A laser emits light at power 6.20 mW and wavelength 633 nm. The laser beam is focused (narrowed) until its diameter matches the 1080 nm diameter of a sphere placed in its path. The sphere is perfectly absorbing and has density 5.00 * 103 kg/m3. What are (a) the beam intensity at the sphere's location, (b) the radiation pressure on the sphere, (c) the magnitude of the corresponding force, and (d) the magnitude of the acceleration that force alone would give the sphere

a) S = 1.69 10⁹ W/m², b) P = 5.63 Pa, c) F = 20.6 10⁻¹² N

Explanation:

a) The intensity defined as the energy per unit area

S = U / A

Area of a circle is

W = 6.2 mw = 6.2 10-3 W

R = 1080 nm = 1080 10⁻⁹ m = 1.080 10⁻⁶ m

A = π R2

A = π (1,080 10⁻⁶) ²

A = 3.66 10 - 12 m²

S = 6.2 10-3 / 3.66 10-12

S = 1.69 10⁹ W / m²

b) The radiation pressure

P = 1 / c (dU / dt) / A

S = (dU / dt) / A

P = S / c

P = 1.69 10 9 / 3. 108

P = 5.63 Pa

c) the definition of pressure is force over area

P = F / A

F = P A

F = 5.63 3.66 10⁻¹²

F = 20.6 10⁻¹² N

d) for this we use Newton's second law

F = ma

a = F / m