According to the law of reflection, the angle of incidence is equal to the angle of reflection. The angle of incidence is given as \(15^\circ\). Therefore, the angle of reflection is also \(15^\circ\).
The deviation of the ray is the total change in its direction. The incident ray approaches the mirror at \(15^\circ\) to the normal, and the reflected ray leaves at \(15^\circ\) to the normal in the opposite direction. The total change in direction is the sum of these angles.
\[ \text{Deviation} = \text{Angle of incidence} + \text{Angle of reflection} \] \[ \text{Deviation} = 15^\circ + 15^\circ = 30^\circ \]
Therefore, the deviation in the ray produced by the mirror is \(30^\circ\).