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JEE Main 2018 · Physics · Atoms, Nuclei and Dual Nature of Radiation · medium

A laser delivers a parallel beam of power 15 W and falls on a perfectly reflecting plane mirror at an angle of incidence of 60^° (measured from the…

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A laser delivers a parallel beam of power 15 W15\ \mathrm{W} and falls on a perfectly reflecting plane mirror at an angle of incidence of 60∘60^\circ (measured from the normal). Taking the speed of light as 3×108 m s−13\times10^{8}\ \mathrm{m\,s^{-1}}, the force exerted by the beam on the mirror is
  1. A. 5×10−8 N5\times10^{-8}\ \mathrm{N}
  2. B. 1×10−7 N1\times10^{-7}\ \mathrm{N}
  3. C. 2.5×10−8 N2.5\times10^{-8}\ \mathrm{N}
  4. D. 8.7×10−8 N8.7\times10^{-8}\ \mathrm{N}
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Answer: (A) 5×10−8 N5\times10^{-8}\ \mathrm{N}

Photons carry momentum p=E/cp=E/c, so the rate of incoming momentum is P/c=153×108=5×10−8 NP/c=\dfrac{15}{3\times10^8}=5\times10^{-8}\ \mathrm{N}. On reflection only the component normal to the mirror reverses; each photon's normal momentum changes by 2pcos⁡60∘2p\cos60^\circ, while the tangential component is unchanged. The force is therefore normal to the mirror with magnitude F=2Pccos⁡60∘=2×5×10−8×0.5=5×10−8 NF=\dfrac{2P}{c}\cos60^\circ=2\times5\times10^{-8}\times0.5=5\times10^{-8}\ \mathrm{N}. Normal incidence would give 1×10−7 N1\times10^{-7}\ \mathrm{N}, and a perfectly absorbing surface at 60∘60^\circ gives 2.5×10−8 N2.5\times10^{-8}\ \mathrm{N}.
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