ray and the second mirror.So, if the first mirror's reflection direction creates an angle of 26°, and the second mirror is angled at 70° relative to the first mirror, the total angle between the light ray and the second mirror is:total=26∘+70∘=96∘θ total=26 ∘+70 ∘=96 ∘ 3. Final Reflection on the Second Mirror:The law of reflection applies again at the second mirror, so the light will reflect off the second mirror at an angle equal to the angle of incidence (relative to the normal of the second mirror). The angle of incidence on the second mirror can be calculated by:incidence2=96∘−90∘=6∘ (since the normal to the second mirror is at a 90° angle to it).So, the light will be reflected at an angle of 6° with respect to the normal of the second mirror.Conclusion:The light will reflect at an angle of 6° after it hits the second mirror.The key here is using the principle of the law of reflection and understanding how angles between mirrors and the light path interact geometrically.
