HW 10 : 6 : Please help me answer this question: Item 6 Laser light can be focus

Question

HW 10 : 6 : Please help me answer this question:

Item 6 Laser light can be focused (at best) to a spot with a radius r equal to its wavelength A. Suppose that a 0.70- W beam of green laser light (A 5 x 10 m) is used to form such a spot and that a cylindrical particle of about that size (let the radius and height equal r is illuminated by the laser as shown in the figure. (Figure 1) of 1 Figure 1 5 x 10-7 m Part A Estimate the acceleration of the particle, if its density equals that of water and it absorbs the radiation. his order-of-magnitude calculation convinced researchers of the feasibility of "optical tweezers," p. 829 in the textbook.] Express your answer to one significant figure and include the appropriate units. a Value Units Submit My Answers Give U vide Feedback Continue

Explanation / Answer

we know that

S x A = dU/dt = power

Given

power = 0.7 W

so

S x A = dU/dt = 0.7

now

acceleration = force / mass

a = F/m

but

F = Pressure x area

so

a = PA/m

we know that

pressure = intensity (S) / speed (c)

P = S/c

so

a = (s/c) x A / m

a= s x A / c x m

also

mass = density x volume

voume of cylinder = pi x r2 x h

given

h= r = waven length = 5 x 10-7 m

so

volume = pi x r2 x r = pi x r3

so

mass = d x pi x r3

so

a = S x A / c x d x pi x r3

substituting the values we get

a = 0.7 / 3 x 10^8 x 1000 x ( 5 x 10-7)^3

a = 1.866 x 10^7

so the acceleration is 1.866 x 10^7 m/s2

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