Circular apertures Circular apertures On a sunny day, the pupil of your eye cont

Question

Circular apertures

Circular apertures On a sunny day, the pupil of your eye contracts to a typical diameter of 2 mm. Diffraction from this circular aperture limits your ability to resolve objects that are very close together in an angular sense, according to the Raylcigh criterion - at least in in principle. To get a sense of how significant an effect this is, suppose you arc looking at two bright point-like lights at a distance of 100 m from you (during the day, when your pupils arc contracted). What minimum separation must they have (in meters, cm or mm) in order for you to be able to resolve them as separate points? You sec using visible light, of course, so use a typical wavelength for visible light.

Explanation / Answer

use the raylegih critertion R = 1.22 Ld/D

d = RD/1.22 L

d = 500 e-9 * 1.22*100/(2 e -3)

d = 3.05 cm

t B :

1 LY = 9.41 e 15 m

Distance from sun to earth = 1.5 e 11 m

so The angular separation is Alpha A = 1.5 e11/(15* 9.41 e 15)

A = 1.06 e -6 rad

resolving powe of a telescope is Alpha = 0.25 L/D

Diameter of lens is D = 0.25 /

D = 0.25 * 500 e-9/1.06 e -6

D = 0.118 m or 12 cm nearly

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