A parallel beam of monochromatic light of wavelength `600nm` is incident on a totally reflecting plane mirror. The angle of incident is `60^(@)` and the number of photon striking the mirror per second is `2.0xx10^(19)`. The force exerted by the light beam on the mirror is `axx10^(-8)N`. what is the integer value of `a`? Given `h=6.6xx10^(-34)Js`

Explanation

Energy falling per second on the mirror, `E=(nhc)/(lambda)`
Momentum of the incident light per second,
`p=E/c=(nh)/lambda`
Momentum of the incident light per second normal to the plane mirror, `p_(1)=pcos 60^(@)`, towards mirror Momentum of the reflected light per second normal to the plane mirror, `p_(2)=pcos 60^(@)`, away from mirror.
`:.` Force on mirror `=p_(2)-(-p_(1))=p_(2)+p_(1)`
`=2pcos60^(@)`
`=(2nh)/lambda cos 60^(@)=(2xx(2xx10^(19))xx(6.6xx10^(-34)))/(660xx10^(-19))xx1/2`
`=2xx10^(-8)N`