Optics: Reflection

1. The first Law of Geometrical Optics:

   When light is incident on an interface between two different media, various phenomena could occur. Light can be totally or partially reflected, transmitted by refraction, scattered at the interface or absorbed in the medium.

In Geometrical Optics, we consider the simple case of the propagation of light is rectilinear ( straight lines), media are homogeneous and transparent , interfaces are not uneven (smooth) that gives specular (regular) reflections, and no absorption of light by media.

2. Reflection of light:

When light is incident at a plane surface, it is partially or totally reflected.

The angle of incidence (i) that the incident light ray makes with the normal at the point of incidence is equal to the angle of reflection(r) that the reflected light ray makes with the same normal. The incident ray, reflected ray, and normal lie in the same plane.

Using Huygen's principle, in terms of plane waves, the wavefront (wavefront-1) at the time "0" is tangent to the wavelets wave-1 and is represented by the line "AB". When the related left ray (ray-1) reflects from the interface at the point "A", the right wavelet at "B" will reflects at the time "t" after. Therefore AC = BD = ct, where c is the speed of light. At tis time "t", the right light ray "ray-1" reflects from the point B and becomes the reflected ray "ray-2", we have a new wavefront (wavefront-2) represented by the line CD tangent to the wavelets "wave-2".

DB is normal to AB and AC is normal to CD, because the ray is perpendicular to its correspondent wavefront. The rectangular triangles ΔACD and ΔABD are similar because they have two same side AC = BD = ct, and the AD is common. Therefore, the angle <CAD and <ADB are equal. We have:

i + l + <CAE = π/2
l + <CAE + <EAD = π/2.

Then: i = <EAD
<EAD = π/2 - <ADB, = π/2 - <CAD
<CAD = <CAE + <EAD. Hence:
i = <EAD = π/2 - <CAE - <EAD =
π/2 - <CAE - i = i + l - i = l.

We get:

i = l

The angle of incidence (i) is equal to the angle of reflection (l).