Wave OpticsNEET Physics · Class 12 · NCERT Chapter 10

Introduction

Ray optics treats light as straight rays. That works when the apertures and obstacles are much larger than the wavelength. When they get small (slits, fine gratings) or when two beams overlap, you start seeing patterns that rays cannot explain. Wave optics treats light as a wave and explains all of it: interference (Young's experiment), diffraction at single slits and apertures, polarisation, and the resolving limit of every telescope and microscope.

Expect 1 to 2 NEET questions every year. Common asks: fringe width in YDSE, intensity at a point given path difference, fringe shift due to a glass slab, single-slit central maximum width, Brewster's angle, Malus' law, and resolving power formulas.

Wavefronts

A wavefront is a surface where every point is at the same phase of oscillation. Three common shapes:

• Spherical: from a point source, expanding outward like ripples in a pond.
• Plane: from a very distant source. Wavefronts arrive nearly flat.
• Cylindrical: from a line source.

The direction of propagation is always perpendicular to the wavefront (the "ray" in ray optics).

Huygens' principle

Every point on a wavefront acts as a source of secondary spherical wavelets. The new wavefront a short time dt later is the envelope of all those secondary wavelets. This single idea explains:

• Why light travels in straight lines in a uniform medium.
• The law of reflection (angle of incidence = angle of reflection).
• Snell's law (from speed difference between media).
• Why diffraction and interference happen.

Each wavefront is the envelope of secondary wavelets from points on the previous wavefront. Watch the wavefronts expand outward at constant speed.

Reflection and refraction by Huygens

Apply Huygens to a plane wave hitting a flat interface. The wavefront has its leading edge in one medium while the trailing edge is still in the other; matching the wavelet timing on both sides gives:

Same logic explains reflection: the reflected wavefront is constructed in the same medium with reversed normal component.

Coherent and incoherent sources

Two sources are coherentif they emit waves of the same frequency with a constant phase relationship. Two independent bulbs are not coherent: their phases drift randomly, so any interference pattern averages out. To get sustained fringes you need either one source split into two (Young's slits) or two lasers locked in phase.

Principle of superposition

At a point where two coherent waves arrive, the displacements add. With amplitudes a_1 and a_2 and phase difference φ:

Since intensity scales as amplitude squared, the formula in intensities is:

Maximum (constructive): φ = 0, 2π, 4π... → $I_{\max }=(\sqrt{I_1}+\sqrt{I_2}{)}^2$.

Minimum (destructive): φ = π, 3π... → $I_{\min }=(\sqrt{I_1}-\sqrt{I_2}{)}^2$.

Path difference Δx and phase difference φ are related by:

Two coherent sources of intensity I_1 and I_2 give a resultant intensity that depends on the phase difference between them.

Young's double slit experiment

Single source illuminates two narrow slits S_1, S_2 separated by d. Light from these acts as two coherent sources. On a screen at distance D, alternating bright (max) and dark (min) fringes form. For point P at distance x from the central axis:

Bright fringes (path difference = nλ): $x_n=n\lambda D/d$.

Dark fringes (path difference = (n + 1/2)λ): $x_n=(n+1/2)\lambda D/d$.

Fringe width and intensity

Fringe width β = distance between adjacent bright (or dark) fringes:

For equal-intensity slits, intensity at P:

Maximum (4 I_0) at bright fringes; zero at dark fringes.

Drag any slider; the bright fringes get closer or farther. Fringe width β = λD / d.

Fringe shift with a glass slab

Place a slab of refractive index n and thickness t in front of one slit. The light through that slit gains an extra optical path (n - 1) t. The whole pattern shifts towards the slab side by:

In units of fringe widths: shift = (n - 1) t / λ fringes.

Adding a glass slab in front of one slit shifts the whole pattern towards that slit by an amount proportional to the extra optical path (n - 1) t.

Diffraction at a single slit

Light passing through a single slit of width a spreads out. On a screen at distance D, the pattern shows a bright central maximum and dimmer secondary maxima. Minima occur at:

First minimum on either side of centre at sin θ = λ / a. Width of the central maximum:

This is twice the spacing of secondary fringes. Narrower slit → wider central max (more diffraction).

Diffraction at a single slit gives a bright central maximum twice as wide as the side maxima. Slit minima: a sin θ = nλ.

Interference vs diffraction

• Interference: two coherent sources, equally bright fringes, equally spaced, all the same width.
• Diffraction: wavelets across one aperture, central max dominates, side maxima decrease in brightness, central max twice as wide.

Resolving power

Two close objects can be told apart only when their diffraction patterns separate. Rayleigh criterion: just resolved when the central max of one falls on the first min of the other.

Telescope: angular limit

Larger aperture D → finer resolution. Hubble (D = 2.4 m) at 550 nm gives Δθ ≈ 0.05 arcsec.

Microscope: smallest resolvable distance d = λ / (2 NA), where NA is the numerical aperture.

Two close objects look distinct only when their angular separation exceeds the resolving limit. Bigger aperture or shorter wavelength gives finer detail.

Polarisation

Only transverse waves can be polarised. Ordinary unpolarised light has its E vector pointing in random directions perpendicular to propagation. A polariser (e.g. a Polaroid sheet) lets through only the component along its transmission axis.

Brewster's law

Sometimes reflection itself produces polarised light. Brewster found that at a particular angle of incidence θ_B, the reflected ray is fully plane-polarised perpendicular to the plane of incidence. At this angle:

For glass-air (n = 1.5), θ_B ≈ 56.3°. Why polarised sunglasses help: at a typical glance angle to a wet road or car windshield, the reflected glare is partially polarised; the sunglasses block that polarisation.

At Brewster's angle, the reflected ray is fully plane-polarised (perpendicular to plane of incidence) and the reflected and refracted rays are perpendicular to each other.

Malus' law

Polarised light of intensity I_0 enters a second polariser whose axis makes angle θ with the polarisation direction. Transmitted intensity:

Special cases: θ = 0 (parallel) → full transmission. θ = 90° (crossed) → zero. Unpolarised light through one ideal polariser: intensity drops to I_0 / 2 (cos² averaged is 1/2).

Already polarised light passing through a polariser at angle θ has intensity I = I_0 cos² θ. At 90° (crossed), no light passes.

Worked NEET problems

Summary cheat sheet

• Wavefront: surface of constant phase. Huygens: envelope of secondary wavelets.
• Coherent sources: same f, constant phase difference.
• Path-phase: $\varphi =(2\pi /\lambda )\Delta x$.
• Resultant intensity: $I=I_1+I_2+2\sqrt{I_1{I}_2}\cos \varphi$.
• YDSE fringe width: $\beta =\lambda D/d$.
• Bright at: $x_n=n\lambda D/d$. Dark at: $(n+1/2)\lambda D/d$.
• Slab fringe shift: $\Delta y=(n-1)tD/d$.
• Single slit central max: $W=2\lambda D/a$.
• Telescope resolution: $\Delta \theta =1.22\lambda /D$.
• Brewster: $\tan {\theta }_B=n$.
• Malus: $I=I_0{\cos }^2\theta$.

Next: try the interactive widgets for YDSE, single-slit diffraction, polarisation and resolving power, or work through the 31 NEET PYQs with full solutions. To time yourself, take the free 10-question mock test.