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. `1^(@)//s`
B. `2^(@)//s`
C. `-1^(@)//s`
D. `-2^(@)//s`

Answer

D

Explanation

From geometry `beta = (180^(@) - 2 theta)`
So, `(d beta)/(dt) = -(2 d theta)/(dt)`