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## Homework Statement

A laser beam ([tex]\mathrm{Power} = 1\ \mathrm{W})[/tex] is completely reflected by a mirror perpendicular to the beam. Light is made of photons, and each photon carries an energy [tex]E = h\nu[/tex] and a momentum [tex]P = h/\lambda[/tex], where [tex]\nu[/tex] is the frequency, [tex]\lambda[/tex] is the wavelength and [tex]h[/tex] is Planck's constant. Find the force with which light pushes the mirror.

## Homework Equations

Apart from those already present in the problem statement, I have:

[tex]\lambda \nu = c[/tex]

[tex]F = \frac{dp}{dt}[/tex]

## The Attempt at a Solution

Each second, the light source emits [tex]n[/tex] photons, each one carries an energy [tex]E = h\nu = hc/\lambda[/tex], for a total power of [tex]1\ \mathrm{W}[/tex]. This gives:

[tex]\displaystyle n = \frac P E = \frac{\lambda}{hc}[/tex]

In one second then, [tex]n[/tex] photons hit the mirror and bounce back, which gives:

[tex]\displaystyle F = \frac{dp}{dt} = n \cdot 2p = 2 \frac{\lambda}{hc}\cdot \frac{h}{\lambda} = \frac 2 c \approx 6.67\cdot 10^{-9}\ \mathrm{N}[/tex]

The result is somewhat intuitively pleasing, can you check it is correct, please?