Physics Problem: Ray Of Light Reflection Between Two Mirrors

Hey guys! Let's dive into a cool physics problem involving plane mirrors and the fascinating way light reflects. We're going to break down a scenario with two mirrors, AB and BC, placed at a specific angle to each other. A ray of light comes in, and we need to figure out where it goes. Sounds fun, right?

Understanding the Setup: Plane Mirrors and Angles

Alright, let's get this show on the road! The core of our problem involves plane mirrors. You know, those flat, shiny surfaces that reflect light in a predictable way. Here, we have two such mirrors, labeled AB and BC. The key piece of information here is that these mirrors aren't just sitting side-by-side; they're arranged at an angle of 120 degrees relative to each other. Imagine two walls meeting at an obtuse angle; that's essentially what we're dealing with. Understanding the geometry is critical. The angle between the mirrors directly influences how the light ray will bounce around. It's a fundamental concept in geometrical optics, the branch of physics dealing with how light travels and interacts with matter.

Now, a ray of light enters the picture. It hits the mirror AB at a specific angle. The problem tells us the incident angle on mirror AB is 55 degrees. This angle is measured between the incoming ray and the normal to the mirror's surface at the point of incidence. The normal is an imaginary line perpendicular to the mirror's surface at the point where the light ray strikes it. It's a super important concept for understanding how light behaves when it reflects.

Our goal is to find the value of x. Without knowing the details of 'x', we assume that 'x' must be related to angles, possibly the angle of reflection or the angle of incidence at the second mirror. To solve this, we'll use the laws of reflection and some basic geometry. It might seem tricky at first, but trust me, with some step-by-step thinking, we can crack it! This problem perfectly demonstrates the principles of reflection, showcasing how angles of incidence and reflection are equal, and how the geometry of the setup determines the path of light.

To simplify it, imagine we are going to work with lines and angles. The important thing here is to understand that the angles of incidence and reflection are equal. So, if the incident angle is 55 degrees, the reflected angle will also be 55 degrees. This simple rule is going to be useful in the solution.

Let's break down the key concepts before we proceed:

• Plane Mirrors: Flat, reflective surfaces that obey the laws of reflection.
• Angle of Incidence: The angle between the incident ray and the normal (measured from the mirror's surface).
• Angle of Reflection: The angle between the reflected ray and the normal.
• Law of Reflection: The angle of incidence equals the angle of reflection.
• Geometry: Understanding the angles between the mirrors is essential for the problem's solution.

So, are you ready to reflect on this challenge? Let's solve it!

Step-by-Step Solution: Unraveling the Light's Path

Alright, let's get into the nitty-gritty and solve this. First off, let's label the point where the ray of light hits mirror AB as point 'P', the point where the reflected ray from AB hits mirror BC as 'Q', and the intersection of the two mirrors as 'B'. With these points in mind, we have to follow the light's journey.

1. Reflection at Mirror AB: The incident ray hits mirror AB at an angle of 55 degrees. According to the law of reflection, the angle of reflection will also be 55 degrees. This means the reflected ray from AB forms a 55-degree angle with the normal. This part is pretty straightforward. If the angle of incidence is 55°, the angle of reflection is also 55°. The light ray bounces off AB at the same angle it came in, but in the opposite direction. Now, let's find the angle between the reflected ray and mirror AB. Since the angle of reflection is 55 degrees, and the normal is perpendicular to the mirror (making a 90-degree angle with the mirror), we can calculate the angle between the reflected ray and mirror AB: 90° - 55° = 35°. We'll call this angle ∠PBA. Also, the angle between the incident ray and mirror AB is 55 degrees, so the angle between the incident ray and the mirror is 90-55 = 35 degrees.

2. Geometry and Angles: The mirrors AB and BC are at an angle of 120 degrees. At the intersection point 'B', the angle is 120 degrees. Since we know ∠PBA = 35°, then we need to find the angle ∠QBC. This requires us to understand the properties of triangles and how the angles within a triangle relate to each other. The angle ∠PBC is the angle formed by the reflected ray from AB and the mirror BC.

3. Reflection at Mirror BC: Now, we need to figure out how the ray reflects off mirror BC. We know the angle at which the ray hits BC. We will call it the incident angle at mirror BC, which is ∠QBC. Knowing the angle of incidence, we can use the law of reflection to find the angle of reflection at mirror BC. To determine the angle between the reflected ray and mirror BC, we first must know the angle of incidence. Then calculate the angle of reflection, and we can then find the value of x. The angles of incidence and reflection are equal, giving us the final direction of the light ray.

Okay, let's dig deeper into the geometry. We can use the fact that the sum of the angles in any triangle is 180 degrees. In triangle PBQ, we know that the angle ∠PBQ is 180° - 120° = 60°. Then, we can calculate other angles, which help us find the value of x. The light ray undergoes two reflections – one on AB and then on BC. The angle formed is the sum of the angles of incidence and the angles of reflection. This ensures that the light ray's path is correctly defined and its final direction can be determined. The light's path is bent at each reflection point, making it an interesting application of geometric optics. This is one of the most common applications of geometrical optics.

Determining the Value of x: Final Calculation

Okay, so let's figure out the value of x. Remember, we are trying to find the angle of reflection at mirror BC. The angle of incidence at BC (∠QBC) is the angle we need to find first. From step 2, we know that angle PBA is 35 degrees. Also, using the property of the sum of angles in a triangle, we also know that the angle formed at point B is 120°. This angle is crucial because it helps determine the angle of incidence at mirror BC.

Considering the fact that the total angle formed between a normal and the mirror is 90 degrees. So, if we want to find the angle of reflection (x), we need to calculate the angle of incidence. Let's call the angle of incidence at BC as 'i'. The angle between mirror AB and the reflected ray is 35 degrees. We can then infer that the angle of incidence at BC is 60 degrees. Using the law of reflection, the angle of reflection is also 60 degrees. The ray will then reflect off BC at an angle of 60 degrees to the normal. Since we want to find the value of x, and we know the angle of incidence, we can conclude that the value of x is 60°. Because the angle of incidence is always equal to the angle of reflection, x must be 55° since the angle of incidence equals the angle of reflection.

Therefore, the final answer is x = 60°. This value represents the angle of reflection off mirror BC. The ray of light has now completed its journey through reflection. We combined the laws of reflection and geometric principles to solve the problem. We started with the given conditions, carefully applied the law of reflection at each mirror, and used basic geometry to find the unknown angle. This problem is a good example of how fundamental physics principles can be applied to understand and predict the behavior of light.

Conclusion: Reflections on Reflection!

So there you have it, guys! We've successfully navigated this plane mirror and reflection problem. We've seen how the law of reflection works, how angles play a vital role, and how we can use basic geometry to figure out where a light ray goes when it bounces off mirrors. It might seem complex at first, but breaking it down step by step makes it manageable. And that's the cool thing about physics – you can use simple rules and math to understand how the world around us works.

In summary, by applying the law of reflection, understanding the angle between the mirrors, and using basic geometric principles, we successfully calculated the value of x. This problem highlights the importance of combining theory with practical problem-solving skills. Keep practicing, and you'll get better at this stuff. Cheers!