Q.What is the shape of the wavefront in each of the following cases:

The key idea is Frequency Invariance — the wavefront shape depends on the geometry of the source and the medium, not on frequency.

1. A point source emits light uniformly in all directions. The wavefronts are spheres centred at the source.
2. A convex lens converts a spherical wavefront from its focus into a plane wavefront. All rays emerge parallel, so the wavefront is planar.
3. A distant star is effectively a point source at infinity. The tiny portion of its spherical wavefront reaching Earth is nearly flat — a plane wavefront.
   ✓Final answer

   1. Spherical,
   2. Plane,
   3. Plane.

The key idea here is frequency invariance — the frequency of light does not change when it travels through different media or optical systems, but the wavefront shape changes based on how the light propagates. A wavefront is a surface of constant phase; its shape tells you how the light is spreading or converging.

Let’s break it down case by case.

1. Light diverging from a point source

A point source emits light equally in all directions. Imagine a tiny bulb at the centre of a dark room — the light spreads out as concentric spheres. At any given instant, all points on a sphere centred at the source have travelled the same distance from the source, so they are at the same phase. That surface of constant phase is a sphere.

So the wavefront is spherical, with the source at the centre.

2. Light emerging from a convex lens when a point source is placed at its focus

Place a point source exactly at the focus of a convex lens. Light rays from the source strike the lens and are refracted. Because the source is at the focus, the lens bends the rays so they emerge parallel to the principal axis. Parallel rays mean the wavefront is a plane — all points on a plane perpendicular to the rays have the same phase.

Why? The lens introduces a path difference that exactly cancels the spherical curvature of the incoming wave. The emerging wavefront is flat.

So the wavefront is planar (a plane wave).

3. The portion of the wavefront of light from a distant star intercepted by the Earth

A star is so far away that the light reaching Earth has travelled an enormous distance — effectively infinite compared to Earth’s size. The spherical wavefront from the star has a radius of many light-years. Over the small patch intercepted by Earth (a few thousand kilometres across), the curvature is negligible. A tiny arc of a huge sphere looks flat.

So the intercepted wavefront is planar (a plane wave).

Method: Wavefront Construction using Huygens' Principle

Concept-first understanding: A wavefront is a surface of constant phase — all points on it are in the same state of vibration. The shape depends on how the wave propagates from the source.

(a) Light diverging from a point source

Shape: Spherical wavefront

Why:

• A point source emits light equally in all directions.
• Each point on the wavefront is at the same distance from the source.
• The locus of points at a fixed distance from a point is a sphere.

Key point: The wavefront expands outward, with radius increasing with time.

(b) Light emerging from a convex lens when a point source is at its focus

Shape: Plane (or planar) wavefront

Why:

• Rays from the focus, after refraction through a convex lens, emerge parallel to the principal axis.
• Parallel rays correspond to a wavefront that is flat — all points have the same phase along a plane perpendicular to the rays.

Key point: The lens converts a diverging spherical wavefront into a plane wavefront.

(c) Portion of wavefront from a distant star intercepted by Earth

Shape: Plane wavefront (approximately)

Why:

• A star is so far away that the spherical wavefront has an enormous radius.
• Over the small region intercepted by Earth, the curvature is negligible.
• The small patch behaves like a plane wavefront.

Key point: This is the far-field approximation — a tiny arc of a huge circle looks like a straight line.

Summary Table

Final takeaway: The shape of a wavefront is determined by the geometry of the source and the optical elements in the path.

Here are the common mistakes students make on this exact question (from the wave optics chapter in Class 12 Physics), along with how to avoid each.

Mistake 1: Confusing the shape for part (b)

The error:

Students often say the wavefront is converging (spherical) when light emerges from a convex lens with a point source at its focus.

Why it happens:

They think "lens converges light" and forget that if the source is at the focus, the emerging rays are parallel, not converging.

How to avoid:

• Draw the ray diagram: rays from focus → lens → emerge parallel to the principal axis.
• Parallel rays mean a plane wavefront.
• Key rule:
  • Source at focus → plane wavefront after lens.
  • Source beyond focus → converging spherical wavefront.

Correct answer: Plane wavefront.

Mistake 2: Calling part (c) a "spherical wavefront"

The error:

Students say the wavefront from a distant star is spherical.

Why it happens:

They know stars are point sources and think the wavefront remains spherical even at Earth.

How to avoid:

• A distant star is so far away that the tiny portion of the spherical wavefront reaching Earth is almost flat.
• Think of a huge balloon — a small patch on it looks like a flat sheet.
• Key rule:
  • Very large radius of curvature → plane wavefront locally.

Correct answer: Plane wavefront (or nearly plane).

Mistake 3: Mixing up "wavefront" with "ray direction"

The error:

Students describe the direction of rays instead of the shape of the wavefront.

Example: For part (a), they say "rays go outward" — that’s not the wavefront shape.

How to avoid:

• Remember:
  • Rays are perpendicular to wavefronts.
  • Wavefront is the surface of constant phase.
• For a point source, all points at the same distance from the source form a sphere.

Correct answer for (a): Spherical wavefront.

Mistake 4: Forgetting the "portion" in part (c)

The error:

Students answer "spherical" because the full wavefront from a star is spherical.

Why it happens:

They ignore the phrase "the portion of the wavefront intercepted by the Earth".

How to avoid:

• Read the question carefully — it asks for the shape of the intercepted portion, not the whole wavefront.
• A tiny arc of a huge circle is nearly a straight line.

Correct answer: Plane wavefront.

Quick Summary Table

Final tip for exams:

Always draw a quick sketch of the rays first, then draw the wavefront perpendicular to them. This will save you from all four mistakes above.