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Question

What is multiple reflection and how is image formed in it?

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Solution

Multiple reflection-

if the light is reflected for more than one time the image acts as the object for the mirror so the mirror reflects the image of the object and forms the new image, this process continues.

**Formation of an Image Due to Multiple Reflection of Light**

Principle

If an object is placed between two plane mirrors inclined at an angle we get more than one image due to multiple reflection of light.

The number of images n, obtained when two mirrors are inclined at angle theta is given by the relation, n is equal to 360 divided by theta minus 1.

If 360 divided by theta is not a whole number, then the number of images will be rounded off to the nearest integer.

When the angle of inclination between the mirrors is 120 degrees

You can see here that when two plane mirrors are kept inclined at 120 degree, only two images are formed.

Go through the mathematical proof given here and click on the button to see the ray diagram.

Image Formation when an object is placed between two mirrors inclined at 120 degrees

Place the mirrors MM and MM dash in such a way that the angle between them is 120 degrees.

Now place an object O in between the two mirrors.

Let OA and OB be the rays incident on the mirror MM.

OA being perpendicular to the mirror retraces its path whereas OB gets reflected along BC according to the laws of reflection

Extend the reflected rays AO and BC backwards. An image is formed at O1, the point of intersection of these reflected rays.

Let OD and OE be incident on the mirror MM dash.

OE gets reflected along EF according to the law of reflection and OD being perpendicular to the mirror MM dash retraces its path.

Extend EF and OD backwards. The point of intersection O2 gives the position of the image.

Thus when the angle of inclination is 120 degrees, we get two images.

When the mirrors are mutually perpendicular to each other

When two mirrors are placed mutually perpendicular to each other, we obtain three images.

This can be mathematically proved using the relation n is equal to 360 divided by theta minus 1.

Click on the button to view the animation.

Image Formation when the mirrors are mutually perpendicular to each other

Place on object O between two mutually perpendicular mirrors.

OA and OB are the two rays that are incident on the mirror MM.

OA being normal to the surface retraces its path.

OB gets reflected along BC according to the laws of reflection

Extend the rays OA and BC backwards. They meet at O1. O1 is the virtual image of the object.

OD and OE represent the rays that are incident on the mirror MM dash.

OD being normal retraces its path.

OE makes an angle i with the normal N dash and gets reflected along EF according to the law of reflection.

Extend the reflected rays OD and EF backwards. They meet at O2. O2 is the virtual image of O.

Reflected ray BC gets reflected internally by the mirror MM dash along CG. The ray CG appears to come from O3 which is the image of O1.

Similarly EF gets internally reflected by the mirror MM along FH. The ray appears to come from O4. O$ and O3 coincide.

Thus we obtain three images when an object is placed between two mutually perpendicular mirrors.

When two mirrors are placed parallel to each other

You can see here that when two mirrors are placed parallel to each other, infinite images are formed.

Image Formation when an object is placed between two mirrors placed parallel to each other.

Let MM and M dash M dash be placed parallel to each other.

Place an object O in between the mirrors.

OO dash represent the rays incident on the mirror MM.

The ray OA makes an angle i with the normal and gets reflected according to the laws of reflection.

OO dash being normal to the mirror retraces its path.

Extend the rays AB and OO dah backwards. They meet at I1 which is the virtual image of O.

The mirror M dah M dash reflects the reflected ray AB.

Extend OM dash and BC backwards. They meet at I2 to give the virtual image.

Similarly the images I3, I4 are formed.

if the light is reflected for more than one time the image acts as the object for the mirror so the mirror reflects the image of the object and forms the new image, this process continues.

Principle

If an object is placed between two plane mirrors inclined at an angle we get more than one image due to multiple reflection of light.

The number of images n, obtained when two mirrors are inclined at angle theta is given by the relation, n is equal to 360 divided by theta minus 1.

If 360 divided by theta is not a whole number, then the number of images will be rounded off to the nearest integer.

When the angle of inclination between the mirrors is 120 degrees

You can see here that when two plane mirrors are kept inclined at 120 degree, only two images are formed.

Go through the mathematical proof given here and click on the button to see the ray diagram.

Image Formation when an object is placed between two mirrors inclined at 120 degrees

Place the mirrors MM and MM dash in such a way that the angle between them is 120 degrees.

Now place an object O in between the two mirrors.

Let OA and OB be the rays incident on the mirror MM.

OA being perpendicular to the mirror retraces its path whereas OB gets reflected along BC according to the laws of reflection

Extend the reflected rays AO and BC backwards. An image is formed at O1, the point of intersection of these reflected rays.

Let OD and OE be incident on the mirror MM dash.

OE gets reflected along EF according to the law of reflection and OD being perpendicular to the mirror MM dash retraces its path.

Extend EF and OD backwards. The point of intersection O2 gives the position of the image.

Thus when the angle of inclination is 120 degrees, we get two images.

When the mirrors are mutually perpendicular to each other

When two mirrors are placed mutually perpendicular to each other, we obtain three images.

This can be mathematically proved using the relation n is equal to 360 divided by theta minus 1.

Click on the button to view the animation.

Image Formation when the mirrors are mutually perpendicular to each other

Place on object O between two mutually perpendicular mirrors.

OA and OB are the two rays that are incident on the mirror MM.

OA being normal to the surface retraces its path.

OB gets reflected along BC according to the laws of reflection

Extend the rays OA and BC backwards. They meet at O1. O1 is the virtual image of the object.

OD and OE represent the rays that are incident on the mirror MM dash.

OD being normal retraces its path.

OE makes an angle i with the normal N dash and gets reflected along EF according to the law of reflection.

Extend the reflected rays OD and EF backwards. They meet at O2. O2 is the virtual image of O.

Reflected ray BC gets reflected internally by the mirror MM dash along CG. The ray CG appears to come from O3 which is the image of O1.

Similarly EF gets internally reflected by the mirror MM along FH. The ray appears to come from O4. O$ and O3 coincide.

Thus we obtain three images when an object is placed between two mutually perpendicular mirrors.

When two mirrors are placed parallel to each other

You can see here that when two mirrors are placed parallel to each other, infinite images are formed.

Image Formation when an object is placed between two mirrors placed parallel to each other.

Let MM and M dash M dash be placed parallel to each other.

Place an object O in between the mirrors.

OO dash represent the rays incident on the mirror MM.

The ray OA makes an angle i with the normal and gets reflected according to the laws of reflection.

OO dash being normal to the mirror retraces its path.

Extend the rays AB and OO dah backwards. They meet at I1 which is the virtual image of O.

The mirror M dah M dash reflects the reflected ray AB.

Extend OM dash and BC backwards. They meet at I2 to give the virtual image.

Similarly the images I3, I4 are formed.

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