A beam of white light is incident normally on a plane surface absorbing 70% of the light and reflecting the rest. If the incident beam carries 10 W of power, find the force exerted by it on the surface.

(Use h = 6.63 × 10^{-34}J-s = 4.14 × 10^{-15} eV-s, c = 3 × 10^{8} m/s and me = 9.1 × 10^{-31}kg)

#### Solution

Power of the incident beam,* P *= 10 watt

Relation between wavelength (λ) and momentum (*p*):

`λ = h/p` ,

where h is Planck's constant

⇒ `p = h/λ`

On dividing both sides by t , we get :

`p/t = h/(λt)` ...(1)

Energy,

`E = (hc)/λ`

⇒ `E/t = (hc)/(λt)`

Let P be the power . Then,

`P = E/t = (hc)/(λt)`

`P = (pc)/t ................["Using equation (1)"]`

⇒` p/c = p/t`

Force ,

`F = p/t = p/c` `("Since F" = "Momentum"/"Time")`

`"Force, F" = 7/10 " (absorted)" + 2 xx 3/10 ("reflected")`

`F = 7/10 xx P/c + 2 xx 3/10 xx P/c`

`F = 7/10 xx 10/(3 xx 10^8) + 2 xx 3/10 xx 10/(3 xx 10^8)`

`F = 13/3 xx 10^-8 = 4.33 xx 10^-8 "N"`