Two plane mirror are inclined to eachother at an angle `theta = 70^(@)`, Fig. A ray `SO` of light falls at some angle `i` on the mirror `M_(1)`, falls after reflection from it, on the other mirror `M_(2)` from which it gets reflected along a direction parallel to the plane mirror `M_(1)`. Find the value of `/_i`.

Answer

`40^(@)`

Explanation

As ray reflected from `M_(2)` is parallel to `M_(1)`,
`:. /_2 = theta = 70^(@)` (Corres. `/_s`)
Also, `/_1 = /_2 = 70^(@)`
In `Delta OAC, theta + /_1 + /_AOC = 180^(@)`
`70^(@) + 70^(@) + /_AOC = 180^(@)`
`/_AOC = 180^(@) - 140^(@) = 40^(@)`.
According to the laws of reflection,
`/_i = /_AOC = 40^(@)`