The reflecting surface of two intersecting flat mirrors are at an angle `theta (0^(@) lt theta lt 90^(@))`. As shown in Figure. For a light ray that strikes the horizontal mirror, the emerging ray intersects the incident ray at an angle `beta` . If one of the mirrors is rotated at `(d theta)/(dt) = 1^(@)//s`, then the angle `beta` changes aat the rate of

Options

A. `phi=theta`
B. `phi=180^(@)-theta`
C. `phi=90^(@)-theta`
D. `phi=180^(@)-20`

Answer

D

Explanation

Let `i_(1)` be the angle of incidence on mirror `M_(1)` and `i_(2)` be the angle of incidence on mirror `M_(2)`
In `DeltaABC`
`90^(@)-i_(1)+theta+90^(@)-i_(2)=180^(@)`
or `i_(1)+i_(2)=theta` ...(i)
In `DeltaABC , 2i_(1)+2i_(2)+phi=180^(@)`
`phi=180^(@)-2(i_(1)+i_(2))=180^(@)-20^(@)` (Using(i))