Question

Question #46824

Answer 1

`90°`

Explanation:

We know that the reflected ray from the mirror, the mirror and the horizontal will make a triangle.

Sum of angles of a triangle `=180°`

Let's call that triangle `∆ABC`

We know that `A= theta`

As `angle i =theta, angler=theta`

And, `angler +angleABC=90°`
[With the normal]

`therefore angle ABC+theta=90°`
`=>angleABC=90°-theta---(1)`

`angle ABC + theta + angle BCA = 180°`

We want to find `angleBCA`.

So, `angle BCA = 180°-(theta+angleABC)`

Substituting from (1),
`angle BCA = 180°-(cancel(theta)+90cancel(-theta))`

`therefore angleBCA=180-90=90°`

Since `angleBCA=90°`, the angle between the reflected ray and the horizontal would be `90°`