When one light ray is reflected from a plane mirror with $30^{\circ}$ angle of reflection, the angle of deviation of the ray after reflection is :

When a light ray is reflected from a plane mirror, the angle of incidence (i) is equal to the angle of reflection (r). In this case, the angle of reflection is given as $30^{\circ}$, so the angle of incidence is also $30^{\circ}$. <br/><br/> The angle of deviation (D) is the angle between the incident ray and the reflected ray. To find this angle, consider the fact that the angle between the incident ray and the normal to the mirror and the angle between the reflected ray and the normal add up to $180^{\circ}$, since they are supplementary angles. <br/><br/> Thus, we have:<br/><br/> $i + r + D = 180^{\circ}$<br/><br/> Since $i = r$, we can rewrite the equation as:<br/><br/> $2i + D = 180^{\circ}$<br/><br/> Substitute the value of the angle of incidence:<br/><br/> $2(30^{\circ}) + D = 180^{\circ}$<br/><br/> $60^{\circ} + D = 180^{\circ}$<br/><br/> Solve for the angle of deviation (D):<br/><br/> $D = 180^{\circ} - 60^{\circ} = 120^{\circ}$ <br/><br/> So, the angle of deviation of the ray after reflection is $120^{\circ}$.