Calculate No of Images Formed by 2 Mirrors at Angle α

In summary, there is a formula for calculating the number of images formed by two mirrors at an angle, known as α. To understand this formula, one must consider that a mirror acts as a doorway into another world, where everything is reversed front-to-back through the plane of the doorway. By using this concept and applying it to each mirror, one can create a set of images of anything between the mirrors. The number of images you see will depend on where your eye is located and any straight line from your eye that intersects the mirror will lead to an image created by that mirror.
  • #1
SandeshPhy
25
0
Is there any formula for calculating the no of images formed by two mirrors at an angle say α.
If yes,then please guide me to a proof of the same.
 
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  • #2
A mirror acts as though it was a doorway into another world whose inside reverses front-to-back through the plane of the doorway everything that is outside the doorway. That will include any images in any mirrors on the outside of the doorway. Use that on each mirror to iteratively create a set of images of anything between the mirrors, repeated in wedges of that angle. Then any straight line from your eye that intersects the mirror that leads to an image created by that mirror is an image you will see. That should let you figure out how many images you see. I imagine it should depend on where your eye is.
 

Related to Calculate No of Images Formed by 2 Mirrors at Angle α

1. How do I calculate the number of images formed by two mirrors at an angle α?

The number of images formed by two mirrors at an angle α can be calculated using the formula: N = 360/α - 1, where N is the number of images and α is the angle between the two mirrors.

2. What is the relationship between the angle α and the number of images formed?

As the angle α increases, the number of images formed decreases. This is because as the mirrors are angled closer to each other, the reflected rays overlap and create fewer distinct images.

3. Can the number of images formed ever be negative?

No, the number of images formed cannot be negative as it represents a physical quantity of distinct images. However, if the angle α is very small, the formula may result in a decimal value, in which case, the number of images can be rounded down to zero.

4. Do the mirrors have to be perfectly parallel for this formula to work?

No, the formula can still be applied even if the mirrors are not perfectly parallel. However, the result may not be entirely accurate as the formula assumes perfect parallelism between the mirrors.

5. Can this formula be applied to any angle between the mirrors?

Yes, this formula can be applied to any angle between the mirrors. However, for angles greater than 90 degrees, the formula will result in a negative number of images, which is not physically possible. In such cases, the angle should be adjusted to be less than 90 degrees.

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