equation of a refracted straight line

Question

we have got a line $$x-y=1$$ which after refracting from $x$-axis bends at angle $\pi/6$ from normal what's eqation of that line? what i did was that putting $y=0$ to get points on $x$-axis which comes out to be $P(1,0)$ now since it's refracted at angle $\pi/6$ hence it's angle from $x$-axis will be $\pi/2-\pi/3$ which is $\pi/3$ now writing down simply the equation $$(y-0)=\sqrt{3}(x-1)$$ but my answer is incorrect from what's given in textbook , where did i went possibly wrong?