One day, after pulling down your window shade, you notice that sunlight is passi

Question

One day, after pulling down your window shade, you notice that sunlight is passing through a pinhole in the shade and making a small patch of light on the far wall. Having recently studied optics in your physics class, you're not too surprised to see that the patch of light seems to be a circular diffraction pattern. It appears that the central maximum is about 3cm across, and you estimate that the distance from the window shade to the wall is about 3m .

Knowing that the average wavelength of sunlight is about 500 nm, estimate the diameter of the pinhole.

Explanation / Answer

This would be related to the diffraction pattern for a circular aperture. If illuminated by a single wavelength, the angle for the first minimum (which would define the ending of the central maximum) is
Angle = Arcsin(1.22*WL/D)
where:
WL = wavelength
D = aperture diameter

So:
sin(Angle) = 1.22*WL/D

Since
sin(Angle) = 3 cm/(3 m) = 1/100
WL = D*sin(Angle)/1.22
= D/(100*1.22)
= D/122



b) Diameter of pinhole:
D = 122 * WL
= 122 * 500 nm
= 0.61e5*e-9 m
= 0.61e-4 m
= 0.061 mm

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