Wave Optics

The One Thing

Wave optics explains light through wave propagation and superposition: wavefronts advance according to Huygens principle, while interference and diffraction produce observable intensity patterns that support the wave nature of light.

Reactions, Processes and Experiments

Key Terms

• Wavefront: A surface joining all points of a wave that are in the same phase at a particular instant.
• Ray: An imaginary line normal to a wavefront that shows the direction of propagation of light.
• Huygens Principle: Every point on a wavefront acts as a source of secondary wavelets, and the new wavefront is the forward envelope of these wavelets.
• Spherical Wavefront: A wavefront produced by a point source, having the form of expanding spheres.
• Plane Wavefront: A wavefront whose surface is approximately plane, usually produced when a source is very far away.
• Cylindrical Wavefront: A wavefront produced by a long narrow source, having the form of expanding cylinders.
• Superposition Principle: When two or more waves overlap, the resultant displacement is the algebraic or vector sum of their individual displacements.
• Interference: The redistribution of light intensity caused by the superposition of two or more coherent light waves.
• Coherent Sources: Sources that emit waves of the same frequency and maintain a constant phase difference.
• Constructive Interference: Interference that produces maximum intensity when waves arrive in phase.
• Destructive Interference: Interference that produces minimum intensity when waves arrive out of phase.
• Path Difference: The difference between the distances travelled by two interfering waves to reach a point.
• Phase Difference: The difference in phase between two waves, related to path difference by phi = 2 pi Delta x / lambda.
• Young's Double-Slit Experiment: An experiment in which light from two coherent slits produces alternate bright and dark fringes on a screen.
• Fringe Width: The distance between two successive bright fringes or two successive dark fringes in an interference pattern.
• Diffraction: The bending and spreading of waves when they pass through a narrow aperture or around an obstacle.
• Single-Slit Diffraction: The spreading of light after it passes through a narrow slit, producing a broad central maximum and weaker side maxima.
• Diffraction Minimum: A dark position in single-slit diffraction satisfying a sin theta = n lambda, where n = 1, 2, 3, and so on.
• Intensity: The power transmitted per unit area; in interference, it depends on the amplitudes and phase difference of the waves.

Easily Confused

• Interference and diffraction: Interference involves waves from two or more coherent sources, whereas diffraction can be understood as interference among wavelets from different parts of the same aperture.
• Interference and diffraction patterns: Interference fringes are ideally equally spaced, whereas diffraction fringes generally have unequal intensities and a wider central maximum.
• Wavefront and ray: A wavefront is a surface joining points in the same phase, whereas a ray is normal to the wavefront and indicates the direction of propagation.
• Path difference and phase difference: Path difference is a difference in distance travelled, whereas phase difference is the corresponding difference in phase, related by phi = 2 pi Delta x / lambda.
• Constructive and destructive interference: Constructive interference occurs when waves arrive in phase and produces maximum intensity; destructive interference occurs when they arrive out of phase and produces minimum intensity.
• Spherical, plane and cylindrical wavefronts: A spherical wavefront is produced by a point source, a plane wavefront is approximately plane and usually comes from a very distant source, and a cylindrical wavefront is produced by a long narrow source.
• Wavelength and frequency in a medium: In a medium of refractive index n, wavelength becomes lambda_medium = lambda_vacuum / n, while frequency remains unchanged.

What Gets Asked

• Define a wavefront, ray, Huygens principle, coherent sources, interference, diffraction, or intensity; marks are lost by confusing a wavefront with a ray or omitting that rays are normal to wavefronts.
• Use Young's double-slit geometry to obtain the path difference, with Delta x = d sin theta and, for small angles, Delta x = d y / D; marks are lost by using the wrong approximation.
• Determine the positions of bright and dark fringes using y_n = n lambda D / d and y_n = (n + 1/2) lambda D / d; marks are lost by interchanging the constructive and destructive conditions.
• Calculate fringe width using beta = lambda D / d; marks are lost by confusing slit separation d with the screen distance D.
• Calculate resultant, maximum, or minimum intensity using I = I1 + I2 + 2 square root of (I1 I2) cos phi, I_max = 4I0, and I_min = 0; complete darkness additionally requires equal amplitudes and a path difference of an odd multiple of lambda/2.
• Apply single-slit diffraction conditions using a sin theta = n lambda, sin theta = lambda / a for the first minimum, or the central-maximum widths 2 lambda / a and 2 lambda D / a; marks are lost by using slit separation d from Young's experiment instead of slit width a.