Class 12 Physics · NCERT notes for NEET

Wave Optics: NCERT Notes, Formulas and Tricks for NEET

Light as a wave: Huygens wavefronts, Young's double slit, single-slit diffraction and polarisation. NEET usually asks one or two questions here, mostly direct numericals on fringe width, intensity ratio, central maximum width and Malus/Brewster law.

1. Huygens principle
2. Interference and Young's double slit 🔒
3. Diffraction 🔒
4. Polarisation 🔒

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Topic 1

Huygens principle

Light slows down in glass: in 1 ns it covers 30 cm in air but only 20 cm in glass. Huygens used exactly this to derive Snell's law with nothing but circles.

A wavefront is a surface on which every point vibrates in the same phase. Rays are always perpendicular (normal) to the wavefront.
Point source: spherical wavefront. Line source (slit): cylindrical. Far from any source, a small part looks like a plane wavefront.
Huygens principle: every point on a wavefront is a source of secondary wavelets that spread at the wave speed. After time $τ$ , the forward envelope (common tangent) of all wavelets is the new wavefront.
Backward wavelets are ignored. Huygens just assumed this; later wave theory proved the backward amplitude is zero.
Reflection by Huygens construction: the reflected wavefront makes the same angle with the surface as the incident one, so $i = r$ .
Refraction: in time $τ$ , the wave covers $B C = v_{1} τ$ in medium 1 and $A E = v_{2} τ$ in medium 2. This gives $sin i / sin r = v_{1} / v_{2} = n_{2} / n_{1}$ .
So wave theory says light is SLOWER in a denser medium ( $v = c / n$ ). Newton's corpuscular theory predicted faster; experiment supports the wave theory.
On refraction the frequency does not change. Speed and wavelength both drop by the factor $n$ : $λ^{'} = λ / n$ .
Going from denser to rarer, the ray bends away from the normal; beyond the critical angle no refracted wavefront forms: total internal reflection.
A thin prism only tilts a plane wavefront (it stays plane). A convex lens or a concave mirror turns it into a spherical wavefront converging to the focus.

Each blue point sends a wavelet of radius vtau. The orange envelope of their forward halves is the new wavefront; rays stay normal to it. — Each blue point sends a wavelet of radius $v τ$ . The orange envelope of their forward halves is the new wavefront; rays stay normal to it.

While B moves v_1tau to C, the wavelet from A grows only v_2tau in the slower medium. The tangent CE is the refracted wavefront, tilted closer to the surface. — While B moves $v_{1} τ$ to C, the wavelet from A grows only $v_{2} τ$ in the slower medium. The tangent CE is the refracted wavefront, tilted closer to the surface.

Formulas

$\frac{sin i}{sin r} = \frac{v _{1}}{v _{2}} = \frac{n _{2}}{n _{1}} = n_{21}$
Snell's law from Huygens construction
$v = \frac{c}{n}, λ^{'} = \frac{λ}{n}, ν^{'} = ν$
speed, wavelength and frequency in a medium of index $n$
$\frac{λ _{1}}{λ _{2}} = \frac{v _{1}}{v _{2}} = \frac{n _{2}}{n _{1}}$
comparing two media (same frequency)

Tips, tricks and hacks

Frequency is the fingerprintColour is fixed by frequency, which never changes on refraction. Only

v

and

λ

shrink by

n

. Example: 600 nm light in glass (

n = 1.5

) has

λ^{'} = 400

nm but is still orange, not violet.

One ratio for everything

n_{2} / n_{1} = v_{1} / v_{2} = λ_{1} / λ_{2} = sin i / sin r

. If

v

halves,

λ

halves and

n

doubles. Example: water to glass,

n

goes from 4/3 to 3/2, so

λ_{g} / λ_{w} = (4/3) / (3/2) = 8/9

Distance in equal timeLight covers distance

\propto 1/ n

in a given time. In the time it covers 30 cm in air, it covers 20 cm in glass (

n = 1.5

) and 22.5 cm in water (

n = 4/3

Common mistakes

✗ Wavelength stays the same and frequency changes in a new medium.

✓ Frequency is set by the source and stays fixed; $λ$ and $v$ change.

✗ Rays are drawn along (parallel to) the wavefront.

✓ Rays are normal to the wavefront; for a plane wavefront the rays are parallel to each other.

✗ Corpuscular and wave theory both give light faster in water.

✓ Only corpuscular theory says faster; wave theory (and experiment) says slower, $v = c / n$ .

NEET traps

"Which theory predicts the speed of light in water is less than in air?" Answer: wave theory (Huygens), not corpuscular.

Shape question: a point source very far away (like the Sun) gives a plane wavefront, not a spherical one.

Huygens principle explains reflection, refraction and diffraction, but it does not by itself explain why there is no backwave.

Quick check: Light of wavelength 600 nm in air enters glass of refractive index 1.5. In glass its wavelength and frequency are

400 nm, $5 \times 1 0^{14}$ Hz
900 nm, $5 \times 1 0^{14}$ Hz
400 nm, $3.3 \times 1 0^{14}$ Hz
600 nm, $7.5 \times 1 0^{14}$ Hz

Answer: A. $ν = c / λ = 3 \times 1 0^{8} /6 \times 1 0^{- 7} = 5 \times 1 0^{14}$ Hz stays the same; $λ^{'} = 600/1.5 = 400$ nm.

Topic 2 · 🔒

Interference and Young's double slit

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Topic 3 · 🔒

Diffraction

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Topic 4 · 🔒

Polarisation

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