Question

A budding magician holds a 3.98-mW laser pointer, wondering whether he could use it to keep an object floating in the air with the radiation pressure. This might be an idea for a new trick! Assuming the laser pointer has a circular beam 3.00 mm in diameter and the magician rigs up a totally reflecting sail on which to shine the laser, what is the maximum weight the magician could suspend with this technique

Answer 1

F = 2.65 10⁻¹¹ N

Step-by-step explanation:

The radiation pressure for a fully reflective surface is

P = 2S / c

where S is the pointiing vector which is the energy per unit area,

S = I =
`(\ P_(prom) )/(A)`

the area of ​​a circle is

A = π r² = π d²/4

S =
`(3.98 \ 10^(-3) )/( (\pi \ 0.003^2 )/(4) )`

S = 0.563 10⁻³ W / m2

let's calculate the pressure

P = 2 0.563 10⁻³/3 108

P = 0.3753 10⁻⁵ N / m²

this pressure exerts an upward force, the definition of pressures

P = F / A

F = P A

let's calculate

F = 0.3753 10-5 π / 4 0.003²

F = 2.65 10⁻¹¹ N