Light Interference (PDF)

Light is a transverse electromagnetic wave that can be seen by the typical human. The wave all electromagnetic waves, light can travel through a vacuum. The transverse nature of light nature of light was first illustrated through experiments on diffraction and interference. Like can be demonstrated...

Light is a transverse electromagnetic wave that can be seen by the typical human. The wave all electromagnetic waves, light can travel through a vacuum. The transverse nature of light nature of light was first illustrated through experiments on diffraction and interference. Like can be demonstrated through polarization. 7.1 Interference of Light When two beams of light cross each other, the resultant amplitude and intensity may be different from the two beams acting separately. This modification of intensity obtained by the superposition of two or more beams of light is called interference. If the resultant intensity is zero or in general less than the separate intensities, we have destructive interference. If the resultant intensity is greater, it is called constructive interference. The first man successfully to demonstrate the interference of light was Thomas Young. Figure 7.1 (a) and (b) shows the constructive and destructive interference of light. Young\'s experiment, that provided classical investigation into the nature of light and the basic element in the development of the wave theory, was first performed by the English physicist and physician, Thomas Young in 1801. In this experiment, Young identified the phenomenon called interference. Observing that when light from a single source is split into two beams, and the two beams are then recombined. the combined beam shows a pattern of light and dark fringes. Young concluded that the fringes result from the fact that when the beams recombine their peaks and troughs may not be in phase. and a trough coincide they cancel each other, and a dark line results. Young\'s experiment When two peaks coincide they reinforce each other, and a line of light results; when a peak If a white screen is placed in the region beyond the slits, a pattern of bright and dark interference bands (fringes) can be seen. The key to experiment is the use of a single pinhole \'S\' to illuminate the aperture. This provides the necessary mutual, coherence between the light coming from the two slits \'S\' and \'S\'. An equation for the intensity at any point \'P\' on the screen. The phase difference between the two waves arriving at P, having transverse different distances SP and SP given by It is assumed that the waves start out from \'S,\' and \'S\' in the same phase. Furthermore, the amplitudes are practically the same. The intensity at \'P\' was given by equation: P=1A2=4a2 cos2 (8/2) (7.2) Where \'a\' is the amplitude of the separate waves and \'A\' that of their resultant. In Young\'s experiment \'D\' is very practically much larger than \'d\' or \'x\'. Hence\' 0 and 0\' are very small and 0≈0\'. And the path difference is equal to an integral number of wavelengths. d sin 0 = m2 (m = 0, 1, 2, 3, \....) Also the path difference d-d, is d sin 0 = d sin e\'. For small angle 0, sin 0 equals tan and so that sine. Hence the path difference = d2-d, = d sin 0 = d Using equation 7.2 the intensity has maximum values equal to 4a2 whenever 8 is an integral multiple of 2л. This will occur when the path difference is an integral multiple of 2\. Therefore *beams are then Young concl peaks and tro* of light resuls (or) -(7.7) x = mx (Bright fringes) \--(7.6) x = distance of a bright fringe from the center, PO. The minimum value of intensity is zero, and this occurs when 8 = л,зπ,5π,\... For these points xD 2 32 52 1 *d* 2 22\...=(m + 2)2 x= *AD d* (m +1⁄2) (Dark fringes) x = distance of a dark fringe from the center, PO. The whole number \'m\', which characterizes a particular bright fringe, is called the order of interference. Thus, the fringes with m = 0, 1, 2, 3, \....are called the zero, first, second \....etc, order. The distance on the screen between two successive fringes is obtained by changing \'m\' by unity in equation 7.5 or 7.6. It is equal to *2D*