# In geometrical optics, how can we say that rays coming from a distant object are parallel to one another?

If two rays are not parallel in the start, how can they become parallel at the instant when they strike the lens of a telescope? If they don't become parallel, why do we consider them to be, in the ray diagrams of telescopes?

• They're approximately parallel since the object is very far away. – knzhou Jul 11 '16 at 5:08
• Yes object is far away, but how does it make the rays approximately parallel? – rock Jul 11 '16 at 5:28
• Think of it another way... rays that aren't approximately parallel won't both hit your lens. – James Jul 11 '16 at 18:18

The answer is because our ken (field of view) subtends an extremely small angle at the source. Even though the source may emit over a wide angular range, we can only receive a small angular range of that light if we have a limited aperture instrument and our distance from the source is large compared with the aperture.

Suppose we look at Alpha Centauri through a 1 meter diameter aperture. Then the range of angles present in the rays that reach us if Alpha Centauri were a true point would be:

$$\frac{1\text{ meter}}{4.1\times10^{16}\text{ meters}} \approx 2.5\times10^{-17}\text{ radians}$$

The path difference between a central and edge ray would be:

$$\sqrt{(4.1\times10^{16})^2 + 1^2} - 4.1\times10^{16} \approx 1.25\times10^{-17}{\rm m}$$

or less than one hundredth of an atomic nucleus.

Even when we take account of the fact that the star is an extended source, the range of angles is roughly the star's angular subtense at our position. This is still an extremely small number that has no bearing whatsoever on the diffraction of visible light.

In the limiting case, consider that the object and your lens are finite in size and infinitely far apart. Then each appears as a point when viewed from the other. Two rays passing from the object to your lens would then follow the same path and would thus be parallel.