Number of Images Formed by Two Plane Mirrors | JEE

An Introduction to Images Formed by Two Plane Mirrors

The images formed by two plane mirrors depend on the angle at which they are placed to one another. Two plane mirrors can be placed in parallel or perpendicular to one other. As images are formed on the angle between two plane mirrors, when the angle between the mirrors increases, the images formed decrease and vice versa.  Plane mirrors have some interesting properties, which include lateral inversion. Another interesting property of it is the ability to form multiple reflections. Let us understand these concepts thoroughly.

What are Plane Mirrors?

Plane mirrors are nothing but a flat reflective surface formed by an added layer of silver nitrate or aluminium. The image formed by the plane mirrors is erect and is formed by two laws of reflection. These are:

1. Incident ray, reflected ray and the normal all lie on the same plane

2. The angle of incidence is equal to the angle of reflection.

Plane mirrors are all around us. We can find them in offices, schools at our homes and so on. Thus, plane mirrors are used in a plethora of day-to-day applications. When an object is placed in front of a plane mirror the light rays incident on it are either absorbed, transmitted or reflected. The light rays that are reflected predominately are the ones that form an image. 

Image Formed by a Plane Mirror

The images formed by a plane mirror can be infinite or of a finite number. The infinite or the formation of multiple reflections formed by a plane mirror is achieved by using two plane mirrors in parallel. 

Formed by Two plane mirrors

The orientation of the two plane mirrors can also be changed. The two mirrors can also be placed at 90 degrees to one another. In such cases, the images formed are usually of a finite number. 

Formed by plane mirrors placed at 90 degrees

Plane Mirror Image Formula

The plane mirror image formula or the formula of number of images formed by two mirrors is given as,

$n=\dfrac{360}{\theta}-1$

Where $\theta$ is the angle between the two mirrors and n is the number of images formed. 

Let us understand this with an example. Let’s assume that the plane mirrors are placed at 90 degrees to one another. Then $\theta$ would be 90 degrees. Substituting this in the formula $n=\dfrac{360}{\theta}-1$

We have:

$n=\dfrac{360}{90}-1$

$\Rightarrow n=4-1$ 

$\therefore n=3 $

Thus, the images formed here are 3. 

Let us now take another example wherein the angle between the two plane mirrors is 60 degrees. Substituting this in the above formula i.e,

$n=\dfrac{360}{\theta}-1$

We get: 

$n=\dfrac{360}{60}-1$

$\Rightarrow n=6-1$

$\therefore n=5$

The images formed in this case will be 5. 

Thus, it is understandable from above that angle between mirrors is fundamental to get the desired number of images, since this entails the usage of plane mirrors in different applications. Ever wondered why periscopes employ plane mirrors? Plane mirrors in periscopes have the ability to change the direction of light rays, which makes the object viewable to the person viewing from the submarine. 

Periscopes are usually employed when we are not able to see the object on the other side or beyond any obstruction. Kaleidoscope is another interesting application of plane mirrors. Kaleidoscopes form multiple reflections. When we look inside a kaleidoscope, several patterns are seen. This is due to plane mirrors used in them.

Conclusion

The article above talks about the number of images formed by two plane mirrors. The orientation of the two mirrors can be perpendicular or placed in parallel to one another. When the two mirrors are placed in parallel, plane mirrors form multiple reflections of an object. This is an interesting application of plane mirrors that is used in kaleidoscopes. The different angles between two plane mirrors is also discussed. The formula of the number of images by two mirrors is given above and is illustrated using different examples. Thus, the articles clearly discusses the various placement orientation of two mirrors, followed by their application and characteristics.