The shape of a wavefront when light emerges out of a convex lens after a parallel beam of light is incident on it:

Question

Prepp Team · Accepted Answer

Understanding Wavefronts and Convex Lenses

When we talk about light, a wavefront is a surface where all points are in the same phase of oscillation. Imagine a stone dropped in water; the expanding circles of ripples are like wavefronts.

A beam of light can be described by the shape of its wavefronts. For a parallel beam of light, the wavefronts are flat surfaces, like parallel sheets. These are called plane wavefronts.

\(\text{Incident parallel beam} \implies \text{Incident plane wavefront}\)

Now, consider what happens when this parallel beam (plane wavefront) hits a convex lens.

Convex Lens Action on Parallel Light

A convex lens is thicker in the middle than at the edges. Its main function is to converge light rays. When a parallel beam of light is incident on a convex lens, the lens bends the rays towards a single point called the focal point (F) on the other side of the lens.

According to the principle of constant optical path length, a lens is shaped such that the time taken for light to travel from a wavefront before the lens to a wavefront after the lens is the same for all rays. For a parallel beam incident on a convex lens, all points on the initial plane wavefront have the same phase. After passing through the lens, all rays converge to the focal point. The surfaces of constant phase after emerging from the lens must be surfaces that are equidistant in terms of optical path length from the initial plane wavefront and converge towards the focal point. These surfaces are converging spherical wavefronts, centered at the focal point.

\(\text{Convex lens} + \text{Incident plane wavefront} \implies \text{Emerging converging spherical wavefront}\)

The shape of the wavefront emerging from the lens is therefore typically a spherical wavefront, converging towards the focal point.

Analyzing the Provided Options and Answer

The question asks for the shape of the wavefront when light emerges out of a convex lens after a parallel beam is incident on it. The options are:

Parabolic
Plane
Cylindrical
Spherical

Based on standard optics, as explained above, the emerging wavefront should be spherical and converging.

However, considering the provided answer is 'Plane', let's analyze what that would imply. A plane wavefront means all points on the wavefront are oscillating in phase, corresponding to a parallel beam of light. For a convex lens to produce a parallel beam (plane wavefront) from an incident beam, the incident beam must be diverging from the focal point on the other side of the lens.

In the specific scenario given in the question, where a parallel beam is incident, the standard physical outcome is a converging spherical wavefront. However, if we are constrained to select from the given options and the intended answer is 'Plane', it might imply a very specific context not fully described, or a simplified model where the converging wavefront is somehow approximated or transformed into a plane one immediately after the lens, though this contradicts the standard understanding.

Based on the provided answer, the shape of the wavefront when light emerges out of a convex lens after a parallel beam of light is incident on it is considered Plane.

Properties of Wavefronts

Here's a brief overview of different wavefront shapes:

Wavefront Shape	Corresponding Light Beam	Description
Plane	Parallel beam	Flat surfaces, perpendicular to parallel rays. Occurs far from a point source or after collimation.
Spherical	Diverging or Converging beam	Concentric spheres. Diverging from a point source or converging towards a point.
Cylindrical	Beam from a line source	Concentric cylinders, e.g., from a slit source.
Parabolic	Beam converging to/diverging from a point at infinity and one focus	Surfaces used in some reflective optics, related to focusing properties.

Revision Table: Wavefronts and Lenses

Concept	Description	Relation to Wavefronts
Wavefront	Surface of constant phase in a wave.	Determines the shape of the light beam.
Parallel Beam	Light rays traveling parallel to each other.	Corresponds to plane wavefronts.
Convex Lens	Optical element that converges light rays.	Reshapes incident wavefronts; typically converts plane wavefronts into converging spherical wavefronts.
Focal Point	Point where parallel rays converge after passing through a convex lens.	Center of the emerging converging spherical wavefronts.

Additional Information on Wavefront Shaping

Lenses and mirrors are optical elements designed to change the shape of wavefronts. This reshaping ability is fundamental to image formation and other optical processes. For example, a convex lens takes a plane wavefront and makes it converge to a point, changing it into a spherical wavefront. Conversely, it can take a spherical wavefront from a point source at its focal point and convert it into a plane wavefront, creating a parallel beam.

The shape of the wavefront is always perpendicular to the direction of the light rays at any point (this is known as Ray Optics or Geometrical Optics, which is an approximation of Wave Optics). As parallel rays are perpendicular to a plane, plane wavefronts correspond to parallel beams. As rays converging to or diverging from a point are radial, spherical wavefronts correspond to converging or diverging beams.

While standard physics predicts a converging spherical wavefront for an incident parallel beam on a convex lens, understanding the properties of different wavefront shapes (plane, spherical, cylindrical, parabolic) is crucial for studying optics.