Module 4 Lecture 7

Fraunhofer Diffraction and Diffraction Grating

Overview

  • Focus on Fraunhofer diffraction caused by N-slits (grating).

  • Lecture part of electromagnetic theory, quantum mechanics, waves, and optics module.

Definition and Construction of Diffraction Grating

  • A diffraction grating consists of numerous parallel slits of equal width with opaque spaces in between.

  • Typically constructed by ruling lines on a transparent material, with the lines being opaque and the spaces acting as slits (known as plane transmission grating).

  • When line spacing approaches the wavelength of light, significant diffraction occurs.

Theory of Diffraction Grating

  • Grating section placed perpendicular to paper—a representation of slits and opaque spaces.

  • The width of each slit: a and the width of each opaque space: b.

  • The total width affecting diffraction: e = a + b.

  • Monochromatic light of wavelength λ incident normally onto the grating.

Huygen's Principle and Wavelets

  • Each slit acts as a source of secondary wavelets, spreading in all directions.

  • Path difference for waves from slit pairs (e.g., A and C) is given by: CG = (a+b)sinθ.

  • Bright fringe condition occurs when (a+b)sinθ = nλ, with n = 0, 1, 2, 3….

  • The central maximum (n=0) is at point O on the screen.

Order of Maxima

  • First order maximum occurs at (a + b) sinθ1 = λ and continues for higher orders.

  • The nth order maxima show up symmetrically on both sides of the central maxima at angles defined by (a + b) sinθn = nλ.

Condition for Maximum Intensity

  • General condition for maxima:(a+b)sinθ = nλ, where n indicates the order of maximum intensity.

  • For undiffracted light, conditions imply sin(0) = 0.

Spectral Formation

  • At the zero angle, maximum intensity results in a white undispersed image.

  • As θ increases, light progressively passes through half-wavelengths for all colors leading to dark bands, followed by bright spectra for each color.

Practical Applications of Diffraction Grating

  • Diffraction gratings are essential optical devices with substantial applications in spectroscopy.

  • Originally constructed with fine wires; now often made using precision techniques.

  • Replication methods involve using collodion solution to create multiple replicas from one original grating.