CHAPTER 10: WAVE OPTICS

10.1 INTRODUCTION In 1678, the Dutch physicist Christiaan Huygens put forward the wave theory of light. According to this theory, light travels in the form of waves. Huygens assumed that light waves are longitudinal in nature and travel through an all-pervading hypothetical medium called ether.

10.2 HUYGENS PRINCIPLE Huygens principle is a geometric construction that enables us to determine the new position of a wavefront at a later time if its present position and shape are known. 1. Every point on a given wavefront acts as a fresh source of new disturbance, called secondary wavelets, which travel in all directions with the speed of light in the medium. 2. The forward envelope or tangential surface enclosing these secondary wavelets at any subsequent instant gives the new position of the wavefront.

10.3 INTERFERENCE OF LIGHT WAVES AND YOUNG'S EXPERIMENT Interference is the phenomenon of redistribution of light energy in a medium due to the superposition of two or more coherent light waves. For constructive interference (Bright Fringes): Path difference: Δx = nλ (where n = 0, 1, 2, 3...) Phase difference: φ = 2nπ Position of nth bright fringe on screen: y_n = (n * λ * D) / d

For destructive interference (Dark Fringes): Path difference: Δx = (2n - 1) * (λ / 2) (where n = 1, 2, 3...) Phase difference: φ = (2n - 1)π Position of nth dark fringe on screen: y_n' = (2n - 1) * (λ * D) / (2d)

Fringe Width (β): The separation between any two successive bright fringes or two successive dark fringes is constant and given by: β = (λ * D) / d where: λ = wavelength of monochromatic light D = distance between the slits and the observation screen d = distance between the two coherent coherent pinhole slits

10.4 DIFFRACTION OF LIGHT Diffraction is the phenomenon of bending of light around the corners of an obstacle or aperture of the size comparable to the wavelength of light. Condition for minima in single-slit diffraction: a * sin(θ) = nλ Central maximum width: W_c = (2 * λ * D) / a