Question

If a ray of light is incident on a plane mirror at an angle of \(30^{\circ}\) then deviation produced by a plane mirror is (A) \(60^{\circ}\) (B) \(90^{\circ}\) (C) \(120^{\circ}\) (D) \(150^{\circ}\)

Short answer

The deviation produced by a plane mirror when a ray of light is incident at an angle of \(30^{\circ}\) is \(60^{\circ}\). This is calculated using the law of reflection, where the angle of incidence is equal to the angle of reflection. In this case, both angles are \(30^{\circ}\), so the total deviation is \(30^{\circ} + 30^{\circ} = 60^{\circ}\).

Step-by-step solution

Identify the Law of Reflection

According to the law of reflection, the angle of incidence (i) is equal to the angle of reflection (r), which can be represented mathematically as: \(i = r\)

Calculate the angle of reflection

As given in the problem, the angle of incidence (i) is \(30^{\circ}\). We can use the law of reflection to find the angle of reflection (r). \(i = r\) \Rightarrow \(30^{\circ} = r\) So, the angle of reflection is also \(30^{\circ}\).

Calculate the deviation produced by the mirror

Deviation (D) produced by a plane mirror can be calculated as the difference between the angle of incidence (i) and the angle of reflection (r). In this case, it is the sum of the two angles, since both angles are on the same side of the normal line. \(D = i + r\) \Rightarrow \(D = 30^{\circ} + 30^{\circ}\) \Rightarrow \(D = 60^{\circ}\) Thus, the deviation produced by a plane mirror is \(60^{\circ}\), which corresponds to the option (A) in the given exercise.