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Question
A parallel beam of monochromatic light of wavelength 663 nm is incident on a totally reflecting plane mirror. The angle of incidence is 60° and the number of photons striking the mirror per second is 1.0 × 1019. Calculate the force exerted by the light beam on the mirror.
(Use h = 6.63 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)
Solution
Here ,
Wavelength of monochromatic light, `λ = 663 xx 10^-9 "m"`
Angle of incidence, `θ = 60^circ`
Number of photons per second, `n = 1 xx 10^19`
Momentum of photon,
`p = h/λ`,
where h is Planck's constant.
`p = (6.63 xx 10^-34)/(663 xx 10^-9) = 10^-27`
Force exerted on the wall,
`F = n xx [pcosθ - (-pcosθ)] = 2npcosθ`
= `2 xx 1 xx 10^19 xx 10^-27 xx 1/2`
= `1.0 xx 10^-8 "N"`
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