Problem 12 - Master Resource Book in JEE Main Physics

Question

A plane mirror is reflecting a ray of incident light is rotated through an angle of about an axis through the point of incidence in the plane of the mirror perpendicular to the plane of incident, then (a) the reflected ray rotates through an angle \(2 \theta\) (b) the reflected ray rotates through an angle of \(\theta\) (c) the reflected ray does not rotate (d) None of the above

Step-by-Step Solution

Answer

The correct answer is (a); the reflected ray rotates through an angle \(2 \theta\).

Step 1: Understanding the Phenomenon

When a plane mirror is rotated by an angle, the angle between the incident and reflected rays changes. This is due to the law of reflection that states the angle of incidence is equal to the angle of reflection.

Step 2: Determining the Impact on the Reflected Angle

Let the initial angle of incidence be \( heta \). When the mirror is rotated by an angle \( heta \), the new angle of incidence becomes \( heta + heta = 2\theta \). Accordingly, the angle of reflection, which is equal to the angle of incidence, also becomes \( 2\theta \). Thus, the reflected ray rotates by twice the angle through which the mirror is rotated.

Step 3: Identify the Correct Answer

Since the reflected ray rotates through an angle of \( 2\theta \) for a mirror rotated by \( \theta \), the correct option is 'a', where the reflected ray rotates through an angle \(2 \theta\).

Key Concepts

Plane Mirror

A plane mirror is a flat, reflective surface that gives a mirror image. Unlike curved mirrors like concave and convex mirrors, plane mirrors reflect light without distortion. This type of mirror is commonly used in everyday life, such as in bathrooms and dressing rooms.

When a light ray strikes a plane mirror, it creates a reflection that appears as a mirror image. This reflection has the same size as the object but is flipped horizontally.

• The mirror does not alter the size of the image.
• The image produced is virtual, meaning it cannot be projected onto a screen.
• The image is upright, maintaining the same orientation as the object.

Plane mirrors create images at the same distance behind the mirror as the object is in front of it. This is due to the straight-line path that light takes after reflecting off the plane mirror.

Law of Reflection

The law of reflection is a fundamental principle in optics that dictates how light behaves when it encounters a reflective surface. According to this law, the angle of incidence is always equal to the angle of reflection. The rays are measured relative to an imaginary line called the normal, which is perpendicular to the surface at the point of incidence.

Here are some key concepts:

• Angle of incidence ( \( \theta_i \) ): The angle between the incident ray and the normal.
• Angle of reflection ( \( \theta_r \) ): The angle between the reflected ray and the normal.
• The incident ray, the normal, and the reflected ray all lie on the same plane.

This law is critical when dealing with plane mirrors since any rotation in the mirror affects both the incident and reflected angles equally.

Angle of Incidence

The angle of incidence is a specific measurement that determines how a light ray strikes a surface. It is defined as the angle between the incoming light ray (incident ray) and the perpendicular (normal) to the surface at the point of contact.

Understanding this angle is crucial because it directly influences how the light will be reflected. When analyzing problems involving light reflection, note these key points:

• If the plane mirror rotates by a certain angle, the angle of incidence changes, which also alters the angle of reflection.
• The path of the reflected ray is controlled by the angle of incidence according to the law of reflection.
• This concept plays a significant role in determining the behavior of the light rays in various optical designs.

Recognizing the angle of incidence helps in predicting the final direction of the reflected ray, an essential factor when dealing with rotating mirrors.