Question

What is a grating? Define grating element? Discuss the phenomenon of Fraunhofer’s diffraction at a grating and obtain the expression for the intensity?

Answer 1

Diffraction Grating is a polished surface made up of glass (or metal), prepared a large number of very fine equidistant parallel grooves or slits by using fine diamond point and used to produce optical spectra by diffraction of light. Student’s grating consists of 15000 lines/inches. In such small distance large numbers of lines are mounted so that the spacing between the two lines is comparable to the wavelength of the source so that the condition of diffraction is satisfied. Let ‘a’ be the width of slit and ‘b’ be the width of opaque space. Then (a+b) is known as grating element. Suppose the light from a monochromatic wavelength λ is incident normally on the grating surface. According to Huygen’s Principle, each of the slit sends secondary wavelets in forward direction. The secondary wavelets moving without any change in their original path will come to focus at point M gives a central Maximum on screen. The secondary wavelets deviated at an angle θ will come to focus at point N with different phases. The intensity at point N may me found by single and double slit experiment. In diffraction grating final pattern is the superposition of interference on diffraction. The final pattern in N parallel slit consists of a central maximum, primary maxima and secondary maxima and secondary minima. Conditions of primary or principle maxima is given as ( + )   = λ Where n = 1, 2, 3.... Condition of diffraction minima in N parallel slits is given as    = λ Where m = 1, 2, 3.... Condition of first secondary minima which appears after nth primary maxima is given as ( + ) ( + 1) = λ + λ N