dear

  first apply conservation of momentum then  we can apply conservation  of energy

  Its like a bullet striking a bob and bob moves up

 

so initial momentum is beacause of EMW paulse only which can be shown tobe

2E/c

 

2ER/c = mv ( 2 is multiplied because the mirorr reflects )

 

mgl (1-cos theta ) = 1/2 mv^2