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.

Key concepts

Law of Reflection

The Law of Reflection is a fundamental principle in physics. It dictates how light behaves when it encounters a reflective surface, such as a mirror.
When a ray of light hits a plane mirror, it bounces off or "reflects". The rule that governs this behavior is simple:

• The angle at which the light ray strikes the mirror, called the angle of incidence, is equal to the angle at which it leaves, known as the angle of reflection.

This law can be neatly summarized with the equation: \( i = r \)
where \( i \) (incident angle) is the same as \( r \) (reflection angle). It’s crucial for understanding how images are formed by mirrors.

Angle of Incidence

The Angle of Incidence is the tilt at which incoming light strikes a surface. When we speak about this angle, we’re referring to how the light hits relative to an imaginary line.
This line, called the "normal", is perpendicular to the surface at the point of contact.

• To measure the angle of incidence, you look at the angle formed between the incoming light ray and this normal line.
• In the given exercise, the angle of incidence was \( 30^{\circ} \).

The same angle, in accordance with the Law of Reflection, will be replicated on the other side of the normal for the reflected ray.

Angle of Reflection

Just like its counterpart, the Angle of Reflection is directly tied to how the light is redirected off a surface. Once a light ray hits a mirror, it gets redirected away, and the manner of its departure is predictable.

• The angle formed between the reflected ray and the normal line is the angle of reflection.
• It is always equal to the angle of incidence due to the Law of Reflection.

In our context, with an incidence angle of \( 30^{\circ} \), the reflection angle is also \( 30^{\circ} \). This symmetry is fundamental in mirror reflections and ensures that the path of light is consistent.

Light Deviation

Light Deviation refers to the change in a light ray's path after it encounters a reflective surface. This change depends on the initial angle at which the light approached.

• For plane mirrors, deviation can be calculated as the total turnaround the light undergoes, essentially the sum of the angle of incidence and the angle of reflection.
• In the exercise, the angle deviation was determined to be \( 60^{\circ} \) because both the incidence and reflection angles were \( 30^{\circ} \).

Simply put, deviation quantifies how much a ray of light has been redirected, providing insights into light behavior when dealing with reflective surfaces.