Diffraction of light

Basics of Diffraction:

1. Wave Nature of Light:
   Light is an electromagnetic wave, exhibiting both wave and particle properties. When discussing diffraction, we primarily consider its wave nature.
2. Huygens' Principle:
   According to Huygens' principle, every point on a wavefront can be considered as a source of secondary spherical waves. The sum of these secondary waves gives rise to the wavefront at a later time.
3. Wavefronts and Rays:
   A wavefront is an imaginary surface that connects all the points having the same phase in a wave. Rays are perpendicular to wavefronts and indicate the direction of energy propagation.

Diffraction Patterns:

1. Single Slit Diffraction:
   Consider a single slit illuminated by a monochromatic light source (one with a single wavelength).
   • Huygens' principle helps explain how each point on the slit acts as a source of secondary waves.
   • The waves interfere with each other, leading to constructive and destructive interference.
   • This results in a diffraction pattern consisting of a central bright fringe and alternating dark and bright fringes on either side.
2. Intensity Distribution:
   The intensity of the diffracted light varies with angle. The central maximum is the brightest, and the intensity decreases as you move away from the center.
3. Mathematical Expression:
   The intensity distribution for single slit diffraction is given by the single-slit diffraction formula: \[ I(\theta) = I_0 \left(\frac{\sin(\beta)}{\beta}\right)^2 \] where \( \beta = \frac{\pi a \sin(\theta)}{\lambda} \), \( I_0 \) is the intensity at the center, \( a \) is the slit width, \( \theta \) is the angle of observation, and \( \lambda \) is the wavelength.
4. Double-Slit Diffraction:
   For double-slit diffraction, interference between waves passing through the two slits creates a pattern of bright and dark fringes. The pattern is characterized by alternating regions of constructive and destructive interference.

Observations and Applications:

1. Observations:
   Diffraction is more pronounced when the size of the slit or obstacle is comparable to the wavelength of light. Shorter wavelengths result in less diffraction, making the pattern more focused.
2. Applications:
   Diffraction is widely used in various scientific and technological applications, such as in the design of optical instruments, diffraction gratings, and laser systems.