The focal length of a plane mirror is considered infinite because parallel rays of light that strike the mirror are reflected back parallel to each other.
A plane mirror is defined as a flat reflecting surface. Understanding how light interacts with this flat surface is key to grasping why its focal length is infinite.
Reflection of Parallel Rays
According to the principles of reflection, when parallel rays of light hit a plane mirror, they bounce off the surface in such a way that they remain parallel after reflection.
- Incoming Rays: Consider light rays traveling towards the mirror parallel to each other.
- Reflection: Each ray obeys the law of reflection (angle of incidence equals angle of reflection).
- Outgoing Rays: Because the surface is flat and the incoming rays are parallel, the reflected rays emerge parallel to each other.
Why Parallel Rays Mean Infinite Focal Length
In optics, the focal point is the point where parallel rays of light converge after reflection from a mirror (or refraction through a lens), or the point from which they appear to diverge. The focal length is the distance from the mirror's surface to the focal point.
For curved mirrors (like concave or convex mirrors), parallel rays either converge to a real focal point or appear to diverge from a virtual focal point at a finite distance.
However, as the reference states, with a plane mirror:
when the parallel rays of light strike the mirror they get reflected back parallel to each other. So, they never meet or we can say they meet at infinity. So, the focal length of the plane mirror is Infinity.
Since the reflected rays are parallel, they do not converge or diverge from a point at a finite distance. In geometric terms, parallel lines are said to meet at infinity. Therefore, the point where these parallel reflected rays "meet" (or appear to meet, in the case of a plane mirror forming a virtual image) is infinitely far away.
| Mirror Type | Surface Shape | Parallel Ray Reflection | Focal Point Location | Focal Length |
|---|---|---|---|---|
| Plane | Flat | Reflected parallel | At infinity | Infinite |
| Concave | Curved Inward | Converge to a real point | In front of mirror | Finite (+) |
| Convex | Curved Outward | Appear to diverge from a point | Behind mirror | Finite (-) |
Because the focal point is at infinity, the distance from the mirror to this point – the focal length – is also considered infinite.
Practical Implications
While you don't use the focal length of a plane mirror in the same way you do for a curved mirror, understanding its infinite nature helps explain:
- Image Formation: Plane mirrors form virtual images that are the same size as the object and located as far behind the mirror as the object is in front. This is consistent with the idea that the light rays aren't converging or diverging at any finite point to form a real image.
- Magnification: Plane mirrors have a magnification of exactly +1 (image is upright and same size). This is also a consequence of their flat nature and the virtual image formation, related to the concept of an infinite radius of curvature and thus infinite focal length.
In summary, the flatness of a plane mirror causes incoming parallel light rays to reflect as parallel rays. Because parallel lines meet at infinity, the focal point of a plane mirror is at infinity, resulting in an infinite focal length.
