You are comparing the beam waste for two different situations with the goal of using the smallest beam waste possible. A Nd-YAG laser system emits light at 532 nm and the beam is 8 mm in diameter. You also have a Ti-sapphire laser that emits at 855 nm and has a beam diameter of 6 mm. Compare the beam waist for both laser systems using a focusing lens with a focal length of 10 mm. Assume the light fills the lenses in each case

comparing the beam waist for both lasers ( ratio of the beam waists )

4.536 μm / 2.117 μm = 2.14

Explanation:

Nd-YAG laser system : emits at 532 nm , beam diameter = 8 mm

Ti-sapphire laser system : emits at 855 nm , Beam diameter = 6mm

Comparing the beam waist for both lase systems using a focusing lens

Focal length = 10 mm

assumption : light fills lenses in each laser system

Beam waist radius ( W ) =  

β = wavelength , D = diameter illuminated  , F = focal length

For

Nd-YAG laser system

β = 532 mm , D = 8 mm

hence ( Wn ) =   =  ( 2*532 / π ) ( 10 / 8 )   = 2.117 μm

For

Ti-sapphire laser

β = 855 nm ,  D = 6 mm

hence ( Wt )   =  ( 2* 855 ) / π ) ( 50 / 6 ) = 4.536 μm

comparing the beam waist for both lasers ( ratio of the beam waists )

4.536 μm / 2.117 μm = 2.14