REFRACTION GRATING

 In geometric optic property of rectilinear propagation of light is attributed to light. However when light passes through a narrow slit or over a sharp edge, it spreads out even in the region of geometrical shadow.  This phenomenon of bending of light around the edge of an obstacle is termed as diffraction or multiple interference.Inteferencce is the result of super position of only two waves drawn from the same source.  If more than two waves interfere it is called diffraction.

Diffraction gratings consist of a large no: of equally spaced parallel slits of equal width separated from each other by opaque space, which are also of equal width.  Let parallel beam of monochromatic light of wavelength ‘λ’ be incident normally on narrow slit AB.  AB = a be the width of the slit.  When the plane wave front reaches the plane of the slits, each point in the slit give rise to secondary wavelets in all direction.  All the rays proceeding from slits reach P on screen in same phase reinforce each other and form a central maximum.  Rays getting diffracted at an angle ‘θ’ with direction of incident rays after passing through the lenses reaches a point on the screen in different phases.  As a result bright and dark bands are observed on both sides of central maximum.

From theory of Fraunhofer diffracted at single slit, the waves proceeding from all points in a diffracted inclined at an angle ‘θ’ with direction of incident ray are equivalent to a single wave of amplitude

R = (Asinα)/α

Here α = (πasin θ)/λ

            The intensity is proportional to (sin² α)/ α²

I = (I₀sin² α)/ α²

           

            Where I₀ is the peak value of intensity.  The condition maximum for interference occours for those angles for which path  difference between two adjacent sources is equal to an integral multiple of wavelength ,which is given by               

Sin θ = Nm λ

            Where N=1/(a+b) is the No. of rulings.