What is the Centre of Curvature of a spherical mirror?
Understanding the Centre of Curvature in Spherical Mirrors
The question asks for the definition of the Centre of Curvature of a spherical mirror. A spherical mirror is essentially a part cut out from a hollow sphere of glass or plastic.
Let's analyse the given options to determine the correct definition:
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Option 1: It is the centre of a hollow sphere of which the spherical mirror is a part.
This option defines the Centre of Curvature ($\text{C}$). When you consider a spherical mirror as a section of a larger sphere, the center of that original sphere is called the Centre of Curvature of the mirror. It is a crucial reference point for understanding how light reflects off the mirror surface.
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Option 2: It is a point from which the rays of light appear to be coming from on the principal axis of a convex mirror.
This option describes the principal focus ($\text{F}$) of a convex mirror, which is a virtual point. Rays parallel to the principal axis appear to diverge from this point after reflection.
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Option 3: It is the midpoint of a spherical mirror.
This option describes the Pole ($\text{P}$) of the spherical mirror. The Pole is the geometric centre of the mirror's reflecting surface.
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Option 4: It is the point on the principal axis through which rays of light parallel to the principal axis pass after reflection.
This option describes the principal focus ($\text{F}$) of a concave mirror, which is a real point. Rays parallel to the principal axis converge at this point after reflection.
Comparing the options with the standard definitions in geometric optics, Option 1 accurately defines the Centre of Curvature of a spherical mirror.
| Term | Definition for Spherical Mirrors |
|---|---|
| Centre of Curvature ($\text{C}$) | The centre of the hollow sphere from which the mirror is cut. |
| Pole ($\text{P}$) | The geometric centre of the mirror's reflecting surface. |
| Principal Axis | The straight line passing through the Pole and the Centre of Curvature. |
| Principal Focus ($\text{F}$) | The point on the principal axis where parallel rays converge (concave) or appear to diverge from (convex) after reflection. |
Therefore, the Centre of Curvature is intrinsically linked to the original sphere that forms the spherical mirror.
Revision Table: Spherical Mirror Terminology
| Term | Symbol | Description |
|---|---|---|
| Centre of Curvature | $\text{C}$ | Centre of the sphere of which the mirror is a part. |
| Radius of Curvature | $\text{R}$ | Radius of the sphere of which the mirror is a part (distance PC). |
| Pole | $\text{P}$ | Geometric centre of the mirror. |
| Principal Axis | - | Line passing through P and C. |
| Principal Focus | $\text{F}$ | Point where parallel rays meet or appear to meet after reflection. |
| Focal Length | $\text{f}$ | Distance PF. For paraxial rays, $\text{f} = \text{R}/2$. |
Additional Information on Centre of Curvature and Radius
The distance between the Pole ($\text{P}$) and the Centre of Curvature ($\text{C}$) is called the Radius of Curvature ($\text{R}$). This radius is constant for any given spherical mirror because it's the radius of the sphere from which the mirror is derived. The Centre of Curvature is located on the principal axis.
- For a concave mirror, the Centre of Curvature ($\text{C}$) is in front of the mirror (on the reflecting side).
- For a convex mirror, the Centre of Curvature ($\text{C}$) is behind the mirror (on the non-reflecting side).
Understanding the Centre of Curvature is fundamental as it helps define the radius of curvature and the principal axis, which are essential for drawing ray diagrams and applying mirror formulas to locate images formed by spherical mirrors.
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