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Question
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 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)
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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"`
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