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Portable Optical Tweezers Kit Chapter 4: Principles of Optical Tweezers
Rev B, July 8, 2019 Page 11
So far, the force was given as a function of
𝜃
which now has to be expressed in terms of
𝑟
and
𝛽
. Figure 5 shows a partial beam incident on the sphere with angle
𝜃
from the side.
The following statements hold true:
𝑋 = sin 𝜙 ∙ 𝑆 = sin 𝜃 ∙ 𝑅
(19)
and
sin 𝜙 = 𝑟 √𝑟
2
+ 𝑙
2 ⁄
(20)
𝑙
roughly corresponds to the focal length of the objective. Effectively, you can use the
objective’s working distance for this parameter.
Relation Between
𝒓
and
𝜽
 
Then,
𝜃
can be expressed as
𝜃(𝑟) = arcsin (
𝑆
𝑅
𝑟
√𝑟
2
+ 𝑙
2
)
(21)