Explain why a ray of light passing through the centre of curvature of ...
Explanation of Reflection of Light through the Centre of Curvature of a Concave Mirror
When a ray of light is incident on a concave mirror, it gets reflected off the mirror surface according to the laws of reflection. The angle of incidence is equal to the angle of reflection, and the reflected ray passes through the focal point of the mirror. However, when the incident ray passes through the centre of curvature of the concave mirror, it gets reflected back along the same path. This phenomenon can be explained in the following steps:
Step 1: Definition of Centre of Curvature
The centre of curvature of a concave mirror is the point where the mirror surface would intersect if it were extended into a complete sphere. It lies at a distance of twice the focal length from the mirror surface.
Step 2: Reflection at the Centre of Curvature
When a ray of light is incident on the concave mirror at the centre of curvature, it is incident perpendicularly to the mirror surface. According to the laws of reflection, the angle of incidence is zero, and the angle of reflection is also zero. Therefore, the reflected ray is in the same direction as the incident ray, and it passes back through the centre of curvature.
Step 3: Symmetry of the Mirror Surface
The concave mirror is symmetric about the line passing through the centre of curvature and the vertex of the mirror. Therefore, any ray of light that passes through the centre of curvature and gets reflected back along the same path will also be incident on the mirror surface perpendicularly. This means that the angle of incidence will be zero, and the angle of reflection will also be zero. Therefore, the reflected ray will be in the same direction as the incident ray.
Step 4: Conclusion
Therefore, when a ray of light passes through the centre of curvature of a concave mirror, it gets reflected back along the same path because the incident and reflected rays are both perpendicular to the mirror surface, and the mirror is symmetric about the line passing through the centre of curvature and the vertex of the mirror.