Question

Biologists use optical tweezers to manipulate micron-sized objects using a beam of light. In this technique, a laser beam is focused to a very small-diameter spot. Because small particles are attracted to regions of high light intensity, the focused beam can be used to "grab" onto particles and manipulate them for various experiments. In one experiment, a 10 mW laser beam is focused to a spot that has a diameter of 0.82 μm.
Required:
a. What is the intensity of the light in this spot?
b. What is the amplitude of the electric field?

Answer 1

Answer:

a)   I = 1,894 10¹⁰ W / m², b)  E = 1.376 10⁵ N / C

Explanation:

a) intensity is defined as energy per unit area per unit time

          I = P / A

let's reduce the magnitudes to the SI system

         P = 10 mW = 10 10⁻³ W

         d = 0.82 μm = 0.82 10⁻⁶ m

the laser area is

         A =π r² = π d²/4

         A =π (0.82 10⁻⁶)²/4

         A = 5.28 10⁻¹³ m²

we calculate

          I = $\frac{10 \ 10^{-3}}{5.28 \ 10^{-13}}$

          I = 1,894 10¹⁰ W / m²

b) average intensity and electric field are related

          I = E * E

          E = √I

          E = $\sqrt{1.894 \ 10^{10}}$

          E = 1.376 10⁵ N / C