THE POWER OF HUMAN EYE

How far and how clearly we can see? The star we see in the night sky is single or double?
The answer : " We can at the most distinguish things that are 30 centimeters apart at a distance of 1 kilometer". This result from the following formula

Angular dispersion of human eye A = 1.22*L/d
L - wave length of light
d - diameter of aperture of pupil of the eye.
We get A as 0.0003 radian. = 0.0003/1 = 0.0003 km/1 km = 30 cm/1 km.

What is the angular dispersion? Why this restriction to human eye? To explain that, we have to go to the physics principle-dispersion-diffraction.

Let us say, water flow from a lake through a narrow channel to another lake. Once the water exists the channel it will spread out [Dispersion]. That is the nature of all fluids. But a stream of arrows or bullets passing through a hole will not spread out. Light is not particles but waves(like water waves). Whenever it passes through a hole, it will spread out in all directions (0-180). This phenomenon is called diffraction. Diffraction can be observed clearly, when the size of the hole is comparable to the size of light's wave-length.

Now, consider two apples sitting on your table. Lot of light is coming from them, Hence you can clearly distinguish the two apples.
Now look at the 'closely spaced two stars' in the night sky, Limited light is coming from them. The minimum light will spread out in your eyes due to diffraction. And you cannot distinguish the two stars. They will appear as "one" for you. Now, you can understand the limitation [30 cm/1 km] given by the formula.
Some creatures can see using ultraviolet light. UV light has smaller wavelength than ordinary light. Hence they can see long distance with clarity. (use the formula)

We overcome the limitation of our eyes using Telescope. The Hubble telescope can see a strand of "human hair" at the distance of 1 mile.

Note: In text books, diffraction is defined as "bending of light over the edges". But, it is actually the spread and propagation of waves through the holes, around edges and obstacles.
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