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Show that the radiation exerted by an EM...

Show that the radiation exerted by an EM wave of intensity I on a surface kept in vacuum is `(I)/(c )`.

Text Solution

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Pressure `=("Force")/("Area")=(F)/(A) therefore P=(F)/(A)`
Rate of change of momentum is force,
`therefore F=(dp)/(dt)`
Now `E=mc^(2)`
`therefore U=(mc)c " " [because E=U]`
`therefore U=Pc " " [because mc = " P momentum"]`
By taking differentiation both side w.r.t time,
`(dU)/(dt)=c(dP)/(dt)`
`therefore (dU)/(dt)xx(1)/(c )=F " " [because (dP)/(dt)=F]`
Now `P=(F)/(A)=(dV)/(dt)xx(1)/(Ac)`
`therefore P=(I)/(c )" " [because (dV)/(Adt)=" Intensity I"]`
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