The number of images observable between two parallel mirror is
infinity
Understanding Image Formation Between Parallel Mirrors
When an object is placed between two plane mirrors that are parallel to each other, multiple images are formed due to repeated reflections. Let's understand how this happens.
How Images Form in a Single Plane Mirror
A single plane mirror forms one virtual image of an object. The image is located behind the mirror at the same distance as the object is in front of the mirror, and it is laterally inverted.
Images Formed Between Parallel Mirrors
Consider two plane mirrors, M1 and M2, placed parallel to each other. Let an object (O) be placed between them.
- Mirror M1 forms an image of the object (I1). This image I1 acts as a virtual object for the other mirror, M2.
- Mirror M2 forms an image of the object (I'2). This image I'2 acts as a virtual object for the first mirror, M1.
This process continues. The image formed by one mirror becomes the object for the other mirror, leading to the formation of a new image. These images then act as new virtual objects for the mirrors, and so on.
Why an Infinite Number of Images?
Since the mirrors are parallel, the reflections continue back and forth indefinitely. Each image formed by one mirror is in the field of view of the other mirror, causing it to form another image. This chain reaction of image formation continues without end.
The angle between the mirrors is related to the number of images formed by the formula \(n = \frac{360^\circ}{\theta} - 1\), where \(n\) is the number of images and \(\theta\) is the angle between the mirrors.
For parallel mirrors, the angle \(\theta = 0^\circ\). If we conceptually substitute \(\theta = 0\) into the formula, we would get \(\frac{360^\circ}{0} - 1\), which tends towards infinity. This mathematical concept aligns with the physical observation that reflections continue infinitely.
Therefore, due to the continuous process of reflection and re-reflection between the two parallel surfaces, an infinite number of images are observable.
Conclusion on Parallel Mirror Images
When an object is placed between two parallel mirrors, light rays from the object bounce back and forth between the mirrors multiple times. Each reflection creates a new image. Because the mirrors are parallel, this process never stops, resulting in an infinite number of images being formed.
Important Questions from Mirrors and Images
What type of mirror is used in the headlights of vehicles?
- A concave mirror forms a real and inverted image of a distant object at a distance of $15 \text{ cm}$ from the mirror.
If an object is placed $20 \text{ cm}$ in front of this mirror, what will be the nature and magnification of the image formed? An object is placed at a distance of \(\frac{f}{2}\) from a convex lens. The image will be
Which of the following pair is correct?
I. Mirror formula : (1/v) – (1/u) = (1/f)
II. Lens formula : (1/v) + (1/u) = (1/f)
- A beam of parallel light, originating from a distant source, is first incident on a convex lens with focal length $f_2$.
Subsequently, the light passes through the lens and then reflects from a concave mirror having a focal length $f_1$.
The concave mirror is placed at a distance $d$ from the convex lens.
For the light rays to retrace their original path and ultimately emerge from the lens as a parallel beam heading back towards the distant source, the separation distance $d$ between the lens and the mirror must be:
