A helium-neon laser of the type often found in physics laboratories has a beam p

Question

A helium-neon laser of the type often found in physics laboratories has a beam power of 9.50 mW at a wavelength of 633 nm. The beam is focused by a lens to a circular spot whose effective diameter may be taken to be equal to 2.00 wavelengths. Calculate the intensity of the focused beam.

Calculate the radiation pressure exerted on a tiny perfectly absorbing sphere whose diameter is that of the focal spot.

Calculate the force exerted on this sphere.

Calculate the magnitude of the acceleration imparted to it. Assume a sphere density of 3.70×103 kg/m3

Explanation / Answer

Given Data Power of the laser beam, P = 9.50 *10-3 W Wavelength of the light , = 633 *10-9 m Diameter of the spot is, d = 2                                          = 1266 *10-9 m Cross sectional area of the beam, A = d2 /4                                                          = (1266 *10-9 m)2 / 4                                                          = 1.25 *10-12 m2 Sphere density is, = 3.70×103 kg/m3
Solution: Intensity of the beam, I = P / A                                       = (9.50 *10-3 W) / (1.25 *10-12 m2)                                       = 7.6 *109 W/m2 -------------------------------------------------------------------------- Radiation pressure is,                               pr = I / c                                   = (7.6 *109 W/m2) / (3.0 *108 m/s)                                   = 25.3 Pa --------------------------------------------------------------------------- Force exerted on the sphere is,                             F = A ( pr )                                = (1.25 *10-12 m2) (25.3 Pa)                                = 3.16 *10-11 N --------------------------------------------------------------------------- Acceleration imparted to the sphere is,                           a = F / m                              = F / V                              = F / ( d3 /6)                               = 6 (3.16 *10-11 N) / ( 3.70×103 kg/m3)(1266 *10-9 m)3                               = 8.04 * 103 m/s2 Sphere density is, = 3.70×103 kg/m3
Solution: Intensity of the beam, I = P / A                                       = (9.50 *10-3 W) / (1.25 *10-12 m2)                                       = 7.6 *109 W/m2 -------------------------------------------------------------------------- Radiation pressure is,                               pr = I / c                                   = (7.6 *109 W/m2) / (3.0 *108 m/s)                                   = 25.3 Pa --------------------------------------------------------------------------- Force exerted on the sphere is,                             F = A ( pr )                                = (1.25 *10-12 m2) (25.3 Pa)                                = 3.16 *10-11 N --------------------------------------------------------------------------- Acceleration imparted to the sphere is,                           a = F / m                              = F / V                              = F / ( d3 /6)                               = 6 (3.16 *10-11 N) / ( 3.70×103 kg/m3)(1266 *10-9 m)3                               = 8.04 * 103 m/s2                               = 8.04 * 103 m/s2

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