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

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.

Answer 1

Width of the central maxima is the distance between first two minima, ie minima on the left and right side.
Diffraction condition for first minima is, d sin =
sin = /d
= (500 x 10^-9) / d
d = (500 x 10^-9) / sin    ...(1)

Distance to the first minima, h = 6/2 = 3 cm
D is the distance from the pinhole to the wall, D = 3 m
tan = h/D = (3 x 10^-2)/3
= 10^-2.
For small angles, tan = sin
So tan = sin = 10^-2

Substituting sin in (1),
d = (500 x 10^-9) / (10^-2)
= 5 x 10^-5 m