Which of the following statements are correct?
(A) All mirrors follow the laws of reflection.
(B) The angle between the ray of incidence and the plane surface of the mirror is equal to the angle between the plane surface of mirror and the ray of reflection for plane mirror
(C) the rays coming parallel to the principal axis will go after reflection through the focus of the curved mirror
(D) the rays coming to the pole of a curved mirror making an angle with axis will be reflected making the equal angle with the axis on the other side of the axis.
Choose the correct answer from the options given below:
Correct Answer :
(A), (B), (C) and (D)
Solution :
The correct answer is (A), (B), (C) and (D).
Let us analyze each statement step-by-step to understand why all of them are correct:
Statement (A): All mirrors follow the laws of reflection.
The laws of reflection are fundamental principles of optics. They state that the angle of incidence is equal to the angle of reflection, and that the incident ray, the reflected ray, and the normal to the reflecting surface at the point of incidence all lie in the same plane. These laws apply universally to all types of reflecting surfaces, including plane mirrors, concave mirrors, convex mirrors, and even irregular or rough reflecting surfaces. Therefore, statement (A) is correct.
Statement (B): The angle between the ray of incidence and the plane surface of the mirror is equal to the angle between the plane surface of mirror and the ray of reflection for plane mirror.
Let the angle of incidence be represented as and the angle of reflection as , both measured relative to the normal (which is perpendicular to the mirror surface). According to the law of reflection:
The angle between the incident ray and the plane surface of the mirror (the glancing angle of incidence, ) is given by:
Similarly, the angle between the reflected ray and the plane surface of the mirror (the glancing angle of reflection, ) is:
Since , it mathematically follows that:
Thus, the angle made by the incident ray with the mirror's surface is equal to the angle made by the reflected ray with the mirror's surface. Therefore, statement (B) is correct.
Statement (C): The rays coming parallel to the principal axis will go after reflection through the focus of the curved mirror.
By definition of the focal point (focus) of a spherical mirror, any ray of light travelling parallel to the principal axis will, after reflection, either pass through the principal focus (in the case of a concave mirror) or appear to diverge from the principal focus (in the case of a convex mirror). Thus, this is a standard rule of ray optics for curved mirrors, making statement (C) correct.
Statement (D): The rays coming to the pole of a curved mirror making an angle with the axis will be reflected making the equal angle with the axis on the other side of the axis.
The principal axis of a curved mirror acts as the normal to the mirror's surface at the pole (). When an incident ray strikes the pole making an angle with the principal axis, the principal axis behaves exactly like the normal in a plane reflection scenario. Applying the law of reflection, the reflected ray must make an equal angle with the principal axis on the opposite side. Therefore, statement (D) is correct.
Since statements (A), (B), (C), and (D) are all individually correct, the option containing all of them is the correct choice.
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