Question

Two plane mirrors are inclined at an angle $\theta$ as shown. If at an angle ${45}^o$ the final ray horizontal, then find angle $\theta$.

Answer 1

Since,

${\theta }_2=90-\theta \to$ Eq (i)

${\theta }_1=180-[45+\theta ]\to$ Eq (ii)

${\theta }_2=90-{\theta }_1\to$ Eq (iii)

From eq (i), (ii) and (iii);

$90-\theta =90-{\theta }_1$

$\Rightarrow \theta ={\theta }_1\to$ Eq (iv)

Put eq (iv) in (ii);

$\theta =180-[45+\theta ]$

$\theta =135-\theta$

$2\theta =135$

$\theta =\frac{135}{2}=67.5$