Laser Divergence Info

[Fivos]

Laser Divergence Calculator
Example of an almost accurate aligned laser. A 473nm 50mw laser..
Divergence: 1.2mrad


Hope you liked my project...
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Warning: VERY BAD ENGLISH...

 

[Cyparagon]

I like working with ones better. Here's something a little more simple. If a laser diverges 1mm in 1m, the tangent of the angle would be equal to 1/1000:

tan θ = 1/1000
θ = arctan(0.001)
θ = 0.0009999 = 0.001rad = 1mrad

Follow the steps backward to see that 2mrad just means it diverges 2mm for every meter.

 

[DrSid]

Doing arctan of angles bellow 1 degree is redundant. It results in almost the same number.

 

[chipdouglas]

Doing arctan of angles bellow 1 degree is redundant. It results in almost the same number.

I am probably the worst person at math here but if the numbers are "almost" the same, how is it redundant?
i'm not being a smart ass. just looking for an explanation.

 

[DrSid]

I am probably the worst person at math here but if the numbers are "almost" the same, how is it redundant?
i'm not being a smart ass. just looking for an explanation.

It's redundant for most uses .. the difference is too small. For laser divergence for example it's irrelevant if it is 0.001 or 0.00997.
So if you make one measurement of beam diameter at large distance, all you need for divergence is size/distance (both in same units, result in radians).

 

[Fivos]

I didn't know. I'll do some more tests....Thanks...

 

[Cyparagon]

Good point, Dr. Sid. I was going to add that, but I forgot.

You'll see that for values close to zero, the graph of tangent is virtually linear. That is to say y ≈ x.
tan θ ≈ θ

The same is true of sine.

 

[DrSid]

I use different explanation. And that is: what does radian actually mean ? Well .. it measures the 'arc'. If you take pie section of radius 1, its curved side will be of the same length as the angle of the pie in radians. Full circle will be 2*pi.
Now imagine very thin pie section .. it's clear that the curvature has little effect on the length of the side opposite to the angle. Also as the central angle gets small, the other two angles are getting close to 90 degrees. So all height of the triangle, length of the arc, and length of the side opposing the central angle are becoming very similar .. and equal to angle in radians itself.