Sum

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 × 10^{19}. Calculate the force exerted by the light beam on the mirror.

(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)

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#### 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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