# What are the number of laterally inverted images formed in a pair of plane mirrors inclined at: 1) 30 degrees 2) 45 degrees 3) 60 degrees 4) 90 degrees

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### 1 Answer

Suppose the mirror on the right is the mirror #1 and on the left is #2. If we are at a point in the bisecting line between the mirrors, we have:

First case: 30 degrees

The light incide on the mirror #1 with an angle of 0 degrees and is reflected in the same direction (first image). This beam incide and is reflected on the mirror #2, at an angle of 30 degrees relative to the normal; (second image). This latter reflected beam; incide again on the mirror #1 forming an angle of 60 degrees from normal. This last reflection, result in a reflected beam which forms an angle of 60 degrees whith the normal of the mirror # 1 (third image) and also is parallel to the plane of mirror #2 so that, is not reflected again. If we start with the mirror #2, we can make the same analysis and we will obtain three more images. So in this case we obtain six images.

Second case: 45 degrees

The light incide on the mirror #1 with an angle of 0 degrees and is reflected in the same direction (first image). This beam incide and is reflected on the mirror #2, at an angle of 45 degrees relative to the normal; (second image). This latter reflected beam; is parallel to the plane of the mirror #1, so that does not cause more images. If we start with the mirror #2, we can make the same analysis and we will obtain two more images. So in this case we obtain four images.

Third case: 90 degrees

The light incide on the mirror #1 with an angle of 0 degrees and is reflected in the same direction (first image); This reflected beam is parallel to the plane of mirror #2 and does not lead to the formation of other images. If we start with the mirror #2, the analysis leads us to obtain only an other image. Then, in this case only two images are obtained.

In summary we have:

**For an angle of 30 degrees, we get 6 images**.

**For an angle of 45 degrees, we get 4 images**.

**For an angle of 90 degrees, we get 2 images**.

These arrays of mirrors are used in a very curious device called Kaleidoscope.