3.1. Light Visible light is an example of an electromagnetic (em) wave and consists of electric and magnetic harmonic waves that vibrate in phase at the same frequency but at right angles to each other. The electric field is given by E(x,t) =E o sin(kx-  t) and the magnetic field is given by B(x,t) =B o sin(kx-  t) E and B are related through E = cB With c the speed of light. Hence the electric field is very much greater than the magnetic field and light is usually described in terms of the E field.

3.1. Light The energy carried by the wave flows at right angles to both the electric and magnetic fields. It is quantified by the Poynting vector S. The speed of light in a vacuum is given by. We can use the idea of the Poynting vector to determine the time averaged intensity I av of a light source. This gives the energy flow or flux through a surface of area of 1 m 2 in 1 s.

The successive planes show the direction of energy flow

3.2. Generation of an em wave Maxwell showed theoretically that when a charge accelerates the charge generates an electromagnetic wave. The moving charge generates both an electric and magnetic field that are at right angles to each other. This was proved experimentally by Hertz who detected the waves created when an inductor - capacitor (LC) circuit was used to temporally ionize the air in the capacitor. By measuring the output signal Hertz showed the output was an em wave.

3.3. Light rays and Geometrical Optics The Poynting vector allows us to determine the direction of energy flow. The direction of this energy flow can be indicated by a ray The rays are drawn as straight lines that are perpendicular to the wave front. Geometrical optics is concerned with the study of the behaviour of these rays at of the rays at interfaces between different media. Wave front Rays

3.4. Rays and Reflections Consider a perfectly flat reflecting surface. A plane wave front AB is incident on this surface at an angle  i. It is reflected at an angle  r to form wave front CD The lines perpendicular to the reflecting surface are called Normals. All the rays and normals lie in the same plane - the plane of incidence

3.4. Rays and Reflections The rays associated with the wave front AB make are incident at an angle  i to the normal whilst those belonging to CD make an angle  r. In the time taken for the wave front to move from B to D the reflected ray moves from A to C. This is a consequence of Huygens’ Principle.

3.4. Rays and Reflections As the rays are in the same medium then AC = BD But AC = ADsin  r and BD = ADsin  i So  i =  r This is the law of reflection. Whenever a ray is reflected from a surface the angle of incidence is always equal to the angle of reflection.

3.4. Rays and Reflections Whenever a ray is reflected from a surface, the angle of incidence is always equal to the angle of reflection. If the surface is perfectly flat then all the rays are reflected in the same direction -Specular reflection If the surface is rough, even though the rays are incident on the surface at the same angle the rays are reflected in different directions -Diffuse reflection

3.5. Deviation caused by reflection Whenever a ray is reflected from a surface, the angle of incidence is always equal to the angle of reflection. The ray is deviated from its original path. The angle of deviation  is given by  = π - 2  i

3.6. Image formation with plane mirrors Consider an object that is placed a distance P from a plane mirror. The image is formed a distance Q from the mirror. The image is found by projecting the reflected rays back into the mirror. Where the rays cross the image is formed  i ii PQ H PQ Here tani = H/P and tani = H/Q So P = Q. Thus for a plane mirror the image is formed as far behind the mirror as the object is in front. The image is also laterally inverted.

3.6. Real and virtual objects and images The image produced by a plane mirror is a virtual image. It cannot be imaged onto a screen  i ii PQ H PQ Objects and images can be classified by the way the rays behave  A real object - Rays diverge - energy flows from object A real image - Rays converge - energy flows to image A Virtual object- Rays converge - No energy come from object A Virtual image - Rays diverge - No energy goes to image