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MCQ Solution: Electromagnetic Waves

The pressure exerted by an electromagnetic wave of intensity I(watt/m²) on a non-reflecting surface is : [c is the velocity of light]

1) I c
2) Ic²
3) I/c
4) I/c²

Solution

Momentum of a photon
$$\displaystyle =\frac { h }{ \lambda } =\frac { h }{ { c }/{ v } } =\frac { hv }{ c } =\frac { E }{ c } $$
Momentum over unit area
$$\displaystyle =\frac { E }{ Ac } =\frac { I }{ c } \left[ I=\frac { E }{ A } for\quad wave \right] $$
Since surface is non reflecting, final momentum of photon = 0, change in momentum $$\displaystyle =\frac { I }{ c } $$
So, force per unit area $$\displaystyle =\frac { I }{ c } $$
Pressure of radiation $$\displaystyle =\frac { I }{ c } $$