MHT-CET Physics · Wave Optics

Wavefronts, Huygens' Principle and Coherent Sources

A wavefront is a surface of equal phase, always perpendicular to the rays; Huygens' principle builds each new wavefront from secondary wavelets; and only coherent sources — same frequency, fixed phase difference — give a steady interference pattern.

All Wave Optics notes MHT-CET Physics strategy

Why this matters

5 PYQs, none HARD — a short page of recall. What a wavefront is and what happens to it at a boundary, what the wave theory explains that the corpuscle theory does not, and why two different colours cannot interfere.

Concept 1 of 2: Wavefronts and the Wave Theory

Every point on a wavefront sends out a small spherical wavelet; the surface touching all of them a moment later is the new wavefront. In a slower medium the wavelets are smaller, so the wavefront — and the wavelength — shrink; going into a faster, rarer medium they widen.

Definition

A wavefront joins points in the same phase; it is PERPENDICULAR to the direction of propagation.
Wave theory: colour is set by wavelength; light is SLOWER in a denser medium; it explains reflection and refraction. Different 'corpuscle sizes' for colours belong to Newton's corpuscular theory.
Denser to rarer medium: speed and wavelength rise, the wavefront widens.
In a medium $\lambda_m = \dfrac{\lambda}{\mu}$ , so the number of waves in thickness $t$ is $\dfrac{\mu t}{\lambda}$ .

Wavelength in a medium

\lambda_{\text{medium}} = \frac{\lambda_{\text{vacuum}}}{\mu}, \qquad N = \frac{\mu t}{\lambda}

Worked example

Light fits the same number of waves into 4 cm of glass (

\mu = 1.5

) as into a height h of water (

\mu = 1.33

). Find h.

Practice this conceptself-check · 2 quick reps

The same idea in a real exam question:

MHT-CET · 2023 · 9th May Shift 1 · Q13Easy

Example 1 · Wave Optics · Wavefronts, Huygens, and Coherence

A wave-front is a surface

Crediting Huygens with corpuscles

'Different colours are due to different sizes of the corpuscles' is Newton's picture, and the statement a 'NOT correct for Huygens' question wants.

Drill 3 more on wavefronts and the wave theory

Concept 2 of 2: Coherent Sources

Interference needs a phase difference that stays fixed, point by point, for the whole time you look. Two waves of different frequency slip past each other in phase millions of times a second, so no steady pattern forms.

Definition

Coherent: same frequency (wavelength) and a constant phase difference — in practice, two images of ONE source (double slit, biprism).
Two independent lamps, or one slit behind a red filter and the other behind a blue one, give no interference fringes.

Condition for a steady pattern

\nu_1 = \nu_2, \quad \phi_1 - \phi_2 = \text{constant}

Worked example

Two sodium lamps light the two slits of a Young's experiment. Are fringes seen?

Practice this conceptself-check · 1 quick reps

The same idea in a real exam question:

MHT-CET · 2023 · 2nd May Shift 1 · Q31Easy

Example 2 · Wave Optics · Wavefronts, Huygens, and Coherence

In a Young's double slit experiment, the source is white light. One of the holes is covered by a red filter and another by a blue filter. In this case

Expecting red and blue fringes side by side

Each filter passes a different frequency, so there is no pattern at all — not separate red and blue fringe systems, which the options offer.

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 (2)

Wavefronts and the Wave Theory
Wavelength in a medium
$\lambda_{\text{medium}} = \frac{\lambda_{\text{vacuum}}}{\mu}, \qquad N = \frac{\mu t}{\lambda}$
Coherent Sources
Condition for a steady pattern
$\nu_1 = \nu_2, \quad \phi_1 - \phi_2 = \text{constant}$

Watch out for (2)

Crediting Huygens with corpuscles
→ Wavefronts and the Wave Theory
Expecting red and blue fringes side by side
→ Coherent Sources

Test yourself on Wave Optics

20 past MHT-CET questions from this chapter, timed at 18 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

Take the Wave Optics chapter test Drill all 5 questions

Related notes

Interference Intensity →