MP Board · Class 12 · Physics · Wave OpticsWhat is diffraction of light? Differentiate clearly between Fresnel and Fraunhofer diffraction. Explain the phenomenon of diffraction at a single slit, derive the condition for secondary minima, and draw the intensity distribution curve.

Definition of Diffraction of Light\nDiffraction of light is defined as the phenomenon of bending of light waves around the corners of an obstacle or an aperture into the region of geometrical shadow, provided the size of the obstacle or aperture is comparable to the wavelength of the light.

Differences Between Fresnel and Fraunhofer Diffraction

1. Fresnel Diffraction:
   • In this type, either the source of light or the screen (or both) are at a finite distance from the obstacle or aperture.
   • The incident wavefronts are either spherical or cylindrical.
   • The experimental arrangement is relatively simple as it does not require lenses to focus the light.
2. Fraunhofer Diffraction:
   • In this type, both the source of light and the screen are effectively at an infinite distance from the obstacle or aperture.
   • The incident wavefronts are plane.
   • Convex lenses are used in the arrangement to render the light parallel before the obstacle and to focus the diffracted light onto the screen.

Diffraction at a Single Slit and Condition for Secondary Minima

• Experimental Setup: Consider a parallel beam of monochromatic light of wavelength $\lambda$ incident normally on a narrow slit $AB$ of width $a$. A convex lens is used to focus the light onto a screen placed in its focal plane.
• Derivation for Minima:
  • Let the slit be divided into two equal halves, $AC$ and $CB$, each of width $a/2$.
  • For every point in the upper half $AC$, there is a corresponding point in the lower half $CB$ separated by a distance of $a/2$.
  • If the path difference between the secondary wavelets originating from corresponding points is equal to $\lambda/2$, they will interfere destructively, producing a minimum intensity.
  • Therefore, the condition for the first secondary minimum is: $$\text{path difference} = \frac{a}{2} \sin\theta = \frac{\lambda}{2} \implies a \sin\theta = \lambda$$
  • Generalizing this, the condition for the $n$-th secondary minimum is given by: $$a \sin\theta = n\lambda \quad (n = \pm 1, \pm 2, \pm 3, \dots)$$

Intensity Distribution\nThe diffraction pattern consists of a central bright maximum of high intensity, flanked on both sides by alternating secondary minima and weaker secondary maxima of decreasing intensity as we move away from the center.