Wave Optics, also known as Physical Optics, deals with the study of various phenomena like interference, diffraction, and polarization, which cannot be explained by ray optics (geometrical optics). This branch of optics considers light as a wave and explains the behavior of light using the wave theory.
Huygens' Principle is a fundamental concept in wave optics. It states that every point on a wavefront acts as a source of secondary spherical wavelets, and the new wavefront is the tangent to these secondary wavelets.
A wavefront is a surface over which an optical wave has a constant phase. Wavefronts can be:
To understand how wavefronts propagate, consider a point source emitting spherical wavefronts. According to Huygens' Principle:
Tip
Visualize Huygens' Principle by drawing concentric circles (wavelets) from points on the wavefront and then drawing a tangent to these circles to form the new wavefront.
Interference is a phenomenon where two or more waves superimpose to form a resultant wave of greater, lower, or the same amplitude.
This experiment demonstrates the interference of light waves. Light from a single source is split into two coherent sources using two slits.
Consider two slits $S_1$ and $S_2$ separated by a distance $d$, and a screen placed at a distance $D$ from the slits:
Where $n$ is an integer and $\lambda$ is the wavelength of light.
The fringe width $\beta$ is given by: $$ \beta = \frac{\lambda D}{d} $$
Example
Calculate the fringe width if $\lambda = 600 , \text{nm}$, $D = 1 , \text{m}$, and $d = 0.5 , \text{mm}$. $$ \beta = \frac{600 \times 10^{-9} \times 1}{0.5 \times 10^{-3}} = 1.2 , \text{mm} $$
Common Mistake
Do not confuse the distance between the slits ($d$) with the distance between the fringes ($\beta$).
Diffraction is the bending of light around the corners of an obstacle or aperture into the region of geometrical shadow.
When light passes through a single slit of width $a$, it forms a diffraction pattern on a screen placed at a distance $D$.
The intensity $I$ at an angle $\theta$ is given by: $$ I(\theta) = I_0 \left( \frac{\sin(\beta)}{\beta} \right)^2 $$ where $\beta = \frac{\pi a \sin \theta}{\lambda}$ and $I_0$ is the maximum intensity at the center.
The condition for minima (dark fringes) in the diffraction pattern is: $$ a \sin \theta = n\lambda $$ where $n$ is an integer (excluding zero).
Note
The central maximum is twice as wide as the other maxima.
Polarization is the phenomenon in which waves of light or other radiation are restricted to certain directions of vibration.
When unpolarized light strikes a surface at a particular angle known as Brewster's angle ($\theta_B$), the reflected light is completely polarized perpendicular to the plane of incidence.
Brewster's angle is given by: $$ \tan \theta_B = n $$ where $n$ is the refractive index of the medium.
Example
Calculate Brewster's angle for light incident on water ($n = 1.33$). $$ \tan \theta_B = 1.33 \implies \theta_B = \tan^{-1}(1.33) \approx 53^\circ $$
Wave optics provides a comprehensive understanding of various optical phenomena that cannot be explained by geometrical optics. By considering light as a wave, we can explain interference, diffraction, and polarization, which are crucial for many technological applications.
Tip
Always remember to use coherent sources and monochromatic light to observe clear interference patterns.