Question

The angle of incidence of any light passing through the centre of curvature of a spherical mirror is :

• A. \(0^\circ\)
• B. \(45^\circ\)
• C. \(90^\circ\)
• D. \(60^\circ\)

Hint:

For spherical mirrors: A ray of light passing through the Centre of Curvature (C) strikes the mirror normally (perpendicularly). This means the incident ray itself is the normal at that point. Therefore, the angle of incidence is \(0^\circ\), and the ray retraces its path after reflection (angle of reflection is also \(0^\circ\)).

Answer 1

The Correct Option is A

Concept: For spherical mirrors, a line passing through the centre of curvature (\(C\)) and any point on the mirror's surface is a normal to the surface at that point. The angle of incidence is the angle between the incident ray and the normal at the point of incidence. Step 1: Understanding the Centre of Curvature (C) The centre of curvature of a spherical mirror is the centre of the sphere of which the mirror forms a part. Step 2: Properties of a line from the Centre of Curvature to the mirror surface Any line drawn from the centre of a sphere to its surface is perpendicular (normal) to the surface at that point. This applies to spherical mirrors as well. So, if a ray of light is directed towards the mirror along a line that would pass through the centre of curvature, that line itself acts as the normal at the point where the ray strikes the mirror. Step 3: Defining the Angle of Incidence The angle of incidence (\(i\)) is the angle between the incident ray and the normal to the reflecting surface at the point of incidence. Step 4: Analyzing the specific case The question states that the light ray is "passing through the centre of curvature". This means the incident ray itself lies along a radius of the sphere, and thus it lies along the normal to the mirror surface at the point of incidence. When the incident ray coincides with the normal, the angle between the incident ray and the normal is zero. Angle of incidence, \(i = 0^\circ\). Step 5: Reflection of such a ray According to the laws of reflection, the angle of reflection (\(r\)) is equal to the angle of incidence (\(i\)). So, if \(i = 0^\circ\), then \(r = 0^\circ\). This means the reflected ray will also make an angle of \(0^\circ\) with the normal. Consequently, the reflected ray will travel back along the same path as the incident ray (retraces its path). Therefore, the angle of incidence of any light passing through the centre of curvature of a spherical mirror is \(0^\circ\).