In the undiffracted position, θ = 0 and hence sin θ = 0. Where N = 1/a+b, gives the number of grating element or number of lines per unit width of the grating. In general, ( a + b) sin θ = m λ is the condition for maximum intensity, where m is an integer, the order of the maximum intensity. On either side of central maxima different orders of secondary maxima are formed at the point P 1, P 2. Similarly, for second order maximum, ( a + b) sin θ 2 = 2 λ
If ( a + b) sin θ 1 = λ, the diffracted wavelets inclined at an angle θ 1 to the incident direction, reinforce and the first order maximum is obtained. This is called zero order maximum or central maximum. Hence the wavelets proceeding in the direction of the incident rays will produce maximum intensity at the centre O of the screen. ( a + b) sin θ = 0, satisfies the condition for brightness for m = 0. In the undiffracted position θ = 0 and hence sin θ = 0. It will be seen that the path difference between waves from any pair of corresponding points is also ( a + b) sin θ The path difference between the wavelets from one pair of corresponding points A and C is CG = ( a + b) sin θ. Let us consider the secondary diffracted wavelets, which makes an angle θ with the normal to the grating. According to Huygen’s principle, the points in the slit AB, CD … etc act as a source of secondary wavelets which spread in all directions on the other side of the grating. Let a plane wave front of monochromatic light of wave length λ be incident normally on the grating.
AB, CD, EF … are the successive slits of equal width a and BC, DE … be the rulings of equal width b (Fig. MN represents the section of a plane transmission grating. Points on successive slits separated by a distance equal to the grating element are called corresponding points. The combined width of a ruling and a slit is called grating element (e). The rulings act as obstacles having a definite width ‘ b’ and the transparent space between the rulings act as slit of width ‘ a’. The modern commercial form of grating contains about 6000 lines per centimetre. The plane transmission grating is a plane sheet of transparent material on which opaque rulings are made with a fine diamond pointer. An arrangement consisting of a large number of equidistant parallel narrow slits of equal width separated by equal opaque portions is known as a diffraction grating.
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