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Show that the radiation pressure exerted...

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

Text Solution

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Let A be the area of surface kept in vacuum
pressure exerted by the em wave on the surface ,
` P = ( "force ") /( " area ") = (F )/(A) `
Also F = rate of change of momentum `= ( Delta p )/(delta t)`
` therefore P= (1)/(A) ( Delta p // Delta t ) xx (c )/(c)`
` = (1)/( AC Delta t ) xx Delta pc = (1)/( AC Delta t ) xx Delta U `
where `Delta U = c Delta P =` energy imparted by the wave in time `Delta t.`
Then , intensity `I= (Delta U )/( A Delta t ) = pc" " [ " form "(i) ]`
` therefore P=I//c `
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