Correct option is 1. \(\frac{2}{3+\sqrt{3}}\)
Let Q be (h,o)
The equation of emitted ray is y = x/√3 (∵ tanθ = 1/√3)
∵ OP is reflected by line x+y = 1
∴ Image of Q(h,o) lies on line y = x/√3
\(∴\frac{x-h}{1}=\frac{y-o}{1}=\frac{-2(h-1)}{2}\)
∴ x = 1 , y = 1-h
It lies on y = x/√3.
∴ 1 - h = 1/√3
\(∴h=1-\frac{1}{\sqrt{3}}=\frac{\sqrt{3}-1}{\sqrt{3}}=\frac{3-1}{\sqrt{3}(\sqrt{3}+1)}\)
\(=\frac{2}{\sqrt{3}(\sqrt{3}+1)}=\frac{2}{3+\sqrt{3}}\)