75 Naturally occuring coronas (brightly colored rings) are sometimes seen around

Question

75 Naturally occuring coronas (brightly colored rings) are sometimes seen around the moon or the Sun when viewed through a thin cloud. (Warning: When viewing a Sun corona, be sure that the entire Sun is blocked by the edge of a building, a tree, or a traffic pole to safeguard your eyes.) These coronas are due to diffraction of light by small water droplets in the cloud. A typical angular diameter for a coronal ring is about 10°. From that the water droplets can be modeled as opaque disks that fraction pattern from an opaque disk is the same as the pattern from an aperture of the same diameter. (This last statement is known as Babinet's principle.) SsHI

Explanation / Answer

Let's assume a wavelength (Lambda) of 500 nm which falls in the visible spectrum (400 nm to 700 nm)

We have

Sin ? = 1.22 * Lambda / D

Because the distance to cloud is very large, we have

D = 1.22*Lamda / ?

we need to convert the given angular diameter to rad

? = 10*pi/180 = 0.17453 rad

Therefore, D= 1.22*500e-9 / 0.17453

D = 3.495e-6

D = 3.495 um (um - micrometer = 10-6)

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