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218 6 Answers, Hints and Solutions
A2.6 Contamination may be a problem for removable media, but it can be
avoided if we apply some kind of wipingmechanism and head liftingmecha-
nism.

Chapter 3

A3.1 See Fig. 3.2 and Table 3.1 in Sect. 3.1.
A3.2 Consult the followingprocedure:
1. decompose the beam into individual rays with appropriate intensity and
direction
2. trace individual rays
3. find the angle θ 1 (r, β) incident to the microsphere of a ray enteringthe
objective lens aperture at an arbitrary point (r, β)
4. compute the Fresnel transmission T and reflection R coefficients at the
incident point
5. compute the trappingefficiencies Q s (r)and Q g (r), for that ray
6. integrate the contribution of all rays within the convergent angle

2
7. compute total trappingefficiency using Q t = Q + Q 2 g
s
A3.3 See Fig. 3.15.
A3.4 First, we find the incident angle θ 1 (r, β) of a ray enteringthe aperture
of the objective lens at an arbitrary point (r, β) as shown in Fig. 3.12a. The
ray makes an angle α to the xy plane and also makes an angle γ to the y-axis
as shown in Fig. 3.12b. Then the angles become

α = tan −1 R m cot Φ m ,
r
γ =cos −1 (cos α cos β).

Since r 0 sin θ 1 (r, β)= s sin(γ), then the incident angle becomes

θ 1 (r, β)=sin −1 (s sin(tan −1 R m cot Φ m cos β),
r

where R m is the radius of the objective lens, Φ m is the maximum convergent
angle, s is the distance from the laser focus to the center of the microsphere.
Next, the trappingefficiencies Q s (r)and Q g (r) are computed by the vector
sum of the contributions of all rays within the convergent angle in the same
manner described in Example 3.4. See Fig. 3.13b.
A3.5 See Fig. 3.16.