Five equations in three unknowns, you are asking for trouble. However, you get solvability conditions in terms of the parameters:
eqs = {fn1*Sin[a] - fn2*Sin[a] == 0,
fn3 + 2 fn1*Cos[a] - f == 0,
dl1 == dl3*Cos[a],
dl1 == fn1*1/(e1*a1*Cos[a]),
dl3 == fn3*1/(e3*a3)};
vars = {fn1, fn2, fn3};
sol0 = Solve[eqs[[{1, 2, 4}]], vars]
eqs /. sol0[[1]]
Solve[eqs /. sol0[[1]]]