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 deg and the no. of photons striking the mirror per second is 1.0 * 1019 . Calculate the force exerted by the light beam on the mirror.

Answer 1

$\bold \red{solution}$

Force exterted = rate of change of monetum.Since light ray is incident at the angle 60 degree so there is twp component of the monetum.Initian momentum in horizontal

1)direction = PsinθInitian momentum in vertical


2)direction = Pcosθfinal momentum in horizontal

3)direction = Psinθfinal momentum in vertical

direction = −Pcosθwe include negative sign because direction of the final momentum is opposite


= PsinθInitian momentum in vertical direction = Pcosθfinal momentum in horizontal direction = Psinθfinal momentum in vertical direction = −Pcosθwe include negative sign because direction of the final momentum is oppositechange in momentum in horizontal direction = Psinθ − Psinθ = 0change in momentum in vertical direction = Pcosθ − (−Pcosθ) = 2Pcosθwe know wave length and momentum is given by:λ = hpp = hλforce = change in momentumtime takenforce = no of photons per second×change in momentum force = 1019×6.6×10−346.63×10−9cos60force = 10−8 N
Answer is 10-8N