Let us first study what is law of reflection with respect to a single light ray. Look at the following diagram.
Let MM' be a plane mirror which is absolutely smooth. A light ray AO strikes the mirror at O (the incident ray), and it is reflected as ray OA', called as reflected ray. ON is the perpendicular to MM' at O. It is also called as the normal to the surface at the point of reflection.
The angle made by the incident ray with the normal ON is p and q be the angle made by the reflected ray with the same normal. These are called as 'Angle of Incidence' and the 'Angle of Reflection' respectively.
According to the Law of Reflection,Angle of incidence is always equal to angle of reflection.
Now, let us consider a set of rays assuming a plane mirror with a smooth and perfect surface. The situation is explained in the following diagram:
Let ABCD is a set of rays striking a mirror MM'. Obviously, the rays of parallel to each other. When each individual ray strikes the mirror it is reflected as per law of reflection, that is the angle of incidence and the angle of reflection are same for each ray. Thus the set of incident rays are reflected as a set of rays. In other words, a beam of light is reflected as a beam of light if the mirror is plane and its reflecting surface is smooth. This type of reflection of a set of rays is called Specular Reflection.
Thus, observing at this diagram we can Define Law of Reflection as:
When light falls on a surface which is plane, the angle with which the light falls on the surface is equal to the angle with which the light reflects back and the incident ray, reflected ray and the normal ray lies in the same plane.
Does the Law of Reflection Hold for Diffuse Reflection?
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What happens if the reflecting surface is rough or curved? Does the law of reflection hold for diffuse reflection? Does the law of reflection hold for curved mirrors? Diffused Reflection takes place when the incident light falls on the rough surface.
Let us study the situation again considering each ray in a set of rays through the following diagram.
Consider a reflecting surface MM' which is highly exaggerated rough for the purpose of study. A set of rays ABCD strike the reflecting surface. But when you consider the rays individually, the infinitesimally small reflecting surface on which each ray falls is plane. Hence as far as that ray is concerned the law of reflection holds good and the reflection obeys the law that angle of incidence is equal to the angle of reflection. For example, the ray A is reflected as A'. Overall, the set of rays ABCD is reflected as A'B'C'D' as shown in the diagram.
It may be noticed that while the incident rays are parallel, the reflected rays emerge in different directions. This is called scatter reflection or diffuse reflection. Thus the law of reflection still holds in case of diffuse reflection but the net is result different from specular reflection.
Thus, the Law of reflection does not apply to Diffuse Reflection because the diffuse angle spreads to various angular range is different from the incident angle as it has only one ray.
Does the Law of Reflection Hold for Curved Mirrors?
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Now let us consider the case of a curved mirror. As an example a convex mirror is shown in the following diagram.
MM' is a concave mirror and rays A, B and C from an object P emerging out in different directions. Each of these is reflected following the law of reflection at the respective striking points. Thus the law of reflection holds good for curved mirrors also.
The corresponding reflected rays are A', B' and C' respectively and we find these rays meet at a point P' to create an image of the object P.
An incident ray, that is parallel to the principal axis of the mirror is reflected through a point F on the principal axis and an incident ray through F is reflected parallel to the principal axis. This is called two rules of a curved mirror and simplifies the job of drawing a ray diagram. The point F is called the Focal point of the mirror.
Hence, we can Conclude that Law of reflection does not hold for Curved mirrors as the angle of incidence is different from the angle of reflection.