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 3 cm across, and you estimate that the distance from the window shade to the wall is about 5 m.

Part A
Estimate the average wavelength of the sunlight (in { m nm}).
express your answer using two significant figures.

60 { m m}
20 { m mm}
15 { m cm}
550 { m nm}
30 { m AA}
Part B
Estimate the diameter of the pinhole (in { m mm}).
Express your answer using one significant figure.

Explanation / Answer

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. You see that the patch of light seems to be a circular diffraction pattern. It appears that the central maximum is about 1 cm across and you estimate that the distance from the window shade to the wall is about 3 m. What is (a) the average wavelength of sunlight? (b) the diameter of the pinhole? 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) = 1 cm/(3 m) = 1/300 WL = D*sin(Angle)/1.22 = D/(300*1.22) = D/366 a) WL for average wavelength of sunlight: According to the graph in the Wiki article, it looks like a little over 500 nm. On the other hand, another article on visible light gives the wavelength of yellow light as being 570 nm. I'll take 570 nm. b) Diameter of pinhole: D = 366 * WL = 366 * 570 nm = 2.09e5*e-9 m = 2.09e-4 m = 0.209 mm

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