Question

Explain why a ray of light passing through the center of curvature of a concave mirror gets reflected along the same path.

Answer 1

Hint: Any light ray that passes through the center of curvature of a concave mirror strikes the concave mirror at a \[90^\circ \] angle. We know that any light ray that strikes a mirror at a \[90^\circ \] angle is always reflected along the same path. So, any light ray that passes through the center of curvature of a mirror is always reflected through the same path.

Complete answer:
A concave mirror is shown below

So, in a concave mirror, the reflecting coating is on the outer side and the inner side is the reflective side.
We can imagine a concave mirror as part of a spherical mirror that has a reflecting coating on the outer side as shown below.

Now if you imagine a light ray passing through the center of curvature of a concave mirror, then if we consider the whole imaginary spherical mirror, the center of curvature is the center of the sphere. Now, we can see that the light ray that passes through the center of curvature and hits the concave mirror acts as a radius of the whole imaginary spherical mirror.

Now, we also know that the radius of a sphere makes a \[90^\circ \] angle with the surface of the sphere, so the radius of this spherical mirror will also make an \[90^\circ \] angle with the surface. So, any light ray that passes through the center of curvature (center of the imaginary sphere) will also hit the concave mirror at a \[90^\circ \] angle.

Now, we know that any light ray that strikes a mirror at a \[90^\circ \] angle is always reflected along the same path. So, any light ray that passes through the center of curvature of a mirror is always reflected through the same path.

Note:
In the solution we discussed how light rays that pass through the center of curvature of a concave mirror are reflected, this is also true for a convex mirror. This is also true for lenses, when the light passes through the center of curvature of a lens (convex or concave) it is not refracted and passes straight through the lens.