We can say by symetry that fied wil be parallel to plane and perpendicular to dirction of current. As sheet is infinite so field should be uniform as well. Suppose we want to find field at a point P at a distance R from sheer. We make an Ampere's loop in form of rectangle of length l and bredth 2R through P such that sheet divides it in two equall part. AB and CD of length l are parallel to sheet while BC and DA are perpendicular to it.
   Applying amperes law on this loop

 

_{[ ]}^{[ ]} B.ld  = Bl (for AB as path is parallel to field) +0(for BC as path is perpendicular to field)+Bl (for CD as path is parallel to field) +0(for DA as path is perpendicular to field)=2BL = mu_not*i_enclosed =mu_not*lamda*l

So B= mu_not*lamda/2