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 3 m . Part A Knowing that the average wavelength of sunlight is about 500 nm, estimate the diameter of the pinhole. Express your answer to one significant figure and include the appropriate units.

Explanation / Answer

L = 3 m ; x = 3/2 c, = 1.5 cm = 0.015 m

lambda = 500 nm = 500 x 10^-9 m ;

we know that, from Rayleigh criterion

sin(theta) = 1.22 x lambda/D

Using small angle approximations

sin(theta) = x/L

x/L = 1.22 lambda/D

D = 1.22 x L x lambda/ x

D = 1.22 x 3 x 500 x 10^-9/0.015 = 0.122 x 10^-3 m

Hence, D = 0.122 x 10^-3 m = 0.122 mm

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