Wave Optics 

Focus: Nature of light, interference, Young’s double slit experiment, diffraction, polarisation (JEE Main).

1) Nature of Light

• Light is an electromagnetic wave consisting of sinusoidally varying electric and magnetic fields.
• It propagates as a transverse, non-mechanical wave.

Electric and magnetic fields:

E_y = E₀ sin(kx ± ωt)

B_z = B₀ sin(kx ± ωt)

Speed of light in a medium:

v = 1 / √(με)

Field relation:

E₀ = vB₀

Refractive index:

μ = c / v

2) Interference of Light

Interference is the redistribution of intensity due to superposition of two coherent light waves.

Resultant intensity:

I = I₁ + I₂ + 2√(I₁I₂) cos φ

Conditions

Constructive interference (maxima):

Δx = nλ

I_max = (√I₁ + √I₂)²

Destructive interference (minima):

Δx = (2n − 1)λ / 2

I_min = (√I₁ − √I₂)²

3) Young’s Double Slit Experiment (YDSE)

Path difference:

Δx = d sin θ ≈ dy / D

Position of bright fringes:

y_n = nλD / d

Position of dark fringes:

y_n = (2n − 1)λD / 2d

Fringe width:

β = λD / d

• Fringe width is independent of order n.
• All bright fringes are equally spaced.

Effect of thin transparent sheet:

Fringe shift: y₀ = (μ − 1)tD / d

4) Diffraction

Diffraction is the bending of light around obstacles or apertures.

Single Slit Diffraction

Condition for minima:

d sin θ = nλ (n = 1, 2, 3…)

Angular width of central maximum:

θ₀ = 2λ / d

• Central maximum has the highest intensity.
• Subsidiary maxima decrease in intensity.

Circular Aperture (Airy Disc)

Radius of Airy disc:

r = 1.22 λf / d

Rayleigh’s criterion:

θ_R = 1.22 λ / d

5) Diffraction Grating

Condition for principal maxima:

d sin θ = nλ

Dispersive power:

DP = dθ / dλ = n / (d cos θ)

Resolving power:

RP = λ / dλ = nN

• More slits → higher resolving power.
• Closer slit spacing → greater dispersion.

6) Polarisation

• Unpolarised light has vibrations in all planes.
• Plane polarised light vibrates in one plane only.
• Intensity becomes half when unpolarised light is polarised.

Brewster’s Law

tan θ_p = μ

Malus Law

I = I₀ cos² θ

Optical activity (specific rotation):

[α] = θ / (LC)