Light emerges out of a convex lens when a source of light kept at its focus. The shape of wavefront of the light is:

The correct answer is Plane (Option 4).

To understand why, we need to recall two fundamental concepts: how a convex lens works with light from its focus, and what a wavefront is.

Step 1: Understanding Wavefronts
A wavefront is a surface connecting all points of a wave that are in the same phase of oscillation. In other words, it is the locus of all points that a wave reaches at the same instant of time. The shape of a wavefront depends entirely on the nature of the source and the medium through which light travels.

Step 2: What does a point source at the focus produce?
A point source of light placed at the focus of a convex lens emits light as spherical wavefronts, because all rays diverge outward equally in all directions from that single point. As these spherical wavefronts travel outward from the source, they strike the convex lens.

Step 3: Action of the Convex Lens on the Wavefront
A convex lens is thicker at the centre and thinner at the edges. When a diverging spherical wavefront from the focal point enters the lens:

- The central portion of the wavefront (passing through the thicker part of the lens) travels more slowly (because glass is optically denser than air) and is therefore retarded more.
- The outer portions of the wavefront (passing through the thinner edges of the lens) are retarded less.

This differential retardation adjusts the shape of the wavefront so that, after emerging from the other side of the lens, all parts of the wavefront are brought into phase simultaneously along a flat, uniform surface.

Step 4: The Resulting Wavefront Shape
By the principle of wave optics (and confirmed by Huygens' construction), when a point source is placed exactly at the principal focus of a convex lens, the refracted rays emerge as a parallel beam — that is, all rays travel parallel to the principal axis after passing through the lens.

A set of parallel rays corresponds to a wavefront that is perpendicular to all those rays. Since all parallel rays are perpendicular to a flat surface, the wavefront is planar (flat).

Step 5: Connecting to the Standard Rule
There is a direct correspondence between the type of source/wavefront and the resulting beam:

- Point source at infinity → Plane wavefront → Converges at focus (after convex lens)
- Point source at focus → Plane wavefront (after convex lens) → Parallel beam emerges

This is essentially the reverse of the standard rule: just as plane waves converge to the focus, a source at the focus produces plane waves upon emergence. This is a consequence of the principle of reversibility of light.

Conclusion:
When a source of light is placed at the focus of a convex lens, the emerging light consists of parallel rays. The wavefront associated with parallel rays is a plane wavefront — flat and perpendicular to the direction of propagation. Hence, the correct answer is Plane.