## increasing the spot size

PLease see if you could help me over this..

I have a laser beam emanating from am aperture of 50 mm dia. The beam divergence being 0.4 mrad. If i now choose a situation where say instead of the conventional beam expander design to expand the beam size and reduce the beam divergence, i choose to simply put a diverging lens in front (immediate exit) of the beam aperture. what should be the focal length of this lens to produce a spot size of 1m (say) at 100m ?
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 Not very sure but might be around 5335 mm ...
 thanx.. could you please elaborate and explain how did you arrive at this figure?

Recognitions:

## increasing the spot size

If you only have a diverging lens, why do you think you will reduce the beam divergence?
 Your output beam divergence is 0.4 mrad. You want a beam divergence of 10 mrad (1 meter at 100 meters). This is an angular magnification of about 25. So the focal length of the diverging lens should be about -4 meters (-4000 mm).

 Quote by Andy Resnick If you only have a diverging lens, why do you think you will reduce the beam divergence?
I dont intend to reduce the beam divergence.. i want 2 increase the spot size .. beam expanders can help me achieve that (bigger spot size )with an additional advantage of a reduced divergence. but m not interested in following that approach.
 The 5335 mm earlier was a value obtained with geometry in Rhino3D... that is why I'm not 100% about it. Basically I ran a line between a point at 100m with 500mm (half) elevation through a point at 25mm elevation situated at distance 0. the line went further to cross the X axis at -5335 mm. The small value of 0.4 mrad would increase the spot size of the naked laser beam to 120mm at 100m. I've ignored it since it would have made little difference for the diverted 1 m spot.