A2-Diffraction.pdf

Diffraction of Light Diffraction is the phenomena of bending of light rays round the sharp corners and entering into the geometrical shadow region It can be explained only on the basis of wave nature of light or Huygen’s theory  Fraunhofer Diffraction at Single Slit...

Diffraction of Light Diffraction is the phenomena of bending of light rays round the sharp corners and entering into the geometrical shadow region It can be explained only on the basis of wave nature of light or Huygen’s theory  Fraunhofer Diffraction at Single Slit P θ y θ θ a θ x Path difference between two extreme rays diffracted at angle θ 𝒙 = 𝒂 𝐬𝐢𝐧 𝜽 If path difference is λ or its integral multiple, then we get dark fringe instead of bright. Hence conditions of dark and bright fringes get interchanged here For bright fringes (2n+1) 𝒂 𝐬𝐢𝐧 𝜽𝒏 = 𝝀 𝟐 For dark fringes 𝒂 𝐬𝐢𝐧 𝜽𝒎 = 𝒎 𝝀  Fraunhofer Diffraction at Double Slit a b a Intensity distribution on screen is due to two types of phenomena 1. Diffraction pattern due to individual slits which coincide exactly with each other 2. Interference pattern due to superposition of corresponding rays from two slits  1. Diffraction Pattern For bright fringes (2n+1) 𝒂 𝐬𝐢𝐧 𝜽𝒏 = 𝝀 𝟐 For dark fringes 𝒂 𝐬𝐢𝐧 𝜽𝒎 = 𝒎 𝝀 2. Interference Pattern Path difference between any two corresponding rays diffracted at angle 𝜽 is: 𝒙 = (𝒂 + 𝒃) 𝐬𝐢𝐧 𝜽 For nth order interference maximum (𝒂 + 𝒃) 𝐬𝐢𝐧 𝜽𝒏 = 𝒏 𝝀 For nth order interference minimum (2n+1) (𝒂 + 𝒃) 𝐬𝐢𝐧 𝜽𝒏 = 𝝀 𝟐  Missing order of interference If nth order Interference maximum is located exactly at the location of mth order Diffraction minimum, then these orders of interference fringes will be absent from the resultant pattern on screen (𝒂 + 𝒃) 𝐬𝐢𝐧 𝜽 = 𝒏 𝝀 Interference maximum and Diffraction minimum are located exactly at the same 𝒂 𝐬𝐢𝐧 𝜽 = 𝒎 𝝀 angular position 𝜽 𝒂+𝒃 𝒏 Dividing these equations, we get 𝒂 =𝒎 If a = b then n =2m and at m = 1,2,3,…. n = 2,4,6,….will be missing If 2a = b then n =3m and at m = 1,2,3,…. n = 3,6,9….will be missing If b = 0 then n =m and at m = 1,2,3,…. n = 1,2,3,….will be missing i.e. all interference fringes are absent Intensity Distribution on Screen So, distribution on screen consists of Interference pattern within the Diffraction fringes Diffraction Grating/Plane Transmission Grating An arrangement consisting of a large number of equidistant parallel rectangular slits of equal width separated by equal opaque portions is known as a diffraction grating. Constructed by ruling equidistant parallel lines with a fine diamond point on an optically plane glass plate. There can be about 12,000 to 30,000 lines drawn per inch. Ruled lines act as opaque regions called OPACITIES of width b each. While equal sized spaces among lines act as transparent regions called TRANSPARANCIES each of width a. 𝟏 The factor a + b is called grating constant and its reciprocal 𝒂+𝒃 is number of lines per unit length on grating. If a total N lines 𝑵 𝟏 are drawn over a grating of length l then 𝒍 = 𝒂+𝒃 l N- lines Diffraction through Grating Ist 0 Ist  The intensity pattern on screen consists of Principal Maxima and Minima due to interference among corresponding rays and Secondary maxima and minima due to diffraction from whole grating Condition for various order Principal maxima (𝒂 + 𝒃) 𝐬𝐢𝐧 𝜽𝒏 = 𝒏 𝝀 Condition for first order Secondary Minimum just after nth order Principal maxima 𝒂 + 𝒃 𝐬𝐢𝐧 𝜽 + 𝒅𝜽 = 𝒏 𝝀 + (𝝀/N)  Determination of 𝝀 using Grating Method To find 𝝀 we use the following relation (𝒂 + 𝒃) 𝐬𝐢𝐧 𝜽𝒏 = 𝒏 𝝀