# Why do we see Stars as Points?

Q:
I read the answer “Does light from a star travel forever?” and can picture the light as an expanding hollow sphere the thickness of which is the time the star burns. By the time the light gets to us the wave front would be essentially flat. Why do we see the star as a point source, why not like a wave at sea which when it passes stretches away in every direction and has no discernable source??
- Dick Robertson (age 74)
Wilmington, NC
A:

Interesting question. The short answer is that we see stars as point sources because we use lenses—the lenses in our eyes or the lenses in telescopes. If we didn't use a lens or other imaging equipment, we wouldn't see the stars as points. I tried to make a diagram to show how this works:

Look at the blue star (1) first. The dashed concentric circles represent the wavefront of the light it emits. My picture is not at all to scale, but you can see that the curvature of the wavefront near the lens is pretty small, so the "rays" of light are close to parallel. (For other readers who don't know what a wavefront is, don't worry about it. Just look at the rays.) If you exposed a piece of photographic paper or the CCD element from a digital camera to this kind of light, it would only record a dim, roughly uniform illumination.

An ideal lens takes all rays that are parallel to an imaginary line through the center of the lens (the axis) and focuses them to a point behind the lens. The distance at which these rays focus defines the "image plane." The blue star is in the center of the lens's field of view, so it focuses in the center of the image plane. If you're looking through a telescope or taking a picture with a CCD, you'll see the star as a point!

Now look at the orange star (2). It is slightly off-center in the lens's field of view. Its wavefront is still roughly flat and its rays are parallel, but they come from a slightly different direction than the rays from the blue star. Because the orange rays aren't parallel to the axis of the lens, they focus to a different point in the image plane. Looking through your telescope, you'll see the stars as two separate points.

This is a simplified view of things. Real telescopes use multiple lenses (or, more commonly, curved mirrors). Real lenses usually have imperfections that make them not behave exactly as I described, especially when light hits the lens near its edge instead of in the center. I also didn't draw the refraction of light at the second surface of the lens. Finally, there's a limit to how close two stars can be and still show up as separate points, which is determined by both the diameter and focusing power of the lens, and the wavelength of the light.

Rebecca Holmes

PS: Here's the question this mentions about "Does light from a star travel forever?” :

(published on 11/29/2014)

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