Why can sunlight be approximated by plane waves, whereas the light from a nearby lamp cannot?

Question

This is a question from my physics book and I believe it has something to do with Huygen's principle.

Answer 1

Imagine the light wave from a point source like the circular waves produced when you drop a stone in water. As the wave moves out, each point on the wavefront behaves like its own point-source and the constructive/destructive interference of these "wavelets" cause the wave to continue to propagate.

In 3-dimensions, the light from the sun is like a spherical wave propagating out. The wavefront is perpendicular to the direction of travel. The sun is about 93 million miles away, so by the time the wavefront reaches the earth, the tangent to the "spherical" wavefront is essentially the same as the wavefront itself. Hence, it can be represented as a plane wave because the spherical nature of the wave becomes insignificant.

However, with a "nearby" lamp, the spherical wavefront retains its shape - i.e., we cannot neglect the shape of the wavefront. The effect is similar to placing a ruler tangent to circles of different radii. A ruler placed alongside a circle of 93 million mile radius would be virtually indistinguishable from the circle itself.

Answer 2

Light from an incandescent source, such as the lamp, emanates in spherical waves. Think of drawing a circle on a piece of paper. The larger the radius of the circle, the more the circle looks like a straight line for some finite distance.

The light emanating from the sun comes to us from about 93 million miles away. A circle with a radius of 93 million miles looks very much like a line over a short distance of a few inches. The world looks flat because the radius is large, and when we see it close up we don't really see the curvature.

Since the curvature is nearly a straight line the sunlight can be approximated by a plane wave. A nearby lamp is too close; the curvature of the wave is noticeable and cannot be ignored.

There is no need to bring in Huygen's principle, which is that light appears to be the summation of circles originating all along the wavefront. It is somewhat related, since the further the wave propagates the more nearly a straight line the summation of circles becomes.

Answer 3

sun's light reaches a very long distance and it is very large in size compare when compared to a lamp so at any certain point its light is apprroximately a plane wave(i am not sure this is correct)