JEE Mains Physics · Wave Optics

Wavefronts and Light in a Medium

A wavefront is a surface of constant phase and the rays are normal to it; when light enters a medium its frequency stays the same while its speed and wavelength both fall by the factor μ.

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Why this matters

Twelve PYQs, all multiple choice, and two from 2026. Six are about wavefronts: the shape a source or a lens gives, the direction a plane wave travels, what happens when the obstacle is much smaller than the wavelength, and which effects the wave theory cannot explain. Six follow light into a medium, where the frequency stays and the speed and wavelength change. None needs more than one line of working once the rule is clear.

Concept 1 of 2: Wavefronts, rays and Huygens' principle

Drop a stone in a pond and the crests spread as circles. Each circle joins points that move in step, so it is a surface of constant phase: a wavefront. Light travels at right angles to its wavefronts, so the rays are the normals. Far from any source the circles are so large that a small piece of them is flat: a plane wave.

Definition

A wavefront is a surface on which every point has the same phase. Rays are normal to it.
Huygens' principle: every point of a wavefront is a source of secondary wavelets; the new wavefront is the surface that touches them all a moment later.
A plane wavefront $ax + by + cz = \text{constant}$ travels along its normal $(a, b, c)$ . Its angle with the x-axis is $\cos^{-1}\dfrac{a}{\sqrt{a^{2} + b^{2} + c^{2}}}$ .
Size against wavelength: an object much larger than $\lambda$ reflects the wave, one about $\lambda$ in size diffracts it, one much smaller than $\lambda$ scatters it.
The wave theory explains reflection, refraction, interference, diffraction and polarisation. It cannot explain the photoelectric effect or the Compton effect; those need photons.

Source or situation	Shape of the wavefront	Rays
Point source nearby	Spherical	Spread out from the source
Line source, such as a lit slit or a tube light	Cylindrical	Spread out at right angles to the line
Very distant source, such as the Sun or a star	Plane	Parallel
Point source at the focus of a convex lens, after the lens	Plane	Parallel The lens turns a spherical wave into a plane one; this is how a parallel beam is made.
Plane wave after a convex lens	Spherical, shrinking onto the focus	Converge to the focus
Plane wave after a prism	Plane, turned through the deviation	Parallel, bent towards the base
Plane wave after a pinhole much smaller than the beam	Nearly spherical	Spread out from the hole A wider slit lets through a flatter, less curved wave.

The shape of the wavefront tells you the shape of the ray bundle: spherical spreads, plane stays parallel.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2025 · 2 Apr 2025 · Q1Moderate

Example 1 · Wave Optics · Wavefronts and Light in a Medium

A light wave is propagating with plane wave fronts of the type

x+y+z=

constant. The angle made by the direction of wave propagation with the x -axis is :

The wave travels along the normal

The direction of travel is the normal to the wavefront, given by the coefficients of x, y and z, not a line lying in the wavefront.

A prism does not curve a plane wave

A prism only turns a plane wavefront. A lens curves it, and a tiny hole makes it nearly spherical by diffraction.

Photons, not waves

Interference, diffraction and polarisation are wave effects. The photoelectric and Compton effects are particle effects, and the wave theory fails on them.

Drill 5 more on wavefronts, rays and huygens' principle

Concept 2 of 2: Speed, wavelength and frequency in a medium

The source sets the frequency: it is the number of crests it pushes out each second, and no boundary can change that count. Inside a denser medium the light slows down by the factor μ. With the same number of crests each second but a lower speed, the crests must sit closer together, so the wavelength falls by the same factor μ.

Definition

Frequency is unchanged on entering any medium; colour goes with frequency, so the colour does not change either.
$v = \dfrac{c}{\mu}$ and $\lambda = \dfrac{\lambda_{0}}{\mu}$ , where $\lambda_{0}$ is the wavelength in vacuum.
Between two media: $\dfrac{\lambda_{1}}{\lambda_{2}} = \dfrac{v_{1}}{v_{2}} = \dfrac{\mu_{2}}{\mu_{1}}$ , and by Snell's law $\dfrac{\sin i}{\sin r}$ equals the same ratio.
The speed of light in vacuum is the same in every direction and does not depend on how the source moves.
In a medium the speed depends on the wavelength (this is dispersion), but not on the intensity.

Light in a medium

f = f_{0}, \qquad v = \frac{c}{\mu}, \qquad \lambda = \frac{\lambda_{0}}{\mu}, \qquad \frac{\lambda_{1}}{\lambda_{2}} = \frac{v_{1}}{v_{2}} = \frac{\mu_{2}}{\mu_{1}}

Worked example

Light of wavelength 750 nm in vacuum enters glass of refractive index 1.5. Find its speed, wavelength and frequency in the glass. (c = 3 × 10⁸ m/s)

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2026 · 22 Jan 2026 Shift 2 · Q12Moderate

Example 2 · Wave Optics · Wavefronts and Light in a Medium

The wavelength of light, while it is passing through water is 540 nm. The refractive index of water is

\frac{4}{3}

. The wavelength of the same light when it is passing through a transparent medium having refractive index of

\frac{3}{2}

\_\_\_\_

nm.

Frequency never changes at a boundary

Only speed and wavelength change. An option that changes the frequency, or the colour, is wrong however neat its numbers.

The μ ratio is upside down

Wavelength and speed fall as μ rises, so λ₁/λ₂ = μ₂/μ₁. Writing μ₁/μ₂ gives the answer for going the other way.

Go through the vacuum value

Given a wavelength in one medium, multiply by its μ to get λ₀, then divide by the new μ. Skipping the step is where the ratio gets inverted.

Drill 5 more on speed, wavelength and frequency in a medium

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Speed, wavelength and frequency in a medium
Light in a medium
$f = f_{0}, \qquad v = \frac{c}{\mu}, \qquad \lambda = \frac{\lambda_{0}}{\mu}, \qquad \frac{\lambda_{1}}{\lambda_{2}} = \frac{v_{1}}{v_{2}} = \frac{\mu_{2}}{\mu_{1}}$

Reference tables (1)

Wavefronts, rays and Huygens' principle7 rows

Source or situation	Shape of the wavefront	Rays
Point source nearby	Spherical	Spread out from the source
Line source, such as a lit slit or a tube light	Cylindrical	Spread out at right angles to the line
Very distant source, such as the Sun or a star	Plane	Parallel
Point source at the focus of a convex lens, after the lens	Plane	Parallel The lens turns a spherical wave into a plane one; this is how a parallel beam is made.
Plane wave after a convex lens	Spherical, shrinking onto the focus	Converge to the focus
Plane wave after a prism	Plane, turned through the deviation	Parallel, bent towards the base
Plane wave after a pinhole much smaller than the beam	Nearly spherical	Spread out from the hole A wider slit lets through a flatter, less curved wave.

The shape of the wavefront tells you the shape of the ray bundle: spherical spreads, plane stays parallel.

Watch out for (6)

The wave travels along the normal
→ Wavefronts, rays and Huygens' principle
A prism does not curve a plane wave
→ Wavefronts, rays and Huygens' principle
Photons, not waves
→ Wavefronts, rays and Huygens' principle
Frequency never changes at a boundary
→ Speed, wavelength and frequency in a medium
The μ ratio is upside down
→ Speed, wavelength and frequency in a medium
Go through the vacuum value
→ Speed, wavelength and frequency in a medium

Test yourself on Wave Optics

20 past JEE Mains questions from this chapter, timed at 48 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

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