Thursday, November 17, 2005

Image erection system - mirror calculations

how the heck do you figure out what size mirrors you use!?!?
well, the answer is the Pythagorean theorem.
yes, the very equation you learned in school.
a^2+b^2=c^2

so you have a 36x24mm frame size that you need to rotate 180 by going through four mirrors placed at right angles. let's take a look at one mirror set up at as such.



this is a view of my first mirror set up from above.
the 36x24mm image comes in through side A, reflects off of the mirror placed at side C, and exits at side B. this makes a horizontal 90 degree reflection.

since side A and side B form a right angle, this allows us to use pythagorean's theorem to calculate the mirror side, side C.

we know that the image is 36mm wide, and will stay that way.
both entrance and exit frames of the triangle will be 36mm
so that means, A=36 and B=36.
when we plug them into pythagorean's equation, we get the square of C.

36^2 + 36^2 = C^2 = 1296 + 1296 = 2592

now we just square root it and get the length of C.

sqrt 2592 = about 50.9mm (roughly 2")

so we have the length of the mirror, the height of the frame stays constant.
the result is a 50.8x24mm mirror.

we have two mirrors that do this horizontal translation. the first and fourth mirrors.

the second and third mirrors do a vertical translation
instead of a triangle where A=36 and B=36, the sides will be A=24 and B=24.
referring to the image, this would be the 2nd or 3rd mirror as viewed from the side.

same equation

24^2 + 24^2 = C^2 = 576 + 576 = 1152

now square root the result.

sqrt 1152 = about 33.94mm (roughly 1.33")

complete the mirror spec by adding the horizontal length that stays the same.

33.94x36mm mirror size.

1 Comments:

Anonymous Anonymous said...

you betta get that workin with the FX1 mothafucka!

9:59 PM  

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