Selecting a projection lens

[P3D John Bercovitz <bercov@xxxxxxxxxx>]

Most of you probably already know this or have it in a book 
but since I was just using this equation a few days ago and
since there might be some of you who don't know it, I'll post 
it.
 
You may need to know how far from the screen you will have to 
put the projector to fill the screen.  You may need to know 
what focal length of projector lens you would need to fill the
screen from a certain distance.  You may need to know what size 
of screen to buy.
 
The equation is:
 
 (magnification + 1) times (lens focal length) = distance from
                                            projector to screen
where:
 
magnification = screen image size divide by transparency size
 
Examples:
 
1) You have a projector with 4" lenses and you want to fill a 
66"-wide screen with a 7-perf slide.  How far away will you have
to place the projector?
 
First find the magnification.  You have to convert the format's
width to inches or the screen's width to mm which is what the
factor of 25.4 does.
 
       66
m = --------- = 60
     28/25.4
 
distance from projector to screen = (m+1)*F = (60+1)*4 = 244"
 
2) You have a 45" screen and you want to fill it with 5-perf format
slides from 20 feet (240") away.  What focal length of projection 
lenses should you buy?
 
       45
m = --------- = 48
     24/25.4
 
F = distance/(m+1) = 240/48 = 5"
 
3) You have 15' from the projector to where the screen will be.  
Your projector has 5" lenses.  You will be projecting 7-perf slides.
What size screen should you buy?  
 
Why calculate it?  You could project it on a wall and measure it.  8-)
 
(magnification + 1) = (distance from projector to screen)/F
(magnification + 1) = (15 * 12 in/ft)/5 =36
magnification = 35
screen size = 35 * 28 mm /25.4 mm/in = 39"
 
John B
 
PS: These answers are approximate inasmuch as I'm not counting for 
LR image separation so add a little cushion to your calculated numbers.


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